The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031277092 arV17867 Optics Cornell University Library 3 1924 031 277 092 olin.anx OPTICS LIGHT Ai^D SIGHT WITH THEIR APPLICATION TO FINE ART AND INDUSTRIAL PURSUITS By E. NUGENT, C.E. NEW EDITION, WITH A CHAPTEE. ON SPECTRUM ANALYSIS STEAHAN & CO., PUBLISHERS 56 LUDGATE HILL, LONDON 1870 PREFACE. This treatise on Optics is intended for all who desire to attain an accurate knowledge of one of the most interesting and useful branches of science. The author has endeavoured to steer clear of all abstruse mathematical investigation and formulse, so as to render the work easily understood by every intel- ligent reader. Considering the great want of technical education among the industrial classes of the United Kingdom at the present time, and the immense utility to them of the knowledge of the principles of Optics, and of their application to the fine and industrial arts, it is hoped that this treatise will be found useful not only to artists, but to mechanics and artisans generally. As a text-book for schools and colleges for both sexes, such a treatise, coming within the means of all, has long been a desideratum. The author has spared no pains to embody all the most valuable discoveries in the science down to the present period, and to render the work as com- plete as possible, both in regard to the principles IV PREFACE. of Optics and their application to the practical pur- poses of life. The photographer will find numerous illustrations of the best and most recently-invented objectives, or lenses, and cameras by several of the most eminent makers in the world. The illustrations are, in many cases, of the real size of the objectives, and have been kindly fur- nished to the author, in several instances, by the makers themselves. The painter and house-decorator, the milliner and dressmaker, the tailor and outfitter, will, one and all, find the principles of colour and their harmonious rela- tion clearly explained ; whilst the sculptor, the builder, the stonecutter, the mason, the draughtsman, the archi- tect, the engineer — in short, all persons who may be engaged iu any department of human industry — will find the work, it is hoped, worthy of careful study. In no former period of the world's history was the truth of Lord Bacon's apothegm, " Knowledge is power," more apparent than it is in the present. Indeed, the apothegm may be paraphrased — Knowledge is pounds. It is now a generally- admitted fact, that the material progress of a country depends, to a greater extent than ever before, on the knowledge of science and art possessed by its inhabitants. It is confidently hoped that this treatise will contribute to the diffusion of useful know- ledge among the people, and consequently to their pro- gress in wealth and happiness. CONTENTS. CHAPTER I. Definition of optics j Nature of light . 1 Corpuscular theory . 1 TJndulatory theory ." .' 1 Useful properties of light 2 The source of light worshipped .2 Opinions of Pythagoras .3 Opinions of Plato . . S ' Opinions of Aristotle 3 Observations of Seneca 3 Euclid's explanation of phenomena 4 Methods of lighting the sacred fires of the ancient Romans and Druids 4 Ptolemy's knowledge of optics 4 Discoveries of Alhazen 4 Spectacles invented by Armatus ....... 5 Discoveries of Maurolycus 5 Invention of the camera obscura ....... 5 Cnvention of the magic lantern ....... 6 Invention of the telescope 6 Astronomical discoveries by Galileo 6 Discoveries by Kepler 7 Atmospheric refraction determined by Tycho Brahe ... 7 The law of refraction discovered by Snellius .... 7 Exposition of the law of refraction by Descartes ... 7 CHAPTER II. Refraction of light explained 8 The law of refraction illustrated 10, Index of refraction 13 Table of indices of refraction . ., 13 Table of refractive powers of gases 15 Table of absolute refractive powers of bodies . . . .15 Refractive powers of spirituous liquors in proportion to their strength .17- Tl CONTENTS. CHAPTER III. glasses Ee&action of rays by prisms and lenses Forms of prisms and lenses . Refraction througli prisms explained . Refraction of light througli plane glasses Refraction of diverging rays through plane Refraction of converging rays Limit of possible transmission Table of limits of possible trausmissioia Refraction through several parallel media Wonderful atmospheric phenomena explained Refraction of light through curved suriaces Refraction of light through spheres Rule for finding the focus of a sphere . Refraction through convex lenses Rule for finding the focus of convex lenses . Rule for finding the principal focus of a plano-convex lem Converging rays, how refracted through convex lenSfes ilule for finding the focus of converging rays vsrhen the leni is unequally convex .... Rule for finding the focus of convergihg rays -when the lefiS is plano-convex Diverging rays, how refracted through conveS lenseS Rule for findmg the focus of an unequally convex leiis fbt divBtg' ing rays Rule if the lens is equally convex . . ^ . . Rule Vrhen the lens is plano-convex ..... Refraction of light through concave lenses .... Refraction of parallel rays through concaVe leflfees Refraction of converging and diverging rays Refraction through a meniscus and coiica*o-cOnvex IfehSeS" . Rule for a meniscus with parallel rays .... Rule for a meniscus with converging ra;yB .... Rule for a meniscus with diverging ray^ .... Rule for a concavo-convex lens PAGE 18 18 19 22 23 23 24 23 25 26 26 27 29 29 3d Si tl Si 32 32 32 33 3* 33 ■ii 3d Sis 35 35 35 CfiAi'TEE IV. i'ormation of images by lefta64 36 How lenses magnify objects explained . ... 39 Rule for finding the magnifying power of a lens . . .40 Distortion of images . ' 41 Curvature of the field 42 jSberration of thickness 42 Astigmation 42 CHAPTER V. On the reflection of light 42 Mirrors, plane, concave, and convex . . . . 43 CONTENTS. Til The law of reflection explained 43 Reflection of concave mirrors . 44 Beflection of convex mirrors ........ 44 Keflection of parallel rays from plane Kwrorg . . . .46 Reflection of diverging rays . . . . . , . .46 Reflection of converging rays 4g Reflection of parallel rays by concave and convex mirrors . .46 Reflection of diverging rays by concave and convex mirrois . ,47 Reflection of co»vergiog rays by concave and convex mirrors . 49 CHAPTER VI. The principle of the formation of images \y mirrors Formation of images by plane mirrors . Formation of images by convex mirrors Formation of images by concave mirrors "She principle of the reflecting telescope lie principle of the Gregorian telescope The principle of the Cassegrainian telescope The magnifying power of telescopes, hftw determined Cylindrical reflector? Conical reflectors 4niusing deceptions 60 60 61 62 63 63 63 63 6i 64 66 CHAPTER VII. On spherical aberration in lenses and mirrors .... 55 Spherical aberration explained S6 Spherical aberration of different lenses 66 Spherical aberration, how eflaced 68 Chromatic aberration explained 69 Gem lenses 60 Aplanatic lenses .......... 60 Objects invisible to the naked eye, how rendered visible r . 60 CHAPTER Vin. On caustic curves formed by reflection and refraction . . .61 Caustics formed by reflection 61 The mode of formation and general properties of caustics . . 62 Formation of caustics by a white ohma bowl . . . .64 Caustic figures in the form of ladies' fans, tails of fishes, &c., formed by a wash-hand basin 65 Caustic figures formed by refraction 66 Caustic figures formed by a decanter and eyeglass . . .66 CHAPTER IX. Physical optics. — Analysis of light, its decomposition into colour? 67 Sol^r light, compound ^'^ Till CONTENTS. Newton and Fiaunhofer's spectra 8'8 The extreme red and lavender rays 70 The fluorescent ray .......•■ 70 Decomposition of fight by absorption 70 Eed, yellow, and blue light exist at every point of the solar spectrum 73 Views of M. Bernard, Mr. Eobert Hunt, and M. Helmholtz on decomposition by absorption 74 The different views of modem philosophers respecting the number of primary colours in the solar spectrum reconciled . . 75 The doctrine of colours held by the ancient G-reeks and Eomans confirmed 76 CHAPTER X. On the dispersion of light .... Sir Isaac Newton's experiments . Measure of the dispersive power of a body . Table of dispersive powers Different bodies possess difierent dispersive powers Spectra produced by oil of cassia and sulphuric acid Table of the indices of refraction of the mean rays of each of the prismatic colours for certain media The dispersive power, how to find CHAPTER XI. On the principle of achromatic telescopes .... 83 Achromatic telescopes first constructed by Mr. Dollond . . 84 Dr. Blair's discoveries with muriatic acid ..... 84 Flint-glass and crown-glass found in practice most suitable for achromatic lenses 85 On the illuminating power of the spectrum 86 Dark Unes across the spectrum 86 Heating or calorific power of the spectrum 87 Experiments by Melloni show that bodies are not aUke transparent to, or permeable by, light and heat 89 On the chemical infiuence of the spectrum 89 On producing coloured pictures photographically . . . .91 CHAPTER XII. Breadth of waves of Ught Nxunber of waves or undulations in an inch Table of imdulations Inflection or diffraction of light The law of interference The smallest magnitude visible by a microscope Combined efleots of inflection and interfereiioe Examples of the effects of inflection and interference The passage of light through thin transparent plates Iridescence of mother-of-pearl, soap-bubbles, feathers, &c. 92 94 95 96 98 100 100 100 101 102 CONTENTS. IX CHAPTER Xril. Doutle refraction and polarisation of light . Double refraction of Iceland spar . Ordinary la-w of double refraction . Extraordinary law ..... Axis of double refraction .... On substances -with circular double refraction Polarisation of light .... Angle of polarisation .... Polaiiscopes ....... Improved polariscope Polarisation by absorption .... Utility of polarised light Analysis of sugar by polarised light Polarising saccharometer PAGE . 102 . 103 . 105 . lOS . 105 . 106 . 106 . 108 . 108 . 110 . 112 . 112 . 112 . 113 CHAPTER XIV. The human eye ... 113 The sclerotic coat . 1 14 The choroid coat 114 The cornea . . . ' 114 The retina 115 The iris 115 The pupil 116 The crystalline lens 116 The aqueous humour 117 The Titreous humour , 117 The eyelids — conjunctiva 117 The eyebrows 117 Dimensions of the eye 118 Liaiitsof the play of the eyeball 118 Production of the image on the eye 118 On the law of visible direction 119 Erect vision from an inverted image 121 The eye achromatic 122 The eye aplanatic 122 Conditions of single vision with both eyes 123 Inability of some persons to distinguish colours . . . .123 Adaptation of the eye to different distances 125 The size of pictures on the retina 126 CHAPTER XV. Accidental or complementary colours 127 The complementary colour of any colour, how to find . . . 128 The proportions of the three primary colours that compose white light 128 The complementary colour of any colour in a large number of colours seen at a glance . . . . • ■ • • 219 How more than 700 colours may be speedily produced from three 130 Harmony of oolours in art valuable to artists, decorators, &c., . 131 X CONTENTS. CHAPTER XVI. PAGE Optical instruments ... 131 Spectacles a remedy for defective siglit . • • .131 The magic lantern 132 Phantasmagoria 134 The ghost 136 Dissolving views 139 Bi-unieil dissolving-view apparatus 141 The electric light 141 Photographic lenses or objectives 142 .Che form of camera obscura invented by Porta .... 143 Objective invented by Mr. Grubb, of Dublin .... 145 Two kinds of single objectives 145 Dallmeyer's new single objective 147 The globe objective 147 The periscope of Steinheil 149 Mr. Thomas Boss's doublet 149 The orthoscopic lens 150 Petzval's double portrait lens ....... 151 Dallmeyer's triplet 162 Flare in photographic pictures remedied 154 Dallmeyer's wide-angle rectilinear lens 166 Dallmeyer's patent portrait lens ....... 158 Helsby's heHogram 161 Dallmeyer's rectilinear aplanatic lens 161 Photographic enlarging apparatus 161 The American solar camera 162 M. Wothly's apparatus 163 Solar cameras without a reflector . . . . . 163 Van Monckhoven's dyahtic apparatus . . . . 163 Prevention of fracture in the negative 164 ThehcHostat 164 Varieties of heUostat 164 Enlarging photographs by the ordinary camera . . . .165 The magnesiiun light for producing photographic enlargements . 166 The convex heliostat 166 The Drummond light 167 The camera obscura 167 Portrait camera 168 Meagher's binocular camera 168 The Kinnear camera 169 Meagher's new folding camera 169 To erect the camera for use 170 The camera lucida 170 Application to the microscope 171 lIMcroscopes 171 Magnifying power of a simple microscope 172 linear magnifying power 172 Superficial magnifying power 172 The Coddington lens 173 The compound microscope 174 Refracting microscope 174 Reflecting microscope 175 CONTENTS. Xi Pi9E Conditions of efficiency ... ... 176 Smith and Beck's popular microscope 176 Directions for use * 178 Wenham's tinocular tody 180 Additional apparatus 183 The lieterkuhn .... 183 Dark-field illumination 184 Wenham's paraholio reflector 184 The application of polarised light 186 To draw by the camera lucida 186 The micrometer . 188 The lire box 188 The glass trough 188 Stage with mechanical movement 189 The magnifying power of Smith and Beck's popular microscope . 189 Various forms of microscopes 190 Principle of the telescope 190 The simplest construction of the telescope . 191 The astronomical telescope . 191 The Galilean telescope 192 Opera-glassca . . .192 The Newtonian telescope 193 Herschelian telescope . . 193 Lord Eosse's telescope 195 Nasmyth's telescope • 196 Binocular telescope 196 The stereoscope 196 Revolving or magazine stereoscope 199 The graphoscope 199 The kaleidoscope 202 Varieties of kaleidoscope 202 The quadrant .... 202 Sextants and octants 204 ThetheodoUte . . . 204 The engineer's and surveyor's transit 206 The spirit-level 208 Optical toys 209 The phenakistoscope, or magic circle ... . . 209 The anorthoscope 210 OHAPTEE XVII. The principles of optics applied to various useful purposes . .211 Photo-zdncography ■.•■,■,•.•, ^ " " ,}, Manuscripts, maps, engravmgs, &c., how photographed . . ^li Scotch national manuscripts ^1^ Photo-Uthography . ■ • ; . ■, V ' ' " ,,7 Photographic decorations of porcelain, glass, &c ^i/ Influence of solar rays on the growth of plants . . • -218 Germination of seeds prevented 218 Origin of vitality in seeds ^''* XU CONTENTS. PAGR How the vital power is exerted 219 Pevelopment of roots from plant cuttings 219 Light rays essential to the formation of woody fibre . . ,219 Value of seeds speedily determined by blue glass .... 220 The knowledge of optics useful to the engineer, architect, &c. . 221 The laws of Eght applied to the laying of submarine telegraphic cables 221 The illumination of lighthouses 222 The catoptric system 222 The Fresnelian system of illuminating lighthouses . . . 222 Important modification of, by Stevenson 223 The Trench dioptric system of lights 224 The ventilation of lighthouses 227 Faraday's system of ventilation 227 The advantage commerce has derived from Fresnel's system . 228 CHAPTEE XVIII. On the spectroscope and spectrum analysis 229 Description of Dr. WoUaston's experiments 229 M. Fraunhofer's discovery 231 Browning's small spectroscope ....... 233 The Herschel-Browning direct-vision spectroscope . . . 234 How to use the spectroscope ....... 236 To obtain the bright lines in the spectrum given by any substance 236 To view Fraunhofer's lines in the spectrum 237 How two spectra may be seen at the same time .... 237 The prismatic analysis of organic bodies 237 To map out any spectrum 23 S Various forms of the spectroscope 240 How to compare the spectra of terrestrial substances with stellar spectra ........... 242 The micro-spectroscope 243 On a new method of measuring the position of absorption bands with the micro-spectroscope ....... 245 Automatic electric lamp for projecting the spectra of metals . 248 Various experiments on the spectral lines 249 Kirchhoff's theory and experiments 250 Observations on the solar atmosphere 252 Mr. Huggins's observations 255 The spectra of comets | ' 255 The spectra of nebulae " ' 256 Importance of the discoveries made by means of spectrum analysis 257 The new metals _ 258 Application of the spectroscope to the manufactui-e of Bessemer steel 259 Mr. Huggins's new telescope \ 260 OPTICS. CHAPTER I. Optics is the science which treats of vision, or seeing, and of the nature and properties of light^the changes which it undergoes in its qualities or direction when passing through bodies of different forms and sub- stances, when reflected from their surfaces, or when moving past them at small distances. Light is an emanation, or something which proceeds from bodies, and by means of which the external world is rendered manifest to the sense of sight. From the time of Socrates and Aristotle, down to the present day, or for a period of more than two thousand years, the most distinguished philosophera and scientific men have been divided in opinion as to its nature: one party has regarded it as consisting of material particles, or atoms, thrown off with great velocity from the lumi- nous body, in all directions, and as affecting the organs of vision, or the eyes, somewhat in the same way as odours affect the organs of smell; the other party regards it as a fluid, or ether, diffused through all nature, and in which waves, or undulations, are pro- duced by the action of the luminous body, and propa- gated in a manner somewhat similar to that of sound B 2 OPTICS. through the air. This latter theory is now held by the greater number of scientific men who have devoted attention to the subject. In the Mosaic history of the creation, we find that light was created on the first day, and the sun, which we are accustomed to consider as the great source of light, on the fourth day. The Holy Bible declares, in simple and sublime conciseness, "And God said. Let there be light, and there was light." Thus emphatically declaring the importance of this element in the great system of nature. But however savans may difier respecting the origin of light, and the manner in which it passes from one place to another, it has certain most useful and general properties, which have been discovered by obseryation and* experiment. The grass, the herb yielding seed, and the fruit-tree yielding fruit, owe their germination, their growth, their resplendent colours, and their ex- quisite beauty, to the influences of the solar beams. The moving creatures of the waters, the birds that fly above the earth in the open firmament of heaven, the cattle, and the creeping thing, are, one and all, directly dependent for healthful vigour, and the 'continuance of life, on solar power, which seems to have given form to the chaotic earth as it dispelled the darkness from the face of the deep. As it is by the influence of light, acting through the wonderful mechanism of the eye, that a most extensive and important class of impressions are made on the mind of man, he has, from the early dawn of creation, in his untutored and uncivilised state, rendered homage and adoration to the sun, as the apparent source and fountain of light. In the early ages of mankind aU natural phenomena were viewed through a veil woven of threads of mysti- OPTICS. 3 cism and superstition, which n© one ventured to draw aside, or dreamed of lifting up. At length a spirit of inquiry germinated in the mind of man ; he commenced to speculate on the mysteries by which he was environed ; his first efforts " were like the gropings of the blind Cyclops in his cavern," and when searching for the light. of truth, he often wandered into darkness. Among those who were first called philosophers there was a doubt whether external objects were rendered visible by means of something which proceeded from them to the eye of the spectator, or of something else that issued from the eye of the spectator to external objects. It was the opinion of Pythagoras, that vision is caused by particles continually flying off from the surfaces of bodies, and entering the pupil of the eye ; but Plato and Empedocles supposed that the cause of vision is something emanating from the eye, which, meeting with something else that proceeds from the object, is thereby reflected back again. Aristotle main- tained, in opposition, as he says, to the opinion of Empedocles and others, that light is incorporeal. If it were not a mere quality, but a real substance, the motion of it, he says, could not be insensible, in passing from the 'east to the west, though it might escape our notice in a smaller distance. The Platonic philosophers were acquainted with two important properties of light, viz., that light, from whatever it proceeds, is propagated in right lines, and that when it i^ reflected from the surfaces of polished bodies, the angle of incidence is equal to the angle of reflexion. Among other questions propounded by Aristotle, we find one concerning the reason why a straight stick appears bent when it is held obliquely in water ; and Seneca says, that if the OPTICS. light of the sun shine through an angular piece of glass, it will give all the colours of the rainbow. But, without investigating the nature of ths pheno- menon, he contents himself with saying, that this appearance is not of any real, but only a species oi false colour, such as is seen in the neck of a pigeon, which changes with the position. We thus find that the refraction, as well as the reflexion of light, had not escaped the notice of the ancients. In a treatise on Optics, ascribed to Euclid, there is an attempt made to explain the phenomenon of the image of an object appearing as if it were suspended in the air, between the spectator and a concave mirror ; and also an attempt to determine the size and figure of objects, from the angle under which they appear, or that the extremities of them subtend at the eye. The magnifying power of concave mirrors is mentioned both by Seneca and Pliny. It is probable that the ancient Romans and Druids had a method of lighting their sacred fire by means of reflecting concave speculums, and it is related by historians that Archimedes burned the Roman fleet by mirrors. Ptolemy, who lived about 150 years after Christ, was acquainted with atmospheric refraction, and of its being the cause of the sun, moon, and stars ap- pearing higher in the heavens than they would other- wise do. From the days of Ptolemy down to the time of Alhazen, an Arabian philosopher who lived in the twelfth century, a great chasm is found in the history of optics. Alhazen gives a tolerable description of the eye, and treats largely of the nature of vision ; main- taining that the crystalline humour is of principal use for this purpose, but without considering it as a lens ; and asserting that vision is not completed till the im- pressions of external objects are conveyed by the optic OPTICS. nerve to the brain. He accounts for single vision by- two eyes by supposing that when two corresponding parts of the retina are aifected, the mind perceives but one image ; and he first advanced the opinion that the stars are sometimes seen above the horizon by means of refraction, when they are really belbw it, and also that the cause of the twinkling of the stars is refraction. From the writings of Alhazen and some imperfect experiments of Roger Bacon subsequently made, it is probable that the construction of spectacles was hit upon by Salvinus Armatus, a nobleman of Florence, who died in 1317. In the year 1311 a 'work was written by Theodoric, in which a rational explanation of the double rainbow is given. In 1575 a treatise called " De Lumine et Umbr^ " was published by 3Iaurolycu8, teacher of mathematics at Messina, in which he demonstrates that the crystalline humour of the eye is a lens that collects the rays of light issuing from external objects, and throws them upon the retina. He showed that the defects called long-sightedness and short-sightedness proceeded from, too small or too great a refracting power in the eye ; and that in the former case the pencils of rays do not converge fast enough, so that the foci are beyond the retina; and in the latter that the rays converge too fast, and come to a focus before they reach the retina ; and further showed how and why these defects were remedied by the use of convex and concave lenses. He failed to discover the formation of the picture of external objects on the retina, which discovery was afterwards first made by Kepler in 1604. About the time that Maurolycus made his discovery of the nature of vision, Baptista Porta, a Neapolitan philosopher, invented the camera- obsour a, which threw OPTICS. still more light on the same subject. The invention of the camera- obscura suggested to Kircher the invention of the magic lantern, which does that in the night that the camera does in the day. Porta observed that the pupil is contracted involuntarily when it is exposed to a strong light, and expands when the light is small. He was mistaken, however, in his opinion concerning the cause of single vision with two eyes, for he states we never see with more than one eye at one time. The accumulated facts and experiments furnished by various scientific men, and the numerous suggestions of writers on optics, on the construction and use of lenses, and their combinations, had now prepared the way for the ' construction of telescopes and microscopes. The ap- proach to the construction of the telescope was so gradual that the honour of its invention cannot be exclusively ascribed to any one person. It is, how- ever, generally admitted that to Jansen, a spectacle- maker of Middleburgh, the greater share of the credit is due. The first telescope was made by him in 1590. He had no sooner found the arrangement of lenses that produced the desired effect than he enclosed them in a tube, and ran with his instrument to Prince Maurice of Nassau, who immediately conceiving that it might be of use to him in his wars, desired the maker to keep it a secret. But this was found im- possible, though attempted for some time. Among those who applied the telescope to the great ends of astronomical science, the name of Galileo stands foremost. He made a telescope himself which magnified about thirty times, and with which he dis- covered the satellites of Jupiter, the solar spots, and that the milky way and nebulae consisted of a vast number of fixed stars, which, on account of their great OPTICS. 7 distance or extreme smallness, were invisible to the naked eye. Subsequently lie discovered tbat the planet Venus changes her phases like the moon. Kepler suggested important improvements in the construction of telescopes; he also very clearly ex- plained in a most scientific manner the principles of the instrument. He attributed erect vision from an inverted image on the retina to an operation of the mind beyond our power to understand. To him also is due the discovery of the great law of motion of the heavenly bodies, viz., that the squares of the periodical times are as the cubes of the mean distances from the bodies about which they revolve. At the period to which we now refer, the beginning of the seventeenth century, the subject of the refraction of the atmosphere received a great deal of attention from scientific men, particularly from Tycho Brahe, who, perceiving the importance of it to the perfection of astronomy, applied himself diligently to it. He determined the amount of atmospheric refractions^ at certain altitudes, to a tolerable degree of correctness. The honour of the discovery of the law of refraction, like many other important discoveries, cannot be ex- clusively ascribed to any one person, undoubtedly Snellius deserves a large share of the honour ; it is to Descartes that we are indebted for the best exposition of the law of refraction. OPTICS. CHAPTER II. REFRACTION OF LIGHT. Although a ray of light will always move in the same straight line when it is not obstructed, yet many persons must haye noticed that when the light falls on a drop of water, or a piece of glass, or a vial containing any fluid which allows the light to pass, it does not reach the eye or illuminate a piece of paper placed behind those bodies in the same manner as before they were put in its way. This evidently is caused by some power which resides in the body of changing the direc- tion of the light. The branch of optics that explains the law according to which the direction of the light is thus changed is called dioptics, from two Greek words, one of which signifies through, and the other to see, because the bodies which cause this change in the direction of light are those through which we can see or through which light passes. In order to illustrate how this change or bending of light is produced, let w x y z (Fig. 1) represent a Kg. 1. vessel, in one side of which, x z, there is a small hole h. OPTICS. If we place a lighted candle witMii two or three feet of it, so that its flame may be at a, a ray of Kght, a h, proceeding from it will pass through the hole h, and continue in a straight line, a A b c, till it reaches the bottom of the vessel at c, where it will form a bright spot. Having made a mark at c, let water be poured into the vessel till it rise to the height t r, and it will be seen that the spot which was before at c is now at d ; that is, the ray a h, which went straight on to c when the vessel was empty, has been bent at the point b, where it falls on the water, into the line b d. If a little soap be mixed with the water, so as to give it a slight misti- ness, the ray b d will be distinctly perceived to be a straight Hne, and that the bending or change in its direction has been produced entirely at the point b at the surface of the water. This bending of the ray A A B is called refraction, from a Latin word, which means breaking back, because the ray a A b seems to be broken back from its course at b, and the water is said to refract or break back the ray a A b. If we pour salt water in the vessel instead of fresh water, we shall find that the ray a A b is more bent at b. If alcohol be poured in, it will refract the ray more than salt water, and oil more than alcohol. If a piece of glass the exact shape of the water were placed in the vessel, we should find that it would refract the ray still more than oil, and in the line b e. By these facts, and many others that might be mentioned, we are led to the conclusion that when a ray of light passing through air falls in a slanting direction upon the surface of a liquid, or of solid bodies through which light can pass, it is refracted by them, and by different bodies in different degrees. If when the vessel w x y z is empty we place at c any 10 OPTICS. bright object, sucb as a sbilllng, and place tbe eye at a, " in tbe straigbt line a A c, tbe shilling will be distinctly- seen, because the light which proceeds from it must enter the eye at a. If we now pour water into the vessel till it rises to tr, without altering the position of the shilling, then the eye at a wiU no longer see the shilling, but if we move the shilling from c to D, it becomes visible to the eye at A the instant it comes to D. Now as the light from the shilling at d must pass to the eye in a straight line after it comes out of the water, it must pass in the direction B A A, and therefor© the ray of light from the shilling at D, by which it was seen at A, must have been d b, and this ray in passing out of the water must have been refracted at b into the line b A A. A similar effect will be produced if tr is the surface of salt water, alcohol, oil, or glass ; but with these substances we must place the shilling beyond D towards z, so that it may be seen at a. Hence we are led to conclude that when a ray of light passing through a liquid or solid body in a slanting direction to its surface quits it, it is refracted by that body, and by different bodies in different degrees. By the preceding simple experiments we are enabled to observe the nature of the refraction of light when passing from a rare or thin medium, such as air, into a denser medium, such as water, and also out of a dense medium or substance into a rare medium or substance. The Law of Refraction. — Let a circle etsu be described upon a piece of slate or metal, and having drawn the diameters E c s, T c tt, perpendicular to each other, let a small tube a c, be attached to the plate, so that it can move freely round c. If we now put the plate R T s u in a vessel of water, and fix it in such a manner that the surface of the water will coincide with OPTICS. 11 the line t u, but does not touch the lower end, c, of the tube A c, and then move the tube a c into the position K c, and admit a ray of light down through the tube, we shall find that the ray, on entering the water at c, will pass on in the same straight Kne to the point s, showing clearly that a ray of light falling perpendicu- ^i larly upon a refracting sur- y face is not bent or refracted in its perpendicular direc- tion. Ifthe tubeAcbenow placed in the position a c, and a ray of light is caused to pass through it, the ray will not pass on in a straight line, but will be bent or refracted at c into the line c d, and fall on the circle at d. The angle a c r, which the ray or tube makes with the perpendicular r c s is called the angle of incidence ; and the angle d c s, which the bent ray cd makes with the same perpendicular, is called the angle of refraction. If we now measure the length of the lines a b and d f, the shortest distances from the points a and d to the perpendicular e c s, by a scale of equal parts, or by a pair of compasses, we shall find that ab is very nearly one and one-third times the length of d f ; or, more correctly, A b is to DF as 1'336 to 1. If this experiment be repeated when the tube a o is in any other slanting direction, such as a c, in which case the bent ray will be c d, then if the lines a b and fd be measured as before, we shall find that as a J is to fd so is 1-336 to 1. The line a b is called the sine of the angle of incidence a c k, and d f the sine of the angle of 12 opxics. refraction i) c s. It therefore follows that from air into ■water the sine of the angle of incidence is to the sine of the angle of refraction as 1'336 to 1, whatever be the slanting direction of the incident ray with respect to the surface. "When the ray passes in a slanting direction through water into air the reverse rule holds good ; that is, if D c be the incident ray through water on the aerial surface t u, it is bent at c in the direction c a in passing through the air. Hence it follows that from water into air the sine of the angle of incidence is to the sine of the angle of refraction as 1 to 1'336. It will be seen by comparing the two foregoing cases that when the ray a c passes from air into water, the ray c d is refracted towards the perpendicular c s, and the sine of the angle of incidence is 1'336, while the sine of the angle of refraction is 1 ; but when the ray dc passes from water into air, the ray ca is refracted from the perpendicular c R, and the sine of the angle of incidence is 1, while the sine of the angle of refraction is 1'336. By these means we are enabled to determine the direction of any ray after it is refracted by the surface of water. If we want to find the direction of the ray a c (Fig. 2) for example, when it is refracted after falling on the surface Ttr of water at the point c. Draw c r perpendicular to x u, and from a draw a b perpendicular to c R, measure a J by any scale of equal parts, then say as 1-336 is to 1, so is the length of ab as measured by the scale to the length required. This proportion gives the length by the scale of the sine of the angle of refraction. If the length of this line be laid oS from c to e, towards v, and a line be drawn through e parallel to c s till it meet the circumference OPTICS. 13 of the circle at d, a line tlien drawn from do d deter- mines tlie direction of the refracted ray, and df per- pendicular to c s is the sine of the angle of refrac- tion c? c s. The number 1'336 is called the index, or exponent, or co-efi&cient of the refraction of water, and sometimes its refractiye power. If similar experiments to the foregoing were made ■with other fluids and solids we should find that the law of refraction governs all of them, and that the index of refraction varies in each. Why light is thus refracted in passing from one substance or medium into another is still unknown, although attempts to explain the cause of it have been made by Descartes, Termat, Liebnitz, and other eminently scientific men. The following table contains the indices of refraction for several bodies, by means of which we can trace the passage of a ray through these bodies. I. TABLE OP INDICES OF EEFEACTION. Chromate of lead (max. fmin Kul)y silver . . Eealgar, artificial Octohedrite . . Diamond, Kochon Diamond, Newton Nitrate of lead . Blende . . . Phosphorus . . Glass of antimony Sulphur, melted „ native fmax.) Glass, lead 3, flmt 1 . Tungstate of lime (max, (min, Garhonate of lead (max. Jndex of Be&action. 2-974 2-600 2-S64 2-549 2-600 2-755 2-439 2-322 2-260 2-224 2-200 2-148 2115 2-038 2028 2-129 1-970 2-084 Index of Eefraction. Garhonate of lead (min.) 1-813 ■ Calomel 1-970 Zircon (max.) .... 2015 „ (ord.) .... 1-961 Glass, lead 2, sand 1 . . 1-987 „ flint 1 . . 1-830 Sulphate of lea^ .' . . 1-925 Garnet 1-816 Spinelle, ruhy . ■ . . 1-812 SpineUe, Brewster . . . 1-764 Arsenic 1-811 Sapphire, blue .... 1-794 „ white . . . 1-768 Pyrope 1-792 Nitrate of silver (max.) . 1-788 „ (min.) . 1-729 Glass, lead 1, flint 1 . . 1-787 Euby , 1-779 14 OPTICS. Feldspar, spanelle . Cinnamon stone . Glass, lead 3, flint 4 1 9 Axinite . . Epidote (max.) (min.) Chrysoberyl . Nitrate of lead Carbonate of Index of Refraction. 1-764 1-739 1-732 1-724 1-735 1-703 1-661 1-760 1-758 strontian (max.) 1-700 „ (min.) 1-543 Boracite 1-701 Sulphm-et of carbon . . 1-768 Periodot (max.) . . . 1-685 „ (min.). . . . 1-660 Arragonite (ord.) . . . 1-693 „ (ext.) . . . 1-535 Calcareous spar (ord.) . 1-654 „ (ext.) . 1-483 Sulphate of barytes (ext.) 1-647 „ (ord.) 1-631 Topaz, colourless (ext.) . 1-620 (ord.) . 1-610 „ Brazil (ext.) . 1-640 „ „ (ord.) . 1-632 Oil of cassia 1-641 Euclase (ext.) .... 1-663 „ (ord.) .... 1-643 Mother-of-pearl . . . 1-653 Balsam of tolu .... 1-628 Castor ....... 1-626 Muriate of ammonia . . 1-625 Anhydrite (ext.) . . . 1-622 (ord.) . . . 1-577 Guiaoum 1-619 FUnt glass from 1-625 to 1-590 Meionite 1-606 OU of bitter almonds . . 1-603 „ anise seed ^ . . . 1-601 Balsam of Peru . . . 1-697 Gum ammoniac . . . 1-592 Tortoise shell .... 1-591 Pitch 1-686 Balsam of styrax . . . 1-584 Bottle glass 1-582 Horn 1-665 Quartz (ext.) .... 1-558 „ (ord.) .... 1-548 Mellite (ext.) .... 1-566 (ord.) 1-638 Gum mastic 1 Burgundy pitch . . . 1 Kesin 1 Turpentine 1 Rock salt . . Sugar, melted . Gum thus . . Comptonite . . Chalcedony . . Sulphate of copper (max.^ „ (min.' Copal Canada balsam . . . Amber Elemi Oil of tobacco . . . Dichroite ApophyUite .... Plate glass from 1-514 to 1 Colophony 1 Beeswax 1 Olibanum 1 Carbonate of barytes (min,) 1 Crown glass from 1-625 to 1 Caoutchouc 1 Oil of sassafras .... 1 „ cloves 1 Balsam of Capivi Leucite . . . Citric acid . . Shell lac . . . Sulphate of lime Gum myrrh 1 Wavellite Gum tragacanth . . . Mesotj'pe (max.) . . . „ (min.) . . . Saltpetre (nitrate of pot- ash) .... (max.J 1 „ (min.) 1 Tartrate of potash and soda 1 Sulphate of zinc . . . 1 „ potash. . . 1 Gum Arabic I Stilbite 1 OU of cumin l „ pimento . . . . 1 „ sweet fennel seed . 1 „ amber . . . . 1 „ rhodium . . . . 1 „ beech nut ... 1 Indixof ■ Belraction 560 560 669 667n 667, 564 554 563 553 552 531 549 649 647 547 647 644 543 642 643 542 544 640 634 530 634 635 628 527 527 525 625 524 520 620 622 516 514 335 615 507 509 602 608 508 607 506 606 500 600 OPTICS. 15 Oil of nutmeg . Balsam of sulphur Sulphate of iron (max Oil of angelica . . „ carra-way seed Castor oil . . . . TaUow .... Obsidian .... Sulphate of magnesia from 1-4:63 to 1-488 IiideJs T Fig. 25. which R c E is the axis, or the line by a motion round which the section s M would generate a concave mirror. Let c be the centre of its concave surface s e m, and let parallel rays, k a, R E, E. B, fall upon it at the points A, E, B ; these rays will be reflected or made to converge to a focus/, half-way between c and e,* so that the principal focal distance E / is half the radius, c E, of the concave surface. The ray e e falling perpendicu- larly at E, will be reflected backwards in the same line E E, and will pass through/. In order to find the direction E A after reflexion, draw cap, which will be perpendicular to the spherical surface at a ; then since * Provided tlie reflector have not greater treadth than 5° or 6' on each side of its vertex, e. OPTICS. 47 R A c is the angle of incidence, make c a/ equal to it, and a/ will be the reflected ray ; in like manner find b/, the reflected ray for e b. By continuing all the lines in the figure to the other side of the mirror, the very same reasoning may be used to prove that when parallel rays, k' a, k' e, r' b, fall upon a convex mirror, the reflected rays, a r, e r, B r, will diverge as if they proceeded from/, which is called their virtual focus, and. which is the principal focus of parallel rays. Reflexion of Diverging Rays by Concave and Convex Mirrors. — Let s m (Fig. 26) be a concave mirror, whose Kg. 26. axis is c e, and centre c, and let o be its principal focus, or focus of parallel rays. Then if rays r a, re, R B, diverging from r, fall upon it, they will be re- flected to a focus / between o and c, so that r o is to o c as o c is to of; that is, the distance o/is equal to half the radius multiplied by itself and divided by the distance of the divergent point r from the point o. Then by adding o/to half the radius o e, we obtain /e, the conjugate focal length of the mirror for rays proceeding from R. This may be easily proved by projecting the reflected rays, and measxiring the dis- 48 OPTICS. tances on a scale of equal parts ; or it may be demon- strated geometrically in a very simple manner. Let A o be the reflected ray corresponding to tbe incident ray d a, parallel to the axis c E ; then since D A c is equal to c a o, and since b a c is equal to c a /, the remainder d A r is equal to the remainder o a/. But in the triangles a e, o, a/o, the angle a o/ is common, and arc equal to d A R, which is equal to / A o ; therefore the triangles are similar, and r o is to o A as o A is to of ; but o a is equal to o c, conse- quently R o is to c as o c is to of. Hence, when one of the conjugate foci r approaches to c, the other focus / also approaches to c ; and when R coincides with c, / also coincides with it ; so that when rays diverge from the centre of a sphere or a spherical surface, and fall on the concave surface, they are all reflected back again to the same point from which they diverged. "When r passes c towards o, / wiR then pass beyond c, and move farther ofl" as R approaches to o. When r coincides with o, / wiU be infinitely distant, or the reflected rays will be parallel. When R passes o towards e, the reflected rays will diverge like a d', and will have their virtual focus about/' behind the mirror; and as r approaches e, /' will also approach e. If the lines c a, c e, c b be continued behind the mirror in Fig. 26, and if we suppose s m the surface of a convex mirror, upon which rays r' a, r' e, and r' b fall, diverging from r', then it may be proved, by the same system of reasoning, that they will be re- flected in the directions a r, e r', b r, in lines which diverge from a virtual focus /", whose distance from o or e is found by the rule above given for concave lairrors. As r' recedes from the mirror,/" will ap- OPTICS. 49 proach to o, with which, it will coincide when r' is infinitely distant, and the rays become parallel. When b' approaches to e, /" also approaches to e. Reflexion of Converging Rays by Concave and Convex Mirrors. — It is manifest from Fig. 26 that aU rays such as d' a, which fall converging upon the concave mirror s M, will be reflected to a focus /" between o and E, and this focus will approach to e, as the point of convergence /' approaches to e. It may be shown by the same reasoning as for diverging rays, that /' o is to o c as c is to o /", /" being now between o and e. When converging rays r a, r b (Fig. 26) fall upon a convex mirror s m, as if they proceeded to some point f between o and e, they will be reflected to k', whose distance from o or e is found in the same manner as for diverging rays. From this it follows, and it may be proved also by projecting or plotting the rays, that when they converge to any point between o and c, they wUl be reflected as if they diverged from k beyond c. WTien they converge to c, they will be reflected in the same direction as if they came from c; and if they converge to a point beyond c, they will be reflected diverging as if they proceeded from some point between c and o. When they converge to o, they will be re- flected in parallel lines, or their focus wiU be infinitely distant ; and if they converge to a point/" between o and E, they'will be reflected to a real focus at r', which will approach to e as/" approaches to e, according to the law already given. 60 OPTICS. CHAPTER VI. rOKMATION OF IMAGES BY PLANE, CONCAVE, AND CONVEX MIRRORS REELECTING TELESCOPES REFLECTING MICROSCOPES. The principle of the formation of images by mirrors is the same as by lenses, and the place of the image may be found from the place of the object ; and the radius of the mirror, by finding the foci or points of con- vergence of the rays, from the rules in the preceding chapter. We will now explain the application of these- rules. Formation of Images, hy Plane Mirrors. — Let s m (Fig. 27) be the surface of a plane mirror, and l n any object placed before it ;. and let the eye of the observer be placed any- where before the mirror as at y 6. Of all the rays which proceed in every direction from the points L N of the object, and are reflected from the mirror, those which enter the eye are comparatively few in number, and must be reflected from portions a b, c d of the mirror so situated, with respect to the eye and the object, that the angles of incidence of the rays which fall on these portions must be equal to the angles of reflexion of those which enter the eye between f and g. The ray L a, for example, will be reflected in the direction a f, and the ray l b in the direction b g ; in like manner, the ray n c, n d will be reflected in the directions c r, rig. 27. OPTICS. 51 D G. Now the rays a r, b g, by which, the point l is seen, enter the eye f g as if they came from I, as far behind the mirror as l is before it, and the rays c f, D G enter the eye as if they came from a point n, as far behind the mirror as n is before it, — that is, e l is equal to e I, and h n to h w. Therefore, if we join / n, it will be of the same length as l n, and have the same position behind the mirror as the object has before it. If the eye f g is placed in any other position before the mirror, and if rays are drawn from l and n, which after reflexion enter the eye, it wiH be found that these, if continued backwards, will meet at the points I and n, and consequently, in every position of the eye the image will be seen in the same spot, and of the same size, at equal distances from the eye. If the object l n is a person looking into the mirror, he wiU see a perfect image of himself at I n, and hence we have an explanation of the properties of the looking- glass. Formation of Images by Convex Mirrors. — Let s m (Fig- 28) be a convex mirror, whose centre is c, and L N any object placed be- fore it; then, upon the same principles which have been explained for a plane mirror, it will be found that an image of it will be formed at / n, the points I n being ascer- tained by continuing back the reflected rays A f, b g tili they meet at I, and o H,- 1) I till they meet at '^' n. By joining the points l I and n n, and continuing 52 OJ'TICS. the lines till they meet, it will be found that they meet at the centre of the mirror c, whatever be the distance or the position of the object l n. The image I n is always less than the object ; and as it must always be contained between lines l c and n c, which meet at c, its length / n will be to that of the object l n as c w is to c N. When l n approaches to the mirror, I n will also approach to it ; and when L N touches the mirror, / n will also touch it, and become equal to L n. When l n recedes from the mirror, I n wiU become less and less, and recede from the mirror also ; and when i n is infinitely distant, I n will be at e, the virtual focus of parallel rays. Objects, therefore, are always seen diminished in a convex mirror, unless when they toueh it. Formation of Images hy Concave Mirrors. — Let s m (Fig. 29) be a concave mirror, and l n an objectplaced Fig. 29. at a considerable distance from it, and let c be the centre of the mirror, and p its principal focus ; then as the rays from L fall diverging on the mirror, they will be reflected to a focus at I, a little without its principal focus, and there form a representation of the point l ; in like manner the rays diverging from n will be re- flected to n, and there form a picture of N ; so that there will be an inverted image, / n, of the object formed a little without the principal focus f. This image seems OPTICS. 53 to be suspended in the air, and has a very curious ap- pearance when it is received on a thia blue smoke from a chafing-dish placed below l. As the object l n recedes from the mirror, the image I n approaches to f, with which it coincides when l n is infinitely distant, or the rays parallel. This is the principle of the reflecting telescope. If we conceive I n to be a small object, then the rays diverging from it will form an enlarged image of it at L M, which may be viewed by the eye, or, which is better, by a convex lens, in which case it constitutes a reflecting microscope. If the relative sizes of the object l n and its image / « be measured, it will be found that in every case the size of the image is to the size of the object as the distance of the image from the mirror is to the distance of the object from it. If we consider the image / « as a new object, and place a small concave mirror, r s, behind it, so as to form an enlarged image of that image, the rays of which pass through a hole e in the large mirror s m, then this second or enlarged image may be viewed by the eye behind e, or magnified still more by a convex lens. In this case, the combination becomes the Grregorian reflecting telescope, called after its inventor, James Gregory. If we make the small mirror r s convex, and place it between r and I n, so as to intercept the rays before they actually meet their virtual foci / n, then an enlarged image of this virtual image will be formed somewhere about k, and may be magnified as before with a convex lens. In this case the arrange- ment forms the Cassegrainian reflecting telescope, after its inventor, M. Cassegrain. In these telescopes the magnifying power is determined in the same manner 54 OPTICS. as for convex lenses, or combinations of ttem ; tlie size of the image being always to tbe size of its object as the distance of the image from the mirror is to the distance of the object. When an object is placed nearer a concave mirror than its principal focus f, the rays will not have their focus in front of the mirror, but will diverge, as already shown, from conjugate foci behind the mirror, where they wUl form a correct representation of the object. The image is highly magnified when the object is near the focus, but it gradually diminishes as the object approaches the mirror, and it becomes equal to it when the object touches the mirror. Cylindrical Reflectors. — A cylindrical mirror or re- flector may be polished either on the concave or convex side. If a cylindrical mirror be placed vertically before an object, its effects upon the vertical dimensions wiU be the same as those of a plane looking-glass, and its effects upon the horizontal dimensions the same as those of a spherical mirror. If a cylindrical mirror be placed with its axis horizontal before a vertical object, it will have the same effect as a plane mirror on. the horizontal dimensions, and as a spherical mirror on the vertical dimensions. The horizontal dimensions will, therefore, be preserved in the image, while the vertical dimensions will be enlarged, diminished, or reversed, in the same manner as would be the case with a spherical mirror. Conical Reflectors or Mirrors. — A conical mirror, whether concave or convex, is circular in all sections made at right angles to its axis, and rectilineal in all sections made by planes' through its axis. It will, therefore, if placed, with its axis vertical, have the effect of an inclined-plane looking-glass on the vertical dimensions of an object, and will have the effect of a OPTICS. 55 spherical mirror on the horizontal dimensions ; but each horizontal section will be differently magnified or diminished, according to the position of each section with reference to the axis of the cone, since the circular section of the cone will diminish in approaching the axis, and increase in receding from it. An infinite variety ef amusing deceptions are thus produced, CHAPTER VII. ON SPHERICAL ABEKRATION IN LENSES AND MIRRORS. In treating of the refraction of rays at the spherical sarfaces of lenses, and the refleKion of rays at the ispherical surfaces of mirrors, we have generally supposed that all the rays meet exactly in the focus. This, how- ever, is not strictly true. The rules which have been given for dd;erminiag the foci of spherical lenses and mirrors are true only for rays not extending more than ten degrees on each side of the. axes. In order to understand the cause of spherical aberra- 1;ion, let L L (Fig. 30) be a plano-convex lens one of whose surfaces is spherical, and let its plane surface — !• L m L be turned towards parallel rays r l, R l. Let ja' l', r' l' be rays very near the axis a f of the lens, and let F be their focus after refraction. Let e l, e l be 56 OPTICS. parallel rays incident at the margin of tlie lens, and it wiU. be found by projection that the corresponding re- fracted rays, l/, l/, will meet at a point /nearer the lens than r. Intermediate rays between R L and R j! will meet between /and F. Continue the rays i^fj'Lf till they meet a plane g h passing through r, and per- pendicular to the axis. The distance / F is called the longitudinal spherical aberration, and g h the lateral spherical aberration. In' a plano-convex lens like that in the figure, the longitudinal spherical aberration /f is no less than 4J times m n, .the thickness of the lens. It is quite clear that such a lens cannot form a distinct picture of any object ii; its focus r ; every object seen through such a lens, and every image formed by it, wiU be rendered confused and indistinct by spherical aberration. By actually projecting the refracted rays for lenses of different kinds, which we recommend to the reader, he will be able to verify the following results for glass lenses : — 1. In a plano-convex lens, with its plane side turned to parallel rays as in Fig. 30, that is, to distant objects if it is to form an image behind it, or turned to the eye if it be used in magnifying a near object, the spherical aberration will be 4J times the thickness of the lens, or 4g times m n. 2. In a plano-convex lens, with its convex side turned towards parallel rays, the aberration is only l-jY^th of its thickness. 3. In a double convex lens, with equal convexities, the aberration is l-j-^'p-th of its thickness. 4. In a double convex lens having its radii as 2 to 5, with its side whose radius is 5 turned towards parallel rays, the aberration will be the same as in a plano- convex lens, as in the first case ; and if the side whose OPTICS. 57 radius is 2 be turned to parallel rays, tlie aberration will be the same as in tbe second case. 5. Tbe lens wbicb has the least spherical aberration is a double convex one, whose radii are as 1 to 6. When the face whose radius is 1 is turned towards parallel rays, the aberration is only l-j-X_th of its thickness ; but when the side with the radius 6 is turned towards parallel rays, the aberration is 3^^-^^-g-ths of its thickness. These results are equally true of plano-concave and double concave lenses. If we call the aberration of the preceding lens 1, Sir John Herschel has shown that the following are the aberrations of other lenses : — Best form, as ia Case 5 1-000 Double convex or concave, with equal curvatures 1'667 Plano-convex or concave, curved surface towards parallel rays I'OSl Plano-convex or concave, plane surface towards parallel rays . 4-200 As the central parts of the lens l l (Fig. 30) re- fract the rays too little, and the marginal parts too much, it is evident that if the convexity be increased at n, and diminished gradually towards L, the spherical aberration would be removed. The ellipse and the hyperbola furnish us with curves of this kind, in which the curvature diminishes from n to l, and by which the spherical aberration may be entirely rem oved. There are, however, great practical difficulties to be overcome in the construction of lenses whose surfaces are elliptic or hyperbolaic. A meniscus with spherical surfaces has the property of refracting all converging rays to its focus, if its first surface be convex, provided the distance of the point of convergence or divergence from the centre of the first surface is to the radius of the first surface as the index of refraction is to unity. Sir John Herschel has shown that if two piano- 58 OPTICS. convex lenses be used, and so placed that their con- vexities shall he turned towards each other, the plane side of one being turned towards the object, and that of the other towards the eye, their combined aberration will be only 0'248, or a fourth of that of a single lens in its best form, provided that the focal length of one be 2-3 times that of the other. When this combination is used for the object-glass of a telescope, the lens of less curvature must be turned to the object, and when used as a microscope it must be turned towards the eye. If the two plano-convex lenses in this case have the same curvature, the spherical aberration will be 0'603 of the thickness of a single lens in its best form. Sir John Herschel has also shown that the spherical aberration may be wholly effaced by combining a menis- cus with a double convex lens, the latter being turned to the eye when it is used as a microscope, and to the object when it is to be used for forming images, or as a burning-glass. The following are the radii and focal lengths of two combinations of these lenses, as computed by Sir John Herschel : — Focal length of tlie double convex lens Radius of its first or outer surface Radius of its second surface •• . Focal length of tlie meniscus . . Radius of its first surface . . . Radius of its second surface . . Focal length of the compound lens From what has been already explained, it appears that the spherical aberration is increased with the cur- vature of the lens and the shortness of its focal length. Hence it foUows that any contrivance by which a lens of a given focal length can be obtained with a less cur- vature will supply a means of diminishing the aberra- First Second combination. combination. -I- 10-000 . + 10-000 + 5-833 . + 5-833 — 35-000 . — 35-000 --17-829 . .. h 5-497 -- 3-688 . . - 2-054 -- 6-291 . - - 8-128 -- 6-407 . - - 3-474 OPTICS. 59 tion without diminisliing the power of tlie lens. But since the focal length of a lens is diminished as the index of refraction of the substance of which it consists is increasad, it follows that if two lenses of the same focal length be constructed of different materials, that of which the material has the greater refracting power will haye less convexity, and, therefore, less spherical aberration. Chromatic Aberration. — The image of an object a (Fig. SOffl), situated at a distance from a lens l, which is formed at its princi- pal focus F, is deficient in sharpness, because it is there surrounded by a rin g of violet light. At a point r, nearer rig. soa. the lens, the image is encircled by a red ring or aureola. This results from the fact that the object emits white light, which is composed of rays of different refrangi- bility. After refraction these rays are dispersed in different directions, and the violet rays being more refrangible than the red, have their focus at k, while the red rays have their focus at f. If we place a sen- sitised photographic surface at r, where the image ap- pears the clearest, we shall obtain but a confused image, but if we advance the photographic surface to b, the focus of the violet rays, the image will be sharper and more distinct. This arises from the less refrangible rays having little or no influence on the various salts of silver ordinarily used for photographic surfaces, whilst the more refrangible rays, blue, indigo, and violet, are the most active. For this reason the bright focus of the lens at f, as judged of by the eye, is called the visual focus, whilst that determined by photographio 60 OPTICS. surfaces is called the chemical focus. These two foci in a photographic lens, or combination of lenses, should be coincident, else the lens, or combination of lenses, is said to have a chemical focus. Gem Lenses. — One of the most obvious expedients, therefore, to diminish the effects of aberration is to find transparent media suitable for lenses whose refracting power is greater than that of glass. Several trans- parent substances having this important property are found among the precious stones. The diamond par- ticularly has a greater refracting power than any known transparent body. This advantage induced scientific men to cause lenses to be made of diamond, sapphire, ruby, and other precious stones, and great hopes were entertained that vast improvements would result from their substitution for glass lenses. These hopes have, however, proved delusive, for, notwithstanding all that enterprise, skill, and perseverance could accomplish on the part of scientific men and practical opticians, the attempt has been abandoned on account of the hetero- geneous nature of the gems, their double refraction, and the imperfect transparency and colour of some of them, and also on account of their cost. Apkmatic Lenses. — Lenses, or combination lenses, which practically remove the effects of spherical aberra- tion are said to be aplanatic, from two Greek words which signify no straying. Objects Invisible to the Naked Eye rendered Visible. — Lenses and reflectors are capable of rendering objects visible which would be invisible to the naked eye, by increasing the quantity of light proceeding from them which enters the eye. The light which produces vision, as will be more fully explained in a future chapter, enters the eye through a circular aperture called the OPTICS. 61 pupil, which, is the black circular spot surrounded by a coloured ring appearing in the centre of the front of the eye. When the eye receives the rays diverging from a distant object the number of rays which enter the pupil will be those included within a cone whose apex is the luminous point, and whose base is the pupil. None of the rays which fall outside that cone can enter the eye or contribute in any way to produce vision. But if a convex lens be interposed so as to receive a large cone of rays, and if the lens be capable of con- verging these rays to a focus at a short distance beyond it, the eye placed at or very near the focus will receive all the rays into the pupil. Putting aside, therefore, all consideration of the magnifying power of the lens, it will have the effect of increasing the quantity of light received by the eye from each point of the object in the proportion of the superficial area of the lens to that of the pupil ; or what is the same, in the proportion of the square of the diameter of the lens to the square of the diameter of the pupil. CHAPTER YIII. ON CAUSTIC CUKVES FORMED BY REFLEXION AND REFRACTION. Caustics formed hy Reflexion. — It has been already shown that rays of light incident on different points of a concave mirror at different distances from its axis are reflected to different foci in that axis. The rays thus reflected must, it is evident, cross one another at particular points, and wherever the rays cross they will illuminate the white ground on which they are received 62 OPTICS. with, twice as much light as falls on other parts of the ground. These luminous intersections form curve lines, called caustic lines or caustic curves, and their nature and form will vary with the surface and inclination of the mirror, and the distance of tlie radiant point. Caustic curves have received a good deal of attention since they were first discovered by Tschirnhausen in the latter part of the seventeenth, century down to the present time. They have formed th.e suhject of mathe- matical investigation by M. de la Hire,. James and John Bernoulli, M. Bouguer, Dr. Priestley, Sir David Brewster, and other distinguished philosophers. Their mode of formation and general properties may be thus explained. Let a b d be a concave spherical mirror (Fig. 31) whose centre is c, and whose focus for ^9 parallel and central rays is f. Let k a b be a diverging beam of light falling on the upper half, a b, of the mirror at the points 1, 2, 3, 4, 5, &c. If we draw lines to all these points from the centre c, and make the angles of reflexion equal the angles of incidence, we shall obtain the directions and foci of all the incident rays. The OPTICS. 63 ray r 1, near the axis r b, will liave its conjugate focus at /, between f and the centre c. The next ray, e. 2, will cut the axis near r, and go on with all the rest, the foci extending from c to r. By drawing all the reflected rays to these foci they will be found to intersect one another as in the figure, and form by their iatersectiona the caustic curve a/. If light had been incident on the lower half of the mirror a similar caustic, shown by a dotted line, would also have been formed between D and /. If we suppose the point of incidence to move from A to B, the conjugate focus of any two contiguous rays, or an infinitely slender pencil of light diverging from K, will move along the caustic from a to/. If we now suppose the convex surface a b d of the mirror to be polished, and the radiant point r to be placed as far to the right hand of b as it is now to the left, it will he found, by drawing the incident and re- flected rays, that they wHl diverge after reflexion, and that when continued backwards they will intersect one another, and form the imaginary caustic a/d, situ- ated behind the convex surface, and exactly similar to the real caustic. If we suppose the convex mirror A b d to be com- pleted round the same centre, c, as at a e Dy and the pencil of rays stiU to radiate from r, they will form the imaginary caustic a/' d, smaller than a/d, and uniting with it at the points a d. Let the radiant point r be now supposed to recede from the mirror, the line b /, which is called the tan- gent of the real caustic a/d, wiU diminish, because the conjugate focus/ will approach to f, and for the same reason the tangent e / of the imaginary caustic wiU increase. "When R becomes infinitely distant, or the incident rays parallel, the points //', called the cusps 64 OPTICS. of the caustic, will both coincide with f and f', the principal foci, and will have the same size and form. But if the radiant point e approaches to the mirror, the cusp/ of the real caustic will approach t« the centre c, and the tangent c/ will increase ; the cusp/' of the imaginary caustic will approach to E, and its tangent e/' will diminish ; and when the radiant point arrives at the circumference at e, the cusp/' will also arrive at E, and the imaginary caustic will disappear. At the same time, the cusp / of the real caustic will be a little to the right of c, and its two opposite summits wiU meet in the radiant point at e. If we suppose the radiant point k now to enter within the circle a b d e, so that the distance from e to c is less than k to e, a remarkable double caustic will be formed : this will consist of two short ones of the com- mon kind having their common cusp at / (Fig. 31), and of two long branches, which meet in a focus to the right of B. "With a white china bowl I have produced some curious caustics. If the bowl be held in the hand, and its conaave surface turned towards a candle a few feet distant, the caustics will be formed at the bottom of the bowl. By inclining the upper edge of the bowl a little from the candle, the cusps will cross each other and form a figure similar to that of Fig. 32. If the upper edge of the bowl be now inclined gradually towards the candle, the former caustic gradually disappears, and the caustic is formed on the opposite side of the bowl ; if the upper edge is stiU more i''g-s2. iiiclined towards the candle, a figure the re- verse of 32 is produced, like Fig. 33. Let the bowl OPTICS. 65 be now moved by the hand, so that the most distant point in the edge of the bowl from the candle will gradually more round, and the above caustics will be seen to move around the bot- tom of the bowl. I have also produced with a white wash- hand basin, 14 inches in diameter at the edge, and 4|- inches ia greatest depth, not only '®' very remarkable caustic curves, but some curious forms, some like ladies' fans, others like the wings of birds, and still more like the tails of fishes, such as the herring and mackerel. I will now describe the way I produced these forms. A lighted candle was placed on the chimney-piece ; about 2 feet from the candle, mea- sured horizontally, the basin was placed with its lower edge resting on the washstand, which was about 2 feet lower than the flame of the candle. The washstand was in a recess, and was partly in shadow. I turned the concave surface of the basin towards the candle, about -I" of the diameter of the basin being at the time ia the shadow, and the remaining \ in the light. Some of the forms that appeared on the bottom of the basin were like the figures 34 and 35. The means by which I formed these figures and several others are within the reach of every one in his own home. When I produced these figures, the upper part of the edge, or circumference of the basin, was inclined at an angle of about 45° from the perpendicular, and receding from the candle. Caustics formed by Refraction. — If a glass globe filled with water, a solid spherical lens, or a round decanter filled with water, be placed ia the light of the sun, lamp, or candle, and a sheet of white paper be laid flat OPTICS. immediately behind the globe, lens, or decanter, we shall perceive on the paper a luminous figure bounded by two bright caustics, forming a sharp cusp or angle Fig. 34, Fig. 85. at the vertex of the refracted rays. The production of these curves depends upon the iatersection of rays incident on the sphere, lens, or decanter at different distances from the axis, and which are refracted to foci at different points of the axis, and therefore cross one another. If a plano-convex eyeglass or lens be held in this luminous figure so as to intercept the rays, a double caustic will be formed at or near the vertex of the figure, and will present an appearance similar to Pig. 36. In this figure, a b c is the part formed by the sphere or decanter, and doe is the double caustic formed by the plano-convex eye- glass or lens. Tig. 36. OPTICS. 67 CHAPTER IX. PHYSICAL OPTICS ANALYSIS OF LIGHT- SITION INTO COLOURS. -ITS DECOMPO- Solar Light Compound. — White light as emitted from the sun, or-from any luminous body, is, according to the investigations of Sir Isaac Newton, composed of seven different kinds of light, viz., red, orange, yellow, green, blue, indigo, and violet. These colours are rendered visible to the naked eye by refracting a beam of the sun's light through a prism of glass, and receiving the refracted rays on a white screen placed a few feet behind the prism. If a hole about half an inch in diameter is made in the window shutter, e f, of a darkened room, there will be, if the sun is shining, a bright circular spot, p, formed upon the floor, or on a screen placed to receive it. This circular spot of light is an image of the sun, as may be proved by looking through a piece of smoked glass along the path of the beam, when the sim will be distinctly seen through the hole. If in the path of the beam, s l, we interpose a prism of glass A b c (Fig. 37), Fig. 37. whose refracting angle is b a c, so that the beam of light may fall on its first surface c a, and emerge at the 68 OPTICS. same angle from its second surface b a, and if we re- ceive the refracted beam on a white screen w H i T, we should expect, from the principles already explained, that the white beam which fell upon p would suffer only a change in its direction, and fall somewhere upon the screen whit, forming there a round spot like to that at p. This, however, is not the case. Instead of a white spot, there will be formed on the screen an elon- gated image of the sun, containing seven colours visible to the naked eye, viz., red, orange, yellow, green, blue, indigo, and violet. This elongated image of the sun is called the solar spectrum, the prismatic spectrum, or it is sometimes called the Newtonian spectrum, since the first satisfactory examination of the sun-light by pris- matic decomposition was performed by Sir Isaac New- ton. The lowest portion of the spectrum is a brilliant red ; this red tones off gradually into orange, the orange into yellow, the yellow into green, the green into blue, the blue into indigo, and the indigo into violet. It is extremely difficult for the sharpest eye to mark the boundary of the different colours ; indeed, it is scarcely possible that any two persons should give the sam.e limits to any particular colour. Allowing the total length of the spectrum to be 360, the foUowirig are the lengths of the several colours as determined by Newton and Fraunhofer : — Newton. Fraunhofer. Eed . . . . . 45 . . ... 56 Orange . . . . 27 . . ... 27 Yellow . . 40 . . ... 27 Green . . . 60 . . ... 46 Blue . . . . . 60 . . ... 48 Indigo . .... 48 . . ... 47 Violet . . . . 80 . . . . .109 Total length . .360 360 The differences in the lengths of some of the colours OPTICS. 69 are very striking ; indeed, the lengtli occupied by each colour will depend upon the sort of glass, or other mate- rial, of which the prism is composed. In order to examine each colour separately, Sir Isaac ISTewton made a hole in the screen, whit (Fig. 37), opposite the centre of each coloured space, and allowed that particular colour to fall upon a second prism placed behind the hole. This light was not lengthened or elongated as before, and was not refracted into any other colours. Hence he concluded that the light of each different colour had the same index of refraction ; and he called such light simple or homogeneous, white Kght being regarded as heterogeneous or compound. Sir Isaac Newton also proved experimentally that all the seven colours, when again combined *and made to fall upon the same spot, formed, or recomposed, white light. This he established by various experiments. If the screen upon which the spectrum is received is brought nearer the prism, the rays begin to mix ; yet, even when brought close to the prism, the colours are evident. If another prism b a d, as shown by the dotted lines (Fig. 37), made of the same kind of glass, is placed with its angles in an opposite direction to the first prism, the coloured rays are again combined, and a white spot as before falls upon the floor. It has been just stated that Sir Isaac Newton con- cluded that the light of each different colour had the same index of refraction. This is true only for the mean ray of each colour, for the rays of each colour being themselves differently refractible, or, as the term is more generally used, differently refrangible, accord- ing as they fall on different parts of the coloured space, they will, strictly speaking, have different indices of refraction. 70 OPTICS. Sir John Herschel has shown that by looking at the spectrum with a cobalt-blue glass, we perceive a ray, called by him the " extreme red," of a crimson colour, below the ordinary red of the spectrum ; and by throw- ing the spectrum upon paper stained yellow by turmeric, a ray of high refrangibility becomes visible beyond the violet, which ray is of a peculiar neutral colour, and has been called a grey or lavender ray. Thus the number of colours in the spectrum is increased to nine. Pro- fessor Stokes has still further increased this number by the discovery of another colour beyond the lavender ray, which he has called the fluorescent ray, as it resembles the colour of some varieties of fluorspar ; so that the number of colours in the prismatic spectrum is, accord- ing to the researctes of these philosophers, further in- creased to ten. Decomposition of Light hy Absorption. — Sir David Brewster examined the nature of light by absorption; that is, by viewing the spectrum after the rays had been trans- mitted through differently- coloured substances or media, and he concludes that the solar spectrum consists of only three primary colours, viz., red, yellow, and blue. As this distinguished philosopher has contributed more to the science of optics by his discoveries and in- ventions than any other philosopher of recent times, I shall describe the manner by which he reduced the number of colours in the spectrum to three in nearly his own words. If we measure the quantity of light which is reflected from the surfaces and transmitted through the substance of transparent bodies. Sir David says, we shall find that the sum of these quantities is always less than the quantity of Hght which falls upon the body. Hence we may conclude that a certain por- tion of light is lost in passing through the most trans- OPTICS. 71 parent bodies. This loss arises from two causes. A part of the light is scattered in all directions by irregular reflexion from the imperfectly-polished surface of par- ticular media, or from the imperfect union of its parts ; while another, and generally a greater portion, is ab- sorbed, or stopped by the particles of the body. Coloured fluids, such as black and red inks, though equally homo- geneous, stop or absorb different kinds of rays, and when exposed to the sun they become heated in dif- ferent degrees ; while pure water seems to transmit all the rays equally, and scarcely receives any heat from the passing light of the sun. When we examine more minutely the action of coloured glasses and coloured fluids in absorbing light, many remarkable phenomena present themselves, which strikingly elucidate this curious subject. If we take a piece of blue glass, like that generally used for finger glasses, and transmit through it a beam of white light, the light will be a fine deep blue. This blue is not a simple homogeneous colour, like the blue or indigo of the spectrum, but is a mixture of all the colours of white light which the glass has not absorbed ; and the colours which the glass has absorbed are those which the blue wants of white light, or which, when mixed with this blue, would form white light. In order to determine what these colours are, let us transmit through the blue glass the pris- matic spectrum (Fig. 37), or, what is the same thing, let the observer place his eye behind the prism b A c, and look through it at the sun, or rather at a circulai aperture made in the window shutter of a dark room ; he will then see through the prism the spectrum as far below the aperture as it was above the spot p when shown on the screen. Let the blue glass be now inter- posed between the eye and the prism, and a remarkable 72 OPTICS. spectrum will be seen, deficient in a certain number of its differently coloured rays. A particular thickness ab- sorbs the middle of the red space, the whole of the orange, a great part of the green, a considerable part of the blue, a little of the indigo, and very little of the violet. The yellow space, which has not been much absorbed, has increased in breadth. It occupies part of the space formerly covered by the orange on one side, and part of the space formerly covered by the green on the other. Hence it follows that the blue glass has absorbed the red light, which when mixed with the yellow light constitutes orange, and has absorbed also the blue light, which when mixed with the yellow con- stitutes the part of the green space next to the yellow. We have, therefore, by absorption, decomposed green light into yellow and blue, and orange light into yellois and red ; it consequently follows that the orange and green rays of the spectrum, though they cannot be decomposed by prismatic refraction, can be decomposed by absorption, and actually consist of two different colours possessing the same degree of refrangibility. Difference of colour is therefore not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admissible as a general truth, " That to the same degree of refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility." With the view of obtaining a complete analysis of the spectrum, I have examined the spectra produced by various bodies, and the changes which they undergo by absorption, when viewed through various coloured media, and I find that the colour of every part of the spectrum may be changed, not only in intensity, but in colour, by the action of particular media ; and from OPTICS. 73 tlaese observations I conclude that the solar spectrum consists of three spectra of equal lengths, yiz., a red spectrum, a yellow spectrum, and a hlue spectrum. The primary red spectrum has its maximum of intensity about the middle of the red space in the solar spectrum, the primary yellow spectrum has its maximum in the middle of the yellow space, and the primary blue spectrum has its maximum between the blue and the indigo space. The two minima of each of the three primary spectra coincide at the two extremities of the solar spectrum. From this view of the constitution of the solar spec- trum we may draw the following conclusions : — 1. Hed, yellow, and blue Kght exist at every point of the solar spectrum. 2. As a certain portion of red, yellow, and bhie con- stitutes tchite light, the colour of every point of the spectrum may be considered as consisting of the pre- dominating colour at any point mixed with white light. In the red space there is more red than is necessary to make white light with the small portions of yellow and blue which exist there ; in the yellow space there is more yellow than is necessary to make white light with the red and blue ; and in the part of the blue space which appears violet there is more red than yellow, and hence the excess of red forms a violet with the blue. 3. By absorbing the excess of any colour at any point of the spectrum, above what is necessary to form white light, we may actually cause white light to appear at that point, and this white light will possess the remarkable property of remaining white after any number of refractions, and of being decomposable only by absorption. Such a white light I have succeeded in developing in different parts of the spectrum. These 74 OPTICS. views harmonize in a remarkable manner witli the hypothesis of three colours, which has been adopted by many philosophers, and which others had rejected from its incompatibility with the phenomena of the spectrum. In opposition to the foregoing views of Sir David Brewster, Robert Hunt, Esq., F.R.S., states, in his " Eeaearches on Light," that M. Bernard, of Bordeaux, has shown : — 1st. That the intensity of the light has such influence on the sensation of colour, that it may not only modify the aspect of the entire spectrum, but certain tints may disappear altogether. 2nd. That the absorption produced by the action of media hitherto employed on the tints of the spectrum only afiects the intensity of the light, and does not influence the nature of the colours. And, 3rd. That far from destroying the bond which appears to exist between refrangibility and coloration, observations made with care tend to confirm the opposite opinion ; everything, indeed, leads to the belief that to each ray of a given refrangibility, and possessing a determined intensity, corresponds a colour susceptible of being reproduced identically under like circumstances. M. Helmholtz has recently subjected the spectrum to a searching analysis, Mr. Hunt further states, and the result is opposed to the views of Brewster, while they confirm those of Newton. M. Helmholtz is disposed to refer the phenomena observed by Brewster, when view- ing the spectrum through difierently-coloured media, to a diffusion of the light of the adjoining rays over the particular ray under examination ; and he supposes this to arise from extra refraction in the prism and in the transparent-coloured laminae employed, by dust, striae, and the like, produciag secondary images. Helmholtz OPTICS. 75 lias adopted the following arrangement, to make the experiment in such a manner as to avoid all influence of diffusion. A solar spectrum is produced in the usual way, by means of a prism, and a lens placed at a suit- able distance from a narrow slit admittiug the solar rays. The screen which receives the spectrum is itself perforated by a slit, which can b© adjusted at will to any colour; in this way is insulated a very slender luminous pencil of any of the rays under examination, which are rendered thus perfectly homogeneous. This pencil is received on a second prism, to which succeeds a lens; the group of homogeneous rays throws upon a suitably-adjusted screen a narrow image of the slit. It will be evident that by such an arrangement as this a pencil of light may be obtained which will be pure, the very trifling quantity of diffused light by which it may be accompanied being too feeble to be taken into account. The results obtained by this method support the Newtonian law of the strict relation of colour to the refracting angle. For example, pure yellow, seen through blue glass of any thickness whatsoever, always preserves its yellow tint, never passing into white. " Such is the state of the discussion," Mr. Hunt ob- serves, "as to the constitution of the spectrum. Whether the theory of the seven prismatic rays of Newton it to be adopted, or the three spectra of Brewster, it is evident it must imdergo much modification." I have performed many experiments with prisms during the last ten years, and am fully persuaded that Sir Isaac Newton, whose memory every true lover of science sincerely respects, was led unconsciously into mistakes by the mode of making his experiments. The experiments I have made not only reconcile the views of Sir Isaac Newton, Sir David Brewster, and 76 OPTICS. other modern philosophers, respecting the colours of the solar spectrum, but they go farther, and establish the doctrine of colours held by some of the ancient Greeks and Romans, namely, that colours are produced by intermixtures of light and shade. If, when in a room, we look through a prism, with its refracting angle downwards, at a window-sash, we shall find that two colours will appear under each horizontal sash-bar, and one colour at the upper side of the bar. The two colours under the bar are, red next the bar, and yellow below the red ; the colour at the upper side of the bar is hlue. If the refracting angle of the prism be reversed, the position of the colours will be reversed also ; that is, if the red and yellow be above the bar, the blue will be at the lower side of the bar. The same order of the colours will be observed in looking through a prism at a black line extending in a right and left direction on a sheet of white paper placed in a vertical, horizontal, or inclined positiout In short, at whatever object we look through the prism, provided the object presents any contrast of light and shade, the red, yellow, and blue colours will be seen, or these colours will be seen more or less intermixed or combined, according to the positions of the parts of the object presenting the light and shade. Now let us apply these simple facts to Sir Isaac's spectrum. The colours produced by the prism below the upper side of the hole or slit through which he admitted the light were red and yellow; the colour pro- duced above the lower side of the hole or slit was hlue ; these three colours being allowed to proceed at differ- ently refracted angles to a screen placed several feet from the prism, became more or less intermixed, and formed on the screen the seven colours of Sir Isaac's OPTICS. 77 spectrum. Indeed, on account of tlie small size of the liole — one-fourth inch in diameter — through which Sir Isaac admitted the light, the red, yellow, and blue colours must have intermixed before these colours left the second surface of the prism. CHAPTER X. ON THE DISPERSION OF LIGHT. In the prismatic spectrum formed by the prism a b c (Fig. 37), the green, which occupies the middle space, has been called the mean ray of the spectrum; the index of refraction which belongs to it is called the mean re- fractive power of the prism ; and the angle which the middle green ray forms with the line s p, the mean refraction of the prism. Sir Isaac I^ewton in his experiments made use of prisms of different substances, yet he never observed that they formed spectra whose lengths were different when the mean refraction of the green ray was the same. If a prism be made of glass plates, and filled with oil of cassia, and its refracting angle be so adjusted that the middle of the spectrum which it forms falls exactly on the middle green ray in the spectrum formed with the glass prism, then it will be found that the spectrum of the oil of cassia prism will be more than twice the length of that of the glass prism; the oil of cassia is therefore said to disperse the rays of light more than the glass, that is, to separate the extreme red and violet rays more from the mean green ray, and to have a greater dispersive power. In order to find a distinct measure of the dispersive power of a body, let us suppose that the prism a e c is • 78 OPTICS. filled with water, and that by the methods described in Chap. II. we find the index of refraction for the extreme violet ray to be 1"330, and that of the extreme red ray to be 1-342 ; then the difierence of these, or 0-012, would be a measure of the dispersive power of water, if it and all other bodies had the same mean refraction ; but this not being the case, the dispersive power must be measured by the relation between the separation of the extreme rays and the mean refraction, or between the indices of refraction for the extreme red and the extreme violet, and the difference between the sines of incidence and refraction, to which the mean refraction is always proportional. The difference between the indices of the red and violet rays in the diamond is 0-056, nearly five times greater than 0-012, which it is in water ; but the difference between the sines of incidence and refraction in the diamond is 1-439, nearly five times greater than 0-336, which it is in water ; so that the real dispersive power of diamond is not much greater than that of water. The ratio of the dispersive powers is thus expressed : — ^ ^ 1-342 — 1-330 0-012 For water l-33fi ^ — °^ 0^336 ^^ 0-0357 dispersive power. ^ ,. 2-467 — 2-411 0-056 For diamond o-iSQ 1 — °' 1^439 ^^ 0-0388 dispersive power. In the following table the dispersive powers of various media are given as determined by Sir David Brewster. The first column contains the dispersive powers ; and the second, the difference of the indices of refraction for the red and violet rays, or the part of the whole re- fraction to which the dispersion is equal. Therefore if we add the half of the numbers in the last column to the index of refraction as given in page 13, we shall OPTICS. 79 have the index of refraction for the extreme Yiolet ray ; and if we subtract it, we shall have the index for the extreme red ray. By means of the second column in the table we may obtain the length of the spectra formed by prisms of any of the substances it contains, for any refracting angle, for any position of the prism, and for any distance of the screen upon which the spectrum is received. In doing this, however, it must be remembered, that the measures here given are suited to the ordinary daylight ; and that when the sun's image is used, and great care taken to screen the middle rays of the spectrum, the red and violet are found to extend to a greater distance from the mean ray. TABLE OP DISPERSIVE POWERS. Dispereive power. Chromate of lead (gr. refr. ext.) . 0-400 , „ „ (least refr.) . 0-262 , Realgar, melted 0-260 , Oil of cassia 0-139 . Sulphur, after fusion .... 0-130 . Phosphorus 0-128 , Sulphuret of caxhon 0-115 , Balsam of Tolu 0-103 , Balsam of Peru 0-093 . Barbadoes aloes 0-085 , Oil of bitter almonds .... 0-079 , Oil of anise seed 0-077 . Acetate of lead, melted .... 0-069 . Balsam of styrax 0-067 Guaiaoum 0-0B6 Oil of cumin 0-065 . Oil of tobacco 0-064 . Gum ammoniac 0063 . Oil of Barbadoes tar 0-062 . OU of cloves 0-062 . Sulphate of lead 0-060 . Oil of sassafras 0-060 . Muriate of antimony .... 0-050 . Rosin 0-067 . Oil of sweet fennel seed . . . 0-055 . Oil of spearmint 0054 . Rock salt 0-053 . Caoutchouc 0-062 . Difl. of index of refr. for extreme rays. . 0-770 . 0-388 . 0-384 . 0-089 , 0-149 . 0-156 , 0-077 . 0-065 . 0058 . 0-068 , 0-048 , 0-044 , 0040 . 0-039 , 0-041 , 0-033 , 0-035 . 0-037 , 0-032 , 0-033 , 0-066 0-032 0-036 0-032 0-028 0-026 , 0-029 0-028 80 OPTICS. Oil of pimento . Flint glass . . Oil of angelica Oil of thyme . Oil of fenugreek Oil of caraway seed Giun thus . . Oil of juniper . Nitric acid . . Canada balsam Cajeput oil . . Oil of rhodium Oil of poppy . Zircon (gr. refr.) Muriatic acid . Grum copal . . Nut oil . . . Oil of turpentine Felspar . . . Balaam of capivi Amber . . . Calcareous spar (gr.) Oil of rapeseed Sulphate of iron Diamond Oil of olives Gum mastic Oil of rue Beryl Ether . Selenite . Alum. Castor oil Crown glass, green Gum arahic Water . . Citric acid . Glass of borax Garnet . . Chrysolite . Fluor spar . Crown glass Oil of wine . Glass of phosphorus Plate glass . Sulphuric acid Tartaric acid Nitre (least ref.) Borax Alcohol . Sulphate' of barytes UiBpersive Difl. of index of refr. power. for extreme rays. 0-052 . . . 0-020 0052 . . . 0-026 0051 . . . 0-026 0-060 . . . 0024 0-050 . . . 0-024 0-049 . . . 0-024 0-048 . . . 0-028 0-047 . . . 0-022 0-045 . . . 0-019 0-045 . . . 0-021 0-044 . . . 0-021 0-044 . . . 0-022 0-044 . . . 0-220 0-044 . . 0-045 0-043 . . 0016 0-043 . . 0-024 0-043 . . 0-022 0-042 . . 0-020 0-042 . . 0-022 0-041 . . 0-021 0-041 . . 0-023 0-040 . . 0-027 0-040 . . 0019 0-039 . . 0-019 0-038 . . 0-056 0-038 . . 0-018 • 0-038 . . 0-022 0-037 . . 0-016 0-037 . . 0-022 0-037 . . 0-012 0-037 . . 0-020 0-036 . . 0-017 0-036 . . . 0-018 0-036 . . . 0020 0-036 . . . 0018 0-036 . . . 0-012 0-036 . . . 0-019 0-034 . . . 0-018 0034 . . . 0-018 0-033 . . . 0-022 0022 . . . 0-010 0-033 . . . 0-018 0-032 . . . 0-012 0-031 . . . 0-017 0-032 . . . 0-017 0-031 . . . 0-014 0-030 . . . 0-016 0-030 . . . 0-009 0-030 . . . 0-014 0-029 . . . 0-011 0-029 . , . 0-OU OPTICS. 81 Kook crystal , . . Tourmaline Emerald Borax glaas (1 tor. 2 silex) Blue sapphire .... Bluish topaz .... Chrysoberyl .... Blue topaz Sulphate of strontites . Prussic acid .... CryoUte Disperaive power, 0-026 . 0-028 . 0026 . 0-026 . 0026 . 0025 . 0-026 . 0024 . 0-024 . 0-027 . 0022 . Diff. of index of refr. for extreme ruys. . 0014 , 0019 . 0015 0014 0021 0016 0-019 0-016 0015 0008 0-007 It appears by the preceding table that different bodies possess very different powers of dispersing or of separating the coloured rays of light. If we form two spectra of equal lengths by two bodies of very different dispersive powers, such as oil of cassia and sulphuric acid enclosed in hollow glass prisms, we shall find a remarkable difference between them. Let a b (Fig. 38) ^ be a spectrum produced /""^ /'^ by a prism of oil of cassia, and c D a spectrum pro- duced by a prism of sul- phuric acid ; by care- fully examining these two prisms we shall find that the least colours, red, yellow, will spaces, or will be more "" rig. as. "" contracted in the oil of cassia spectrum than in the sulphuric acid one ; while the most refrangible colours, blue, indigo, and violet, will occupy larger spaces, or will be more expanded. Therefore the coloured spaces have not the same ratio to each other as the lengths of the spectrum ; hence this property is called the irrationality Indyo Green refrangible ^^^ orange, occupy and Me£ mu sffi Mlolef JncUffO Blue (xreeiv Orcnrne Red, 82 OPTICS. at o rH f-^ CO 02 P s « s « 5 n ;^ s 5 H fa « o o »<; o ■s R 1 l-l ^ o M-i o fa o ^ S S s (^ s fn H H d CO r-l i-H ;zi g I _3 82 6 o ^ |2i iiD .g D h tl I •a ;zi I OPTICS. 83 of dispersion, or of the coloured spaces in the spectrum. This property is clearly shown in Fig. 38, by which it also appears that the mean ray, m n, is a,mong the blue rays in the oil of cassia spectrum, and among the green rays in the sulphuric acid spectrum. Thus it appears that although the indices of refrac- tion of the extreme rays for any two substances may be equal, the indices of refraction of each of the inter- mediate rays may be unequal, and the differently- coloured spaces in the two spectra may be also unequal. In the table opposite the indices of refraction corre- sponding to the mean rays of each of the seven principal dark lines in the spectrum are given for several media or substances, according to the experiments of Fraunhofer. By taking the difference between any two indices the dispersion proper to any two of the prismatic colours will be found, and by taking the difference between the extreme indices the total dispersion pro- duced by each medium will be found. For example, the index of the red ray produced by flint glass No. 13 is 1 '627749, and the index of the blue ray produced by the same medium isl*648260; the difference, 0"020511, is the dispersion of the mean red and blue rays ; the index of the red ray for the same medium b^ng !• 627749, and the index for the violet ray being 1"671062, the difference is 0"043313, which is the total dispersion of the red and violet rays produced by flint glass No. 13. CHAPTER XI. ON THE PEINCII'LE OF ACHROMATIC TELESCOPES. The application of the principle of the dispersion of light, explained in Chapter X., to the improvement of 84 OPTICS. tlie refracting telescope, forms one of the most in- teresting portions of optical science. Sir Isaac Newton concluded that it was impossible by the combination of lenses to produce refraction without colour, because he believed that all media, or substances, whether solid or fluid, had the same dispersive power, or produced the same length of spectrum in proportion to their mean refraction ; yet soon after the death of that eminent philosopher, it was accomplished by Mr. DoUond, who constructed excellent refracting telescopes without colour, or, as they are called, achromatic telescopes. If a convex lens is made of crown glass, whose index of refraction is 1'519, and dispersive power 0'036, and a concave lens of flint glass, whose index of refraction is 1-589, and dispersive power 0-0393, and if the focal length of the convex crown-glass lens is made 4-|- inches, and that of the concave flint-glass lens 7-| inches, they will form, when placed close together, a lens with a focal length of 10 inches, and will refract parallel rays of white light striking on the convex lens to a single focus nearly free of colour. The great point to be attained is to find two substances of difierent refractive and dispersive powers, and capable of producing spectra of equal length, and in which the coloured spaces are all equal. If such substances were found a perfect achro- matic lens would be produced ; but as no such substances have as yet been found, other means have been adopted \o remove the imperfection. Dr. Blair discovered that muriatic acid produced a spectrum in which the green rays were among the most refrangible. But as muriatic acid has too low a refractive and dispersive power to fit it for being used as a concave lens along with a convex lens of crown glass, he conceived the idea of increasing the refractive Fig. 3». OPTICS. 85 and dispersive power of the muriatic acid by mixing it witli metallic solutions, such as muriate of antimony ; and he found he could do this to the requisite extent without altering its law of dispersion, or the proportion of the coloured spaces in its spectrum. By enclosing muriate of antimony, l l, between two convex lenses of crown glass, as a b, c d (Fig. 39), he succeeded in refracting parallel rays, r a, k b, to a single focus f, without the least trace of colour. Through s 4 — telescopes made with lenses of this descrip- tion Professors Ex)bi- son and Playfair saw double stars with a dis- tinctness and degree of perfection which astonished them. In practice the materials which have been found most suitable for achromatic lenses are flint glass and crown glass, which differ considerably in both their refracting and dispersing powers. The refractiug and dispersing powers of these sorts of glass vary according to the proportions of their constituents, but they may be always rendered such as to fulfil the conditions necessary for an achromatic lens. The forms of the lenses shown in Fig. 40 are those of a double concave of flint glass, and a double convex of crown glass. It is, however, neither necessary nor expedient that these forms should be always adopted. The crown-glass lens maybe double convex, with unequal convexities, or it may be plano-convex, or even meniscus. The flint-glass lens may be in like manner double- ^ concave, with unequal concavities, or it may be plano-concave, or concavo-convex. In the same way 86 OPTICS. tlie radii of tlie curves of the surfaces may be in- definitely varied, the compound lens having stiU the same focal length. The practical optician, it will thus be seen, has a wide range in the construction of achromatic lenses, of which the most eminent have availed themselves with great skill and address, so as to remove, by the happy combination of curves, not only the spherical aber- ration, but also the chromatic aberration of the eye- glass, and the spherical distortion. On the Illuminating Power of the Spectrum. — By the experiments of Fraunhofer it appears that the place of maximum illumination in the solar spectrum is at the boundary of the orange and yellow rays. Calling the illuminating power at this place 100, the light at other places will be as follows : — At the extremity of the red, O'O ; near the extremity of the red, 3'2 ; near the middle of the red, 9'4; in the orange, 64-0; boundary of the orange and yellow, 100-0 ; in the green, 48'0 ; in the blue, 17*0 ; in the indigo, 3"1 ; near the middle of the violet, 0'56 ; extremity of the violet, O'O. Bark Lines across the Spectrum. — In the year 1802 two dark lines were observed by Dr. WoUaston to extend across the spectrum formed by a fine prism of flint glass, free of veins, when the luminous rays were admitted through a slit the twentieth of an inch wide. This discovery did not attract much of his attention at the time. Without knowing of Dr. "WoUaston's dis- covery, M. Fraunhofer discovered that throughout the whole length of the spectrum it is nearly all covered with these dark lines running parallel to one another, and perpendicular to the length of the spectrum. He also ascertained that these lines are altogether inde- pendent both of the magnitude of the refracting angle, and of the matter of the prism. The number of these OPTICS. 87 dark lines observed by Fraunbofer amounts to 590. This number bas been increased by Sir David Brewster, wbo observed no less than 2,000 dark lines in a spectrum wbicb be examined. In order to observe tbese dark lines it is necessary to use prisms free from veins, to exclude all diffused or extraneous light, and to stop those rays that form the coloured spaces which we are not examining. It is necessary also to use a telescope which magnifies eight or ten times. Heating or Calorific Power of the Spectrum. — It had been supposed up to atbout the commencement of the nineteenth century that the heating power in the spectrum would be proportional to the quantity of light. The late Sir William Herschel, however, proved by experiment that the beating power gradually increased from the violet to the red extremity of the spectrum. He also found that the thermometer continued to rise when placed beyond the red end of the spectrum, where not a single ray of light was then perceived. Sir John Herschel has since discovered the " extreme red " ray in this place by looking through cobalt-blue glass (see page 70). Sir Wm. Herschel determined that the rays invisible to the naked eye exerted a considerable heating power 1^ inch distant from the extreme red ray visible to the naked eye, even though the thermometer was placed at a distance of 52 inches from the prism. These experiments were repeated by Sir Henry Engle- field, with additional precautions against error, and he found that the thermometer rose in the following order : — In the blue rays in . . . 3 minutes from 55° to 56° or lo In the green rays in . . . 3 54 „ 68 „ 4 In the yellow rays in . . 3 66 „ 62 „ 6 In the red rays in ... . 2^ 66 „ 72 „ 16 In the confines of the red in ^ 58 „ n\ „ 164 Below the visihle red in . u 61 ., 79 „ iS »» OPTICS. M. Berard obtained similar results, excepting that lie found the greatest heat at the very extremity of the visible red, instead of beyond. Still more recently M. Seebeck has confirmed the foregoing results, except- ing that he found the place of the greatest heat varies ■with the substance of which the prism is made. Seebeck was assisted in his experiments by M. Wunsch ; they came to the following conclusions : — Colour of space Substance of the Prism. in wliich the heat is greatest. Water yellow Alcohol „ Oil of turpentine „ Sulphuric acid orange Solution of muriate of ammonia . . ,, Solution of corrosive suhlimate . . „ Crown glass middle of the red Plate glass „ „ Flint glass teyond the visihle red Sir John Herschel has more recently made a series of experiments on the heating power of the spectrum, by trying the varying effects of its power when thrown upon sheets of the thinnest post paper smoked on one side in the flame of oil of turpentine, the smoke of a candle, or blackened with Indian ink, till it is coated with a film of deposited black, as nearly uniform a& possible, and soaked on the other side with rectified spirits of wine, which makes the paper uniformly black. The spectrum being thrown upon the wetted side of the paper thus prepared, the heating power of its different parts is manifested by the varying degree of its bleaching power upon the paper produced by the evaporation of the spirits of wine. The result obtained in this way was, that the heating power extended over the whole length of the spectrum, but at a point considerably beyond the limit of the extreme red (visible to the naked eye) the heating OPTICS. 89 power is a maximum or greatest, having gradually increased in ascending from the lowest limit to this point. The heating power then diminishes slightly for a short space, and again increasing, attains a second maximum . It then diminishes until it ceases altogeth er, after which it again increases until it attains another maximum, after which it again diminishes, vanishes, and reappears, and increases until it attains a fourth maximum, and still again a fifth maximum is faintly indicated. M. Melloni has shown by his experiments that bodies are not alike transparent to light and heat. Black mica, obsidian, and black glass in thin laminae, although nearly opaque to light, yet allow a large quantity of -radiant heat to pass through them, and are called by Melloni diathermic bodies; while glasses of a green colour, in combination with a layer of water, or a very clear plate of alum, are called adiathermic, from their being perfectly opaque for heat, notwithstanding light passes through them freely. These results tend to show that flight and heat, though keeping company as it were in the sunbeam, are distinct solar emanations, and not merely different states of one power. On the Chemical Influence of the Spectrum. — ^It has long been known that sunlight changes the colour of certain substances. The celebrated chemist Scheele first observed that muriate of silver is rendered much blacker by i^e- violet than by any of the other visible rays of the spectrum. This fact enabled Daguerre to discover the art of producing portraits, called after the discoverer Daguerreotypes, by the action of light on plates of copper, covered with certain deposits of silver. The same fact also was the germ from which has grown the art of photography, which has elevated and enriched the arts of painting, sculpture, and architecture. 90 OPTICS. Since the art of photograpliy has been developed to sucli importance, a great number of interesting experi- ments have been made upon the chemical effects of the spectrum. Some of the most distinguished philoso- phers of the present age have devoted much attention to the subject. The limits of this work preclude an examination of all the researches that have been made. It appears, however, from the valuable experiments of M. Edmund Becquerel, Sir John Herschel, Mr. Robert Hunt, and M. Niepce de Saint Victor, that the chemi- cal, or actinic, influence of the spectrum upon various mineral and vegetable preparations generally extends from the green rays to the most refrangible violet rays. By Mr. Hunt's researches, it appears that the chemi- cal influence of the spectrum on twenty-nine different mineral and vegetable preparations extended, in aU cases but one, from the green to the most refrangible violet ; the sole exception being the juice of the ten weeks' stock, in which case the chemical influence extended only to the middle of the violet. A remark- able exception is also presented by this juice — the maximum chemical, or actinic, influence is exerted upon it at the middle of the yellow, where no influence is exerted upon any of the mineral preparations. In twenty-five of the twenty-nine preparations, the chemical influence extended beyond the most refran- gible violet ray, and in eleven cases of the twenty-nine, the chemical, or actinic, influence extended even beyond the most refrangible fluorescent ray. In four of the vegetable preparations, viz., the juices of the Cor- chorus Japonica, ten weeks' stocks, wallflowers, and the green of leaves, the chemical, or actinic, influence of the spectrum extended over the yellow and orange, and OPTICS. 91 near to the least refrangible visible red ray. The maximum chemical effect on the preparations of Cor- choms Japonica and wallflowers was at the middle of the indigo, and on that of the green of leaves at the boundary of the blue and indigo. Assuming the length of the N'ewtonian, or visible, spectrum to be 40, by a scale of equal parts, the heat, or caloric, spectrum extended over 75 of such parts, according to some of Mr. Hunt's experi- ments, and the actinic, or chemical, spectrum over 86 of such parts, so that the chemical influence of the spectrum extended over a space more than twice the length of the visible lumiuous spectrum. The foregoing results coincide with some experiments of Sir John Herschel, who found that the chemical, or actinic, influence of the spectrum on paper prepared with nitrate of silver, and washed with hydrobromate of potash, extended over 116"77 equal parts, of which the visible luminous spectrum was only 63-92 parts. On producing Coloured Pictures Photographically. — Various attempts have been made to obtain photo- graphs of objects in their natural colours. These attempts have been so far successful as to produce photographs in which every colour of the original was faithfully represented; even the iridescent colours of the peacock's feather have been beautifully photo- graphed. It is, however, not yet quite certain whether any means have been discovered by which the colours can be permanently fixed, as hitherto they have slowly faded away, and become one imiform reddish tint. It is generally admitted that, up to the present time, the most successful photographer in producing coloured pictures is M. Niepce de Saint Victor, whose process is this : — He takes a Daguerreotype, or sHver- 92 OPTICS. coated plate, and dips it into a weak solution of hypo- chlorite of sodium, having a specific gravity of 1"35, until it has assumed a bright pinkish hue. The plate is then covered with a solution of dextrine, saturated with chloride of lead ; it is then dried, and subse- quently submitted to the action of heat for several hours until the temperature of the plate reaches from 95° to 100°, or else exposes the plate to the rays of the sun as a substitute for artificial heat, under a sheet of paper which had been steeped in an acid solution of sulphate of quinine. The plate is then ready to be placed in the camera obscura, and to receive the coloured picture of the spectrum, or any other object. It is said that he has succeeded in increasing the stability of the colours developed on the sensitive sur- face by covering the plate with an alcohoKc solution of gum benzoin. This branch of photography has been called Heliochromie.* CHAPTER XII. BREADTH OF WAVES OF LIGHT INFLEXION OR DEFRAC- TION OF LIGHT LAW OF INTERFERENCE. The following method of measuring the breadth of waves of differently-coloured light was used by Sir Isaac Newton. He placed a flat plate of glass, d e (Fig. 41), upon a convex lens of glass, the surface of which is represented * It is not the otject of this treatise to descrihe photographic pro- cesses generally. Those who wish to oljtain full information respecting the most approved processes in practical photography will find it in M. Van Monkhoven's Treatise on "Photography," No. 79, Weale's Kudimentary Series. OPTICS. J 93 by A B, but wliicb must be supposed to have infinitely less curvature tban that shown in the figure. The under surface of the flat plate will touch the vertex of the convex lens at c, and the further any point on the under s\irface is from c, the greater the distance Fig. 41. between the surfaces of the two glasses. If c be taken as a centre, and a circle be described round it, at all points of that circle the surfaces of the glasses will have the same distances between them, and the greater that circle is, the greater will be the distance between the surfaces of glass. The glasses having been thus arranged, iffewton found that, by letting a beam of red light fall on the surface of the glass d e, a black spot appeared at the centre c, where the glasses touched ; that immediately around this spot there appeared a circle of red light ; beyond that circle a dark ring; that outside of that dark ring there was another circle of red light, still having the point c as its centre. Outside this circle another dark ring appeared, beyond which there was another circle of red light, and so on, a series of circles of red light alternated with dark rings being formed, all having the point c as their common centre. The distances between the surfaces of glass at which the successive circles of red light were found were too small to be directly measured, but they were easily calculated by measuring the diameters of the circles of light ; and, knowing the diameter of the convex sur- face of the lens A c b, this was a simple problem in geometry easHy solved with the greatest accuracy. 94 OPTICS. Newton found, on making these calculations, that the distance between the glass surfaces where the second red circle was formed was double the distance corre- sponding to the first ; that at the third red circle the distance was triple that of the first, and so on. Of course it followed that wherever the dark rings were formed, the distances between the glass surfaces were not an exact number of times the space corresponding to the first red circle. Newton perceived that these phenomena were the direct manifestation of those efiiects which corresponded to the breadth or amplitude of the waves of light in the undidatory theory, although he used the corpuscular nomenclature. The space between the surfaces of glass at the first red ring was the breadth of a single wave, the space at the second red circle the breadth of two waves, and so on. Within the first red circle the space between the glasses being less than the breadth of a wave, the propagation of the undulation was stopped, and darkness ensued ; in like manner, in the space corresponding to the second dark ring, the distance between the glasses being greater than the breadth of one wave, but less than the breadth of two, the propa- gation was again stopped, and darkness produced. But at the second red circle, the space being equal to the breadth of two waves, the undulations were reflected, and the red ring produced, and so on. It then became evident that, to measure the breadth of the red waves, it was only necessary to calculate the distance between the glasses at the first red ring. Number of Waives or Undulations in an Inch. — "When light of other colours was let fall upon the glass, a similar system of luminous rings was produced, but it was found in each case that the first ring varied in its OPTICS. 95 diameter according to the colour of tlie light, and therefore that the breadth of the waves of lights of different colours is different. It appeared that the waves of red light were the largest ; orange came next to them ; then yellow, green, blue, indigo, and violet succeeded each othsr, the waves of each being less than those of the preceding. But the most astonishing part of this investigation was the minuteness of these waves. It appeared that the waves of red light were so minute, that 40,000 of them would be comprised within an inch, while the waves of violet light were so small that 60,000 would be contained within an inch ; the waves of light of other colours were of inter- mediate magnitudes. Table of Undulations. — In the annexed table are given the length of the waves of each prismatic colour, the number of them which measure an inch, and the number of waves, pulsations, or undulations per second which strike the eye. Colour. Length of an undulation in parts of an inch. Number of undulations in an inch. Number of undulations per second. Extreme red (visible) Red Orange Tellow Green Blue 0-0000266 0-0000266 0-0000240 0.0000227 0-0000211 0-0000196 0-0000185 0-0000174 0-0000167 37640 39180 41610 44000 47460 51110 64070 67490 69760 458,000000,000000 477,000000,000000 606,000000,000000 535,000000,000000 677,000000,000000 622,000000,000000 658,000000,000000 699,000000,000000 727,000000,000000 Indigo Violet Extreme -violet In this table, which was calculated by the eminent Dr. Young, the numbers of waves or undulations per second are given in round numbers, so as to render the principles of the investigation as intelligible as possible. 96 OPTICS. The results contained in the table can scarcely fail to excite in us sentiments of the greatest wonder and astonishment. It is well known that solar light moves at the rate of about 200,000 miles per second; it necessarily follows that a ray of light 200,000 miles in length must enter the pupil of the ^e each second, and as the perception of light and colour is produced by pulsations of the membrane of the eye vibrating in accordance with each ethereal undulation or wave pro- pagated from a visible object, whenever we behold a red object, the retina, or membrane, of the eye trembles or pulsates upwards of 477,000,000,000,000 times every second. For each of the other colours of the spectrum the number of vibrations the eye makes in a second is still greater ; when violet light is perceived it trembles at the rate of about 720,000,000,000 times in a second. That man should be able to m.easure with certainty such almost infinitely small portions of time and space is most wonderful ; for it may be observed that whether we adopt the corpuscular theory of light, according to which the molecules of light are supposed to be en- dowed with attractive and repulsive forces, to have poles to balance themselves about their centres of gravity, and to possess other physical properties, or adopt the undulatory theory, the periods and spaces just given have a real existence. It is not unreasonable to suppose that the heat rays, and chemical, or actinic, rays, which accompany the luminous rays in the solar beam, are endowed with properties analogous to those of the luminous rays, and possess qualities no less wonderful. Inflexion or Diffraction of Light. — The property of light called inflexion, or diffraction, was first discovered OPTICS. 97 by Grrlmaidi in 1665. Since that time the subject has received a good deal of attention from many eminent philosophers, but it is to M. Fresnel that we are indebted for the most successful investigation of the phenomena. If the rays of light diverging from a luminous point F (Fig. 42) fall upon an opaque object a b, all those rays included within the angle a f b will be intersected, so that a screen held at c D will receive none of these rays. If we produce the lines f a and F B to a' and b', they will include upon the screen those spaces which would have been illuminated by the rays proeeedina: from f, which are stopped by the opaque body ab. All the rays included in the angles Arc and b f d will proceed uninterruptedly, and will fall upon the screen. If these rays suffered no change of direction, they would illuminate those portions of the screen included between c and a', and d and b'. There would by this means be a well-defined shadow of the object, ab, formed upon the screen at a' b', and the rest of the screen would be illuminated in the same manner as it would have been if the opaque body, a b, had not been present. It is foimd by experiment that no such exact and well-defined shadow of the opaque object would be formed upon the screen. The outline of the space which would limit an exact and geometrical shadow of A B being determined, it is found that within this space light will enter, and that outside this space the illumi- nation is not the same as it would have been if the object, A B, had not been interposed. Hence it is inferred that the rays of light which pass 98 OPTICS. the edges of the opaque object do not proceed in the same straight lines, a a' and b b', in which they ■would have proceeded if the opaque object was not present. The edge of the shadow is not a well-defined line, Separating the illuminated from the dark part of the screen, but a line of gradually-decreasing brilliancy from the illuminated part of the screen to that in which the shadow becomes decided. The effect produced by the edges of an opaque body upon the light passing in contact with them, by which the rays are bent out of their course, either inwards or outwards, is called inflexion or diffraction. This phenomenon is considered as a consequence of the general property of undidation. When the system of waves propagated round f as a centre encounters the obstacles a b, subsidiary systems of undulation will be formed round A and B respectively as centres, and will be propagated from those points independently of, and simxdtaneously with, the original system of waves whose centre is r, and which will also proceed towards c a' and D b'. In a certain space round the lines a a' and B b', along which the rays, grazing the edge of the opaque body, would have proceeded, the two systems of undulation will intersect each other and produce the phenomena of interference. The Law of Interference. — If two pencils of Hght, radiating from two points close to one another, fall upon the same spot of a piece of paper, in which case they may be said to interfere with one another, for if the paper were removed they would cross one another at that point, then if the lengths of their paths, or the distances between the paper and the two radiant points are the same, they wUl form a bright spot or fringe of light, having, an intensity greater than that which OPTICS. 99 would have been produced by either pencil alone. "Now it is found that when there is a certain difference be- tween the lengths of their paths, a bright fringe is produced exactly similar to what is produced when their lengths are equal. Let us represent this difference by the letter d, then similar bright spots or fringes wiU be formed when the differences in the lengths of the paths are 2 d, 3 d, 4 d, 5 d, and so on. But what is very remarkable, it is clearly proved that if the pencils of light interfere at intermediate points, or at those points in their paths when the differences in the lengths of the paths are half d, one-and-a-half d, two-and-a-half d, three-and-a-half •(?, and so on, then instead of adding to one another's intensity, the two pencils of light destroy each other, and produce a black spot or fringe. The quantity d, or the difference in the length of the paths at which the interfering pencils of light either destroy one another or unite their effects, that is, at which they produce the black ^nd light fringes, is also the breadth, or as it is sometimes caEed the length of an undulation, or a wave of light. M. Fraunhofer found the value of d for the different colours of the spectrum to be nearly the same as those found by Dr. Young, which are given in the firpt column pf the table in page 95. Still more recently M. Fresnel, by some carefully con- ducted experiin,eiits, arrived at nearly the same results. Some important practical consequences follow from the finding of the value or length of d, among which are the following: — When we consider how glass is ground and polished, its surface cannot be mathemati- cally correct ; bUit as long as its inequalities, in reference to their distance from each other, are less than the length d, they will not be ^trimental either to the light which is transmitted, or that which is reflected, 100 OPTICS. and no colours of any kind can be produced in them. It would likewise be impossible by any means to render inequalities of sucb a size visible. The Smallest Magnitude visible ly a Microscope. — ^If any object wbose diameter is equal to d consists of more than two parts, it cannot be recognised as consist- ing of more than two parts. In red light the limit of microscopic vision is the thirteen-millionth part of an English inch, and in violet light the eight-millionth part of an English inch. Combined Effects of Inflexion and Interference. — ^If an opaque body, a b (Fig. 43), be very small, and the focus F be a considerable distance from it, the two pencils formed by inflexion, of which A and b are the foci, will intersect each other as shown in the figure,, and in this case some curious phenomena will ensue. If the light be homogeneous, a bright line of light will be formed under the centre of the opaque object a b, outside which wiU be dark lines, and then bright and dark lines alternately. If the arrange- ment of these lines be examined, they will be found to vary in their relative distance with the quality of the light which radiates from the focus r. If the light radiating from such focus be compound light from Tig. 43. ^^ g^^j^^ ihsa. a series of coloured fringes will be formed. Examples of the Effects of Inflexion and Interference. — A great variety of optical phenomena is produced by light passing the edges of smaU opaque objects, or small openings or slits made in the opaque plates. The principles, however, by which all these appearances are explained are the same. OPTICS. 101 If a fine wire or Bewing-needle be held dose to one eye, the other eye being closed, and be looked at so as to be projected upon the light of a window or a white screen, several needles will be seen. If the eye be directed in a dark room to a narrow slit in the window shutter by which light is admitted, several slits will be seen separated by dark bands. If a piece of card, having a narrow incision made in it, be held between the eye and a candle, a series of slits will be seen parallel to each other, exhibiting the colours of the spectrum. The same appearance may be produced with increased e£Fect by looking through the slit at the sunlight admitted through an opening in the window-shutter. Thin Transparent Plates. — ^When light passes from any transparent medium to another of diflferent density, a part of it is reflected from their common surface, and a part only transmitted. Thus, when light passing through air is incident upon the surface of glass, a certain part of it is reflfected from such surface, but the greater part enters it. When that portion which enters the glass arrives at the second surface, which separates the glass from the air, on the other side, a like effec* ensues, a portion of the light is reflected from the second surface, the greater part, however, penetrating it, and passing into the air. Hence there are two systems of reflected rays — one reflected from the first surface of the glass, and the other by the second surface. The first system is reflected back immediately into the air, the second is thrown back into the glass, and must pass through the first surface of the glass before it returns into the air. If the two surfaces which thus succes- sively reflect a portion of the light which passes through thetransparentmediumbe very close together, and if they 102 OPTICS. be not precisely parallel, the reflected rays wIU intersect each, other and produce the phenomena of interference. Iridescence of Mother-of-Pearl, Soap-bubbles, Feathers, >c. — Hence arise the curious and beautiful appearances of iridescence which are seen whenever transparent substances are exhibited in sufficiently thin plates or laminae, the prismatic colours that are seen in the scales of fishes, in spirit of wine spread in thin films on dark surfaces, in oil thinly diffused over the surface of water, and the thin laminae of crystals and soap-bubbles, and glass bubbles blown to extreme tenuity, in the laminae of mother-of-pearl, in the wings of insects, and feathers of birds. CHAPTER XIII. DOUBLE EEFKACTIOX, AND POLARISATION OF LIGHT. When treating of the refraction of light, in preceding chapters, through different media, it has been supposed that the refracting medium had the same density and structure in every part of it. This, however, is not •always the case. There are two classes of transparent substances, which present optical phenomena depending on certain physical properties inherent in the constitu- tion of each class of substances. When bodies such as gases, fluids, certain transparent solids, such as glass slowly and equally cooled, crystallised bodies, the form of whose primitive crystal is the cube, the regular octo- hedron, and the rhomboidal dodecahedron, have the same temperature and density, and are not subject to any pres- sure, light incident upon any single plane surface will be ^refracted according to the law explained in Chap. II. In almost all other bodies, including crystallised OPTICS. 103 minerals not having tlie primitive forms above menr tioned ; animal substances, such as horn, shells, bones, lenses of animals ; vegetable substances, such as certain leaves, stalks, and seeds ; and artificial bodies, such as resins, gums, jellies, glasses quickly and unequally cooled, and solid bodies haviag unequal d.ensity either from unequal temperature or unequal pressure, a ray or pencil of light incident upon their surfaces will be refracted into two different rays or pencils, differently inclined to one another, according to the nature and state of the substance, or medium, and to the direction in which the ray or pencil is incident. This property of double refraction was first observed in a transparent minera,l substance called Iceland spar, (lalcareous spar, or carbonate of lime, which is composed of 56 parts of lime, and 44 of carbonic acid. In crystallising it generally assumes the form of a rhomb, such as that represented in Fig. 44, a solid bounded by six equal and rhom- boidal surfaces, whose sides are parallel, and whose angles b a c, a c d are 101° 55' and 78° 5'. The inclination of any face A B D c to any of the adjacent faces that meet at a is 105° 5', and to any of the faces that meet at x, 74° 55'. The line a x, called the axis of the rhomb or of the crystal, is equally inclined to each of the six faces at an angle of 45° 23'. The angle formed by any of the three edges that meet at a, or of the three that meet at x, with the axis is 66° 44' 46", and the angles between any of the six edges and the faces are 113° 15' 14" and 66° 44' 46". If we take a rhomb of Iceland spar. Eke Fig. 45, with well-poKshed faces, and each of its edges at least an inch long, and place one of its faces upon a sheet of 104 OPTICS. paper having a black line, l n, drawn upon it ; if we then place the eye at r, and look through the upper sur- face of the figure, we shall probably see the line l n double, but if it be not so, by turning the crystal a little round it will become double, and two lines, ln. In, will then be distinctly ^' ■ Tisible, and by turning the crystal round, keeping the same side on the paper, the two lines will coincide with one another, and form only one at two opposite points during a whole revolution of the crystal ; and at two other opposite points, nearly at right angles to the former, the lines will be at their greatest distance from one another. If a black spot be placed at k, the spot will appear double, as at k and m, to an eye placed at k ; and by turning the crystal round as before, the two images^ will be seen to revolve, as it were, around each other, excepting at the points where they coincide. Let a ray or pencil of light, K r, be now supposed to fall upon the surface of the crystalline rhomb at r, it win be refracted by that surface into two rays or pencils, r K, r M, each of which wiU be again refracted at the points K and m of the second surface, and will then move in the directions k A, m >w, parallel to one another and to the incident ray or pencil s r, which has thus been doubly refracted. If we now measure the angle of refraction of the ray or pencil r k corresponding to different angles of inci- dence, we shall find that when the ray or pencil falls perpendicidarly on the first surface of the crystal, it OPTICS. 105 suffers no refraction, but passes straight through the crystal in one unbroken line ; that at all other angles of incidence the sine of the angle of refraction is to that of incidence as 1 to 1-654; and that the refracted ray- is always in the same plane as that of the incident ray. Thus it appears that the ray /• k is refracted according to the ordinary law of refraction, which has been explained in Chap. II. If we proceed in the same way to measure the ray r m, we shall find that at a perpendicular incidence, the angle of refraction, instead of being 0", is actually 6° 12' ; that at other incidences the angle of refraction is not such as to follow the constant ratio of the sines, and that it lies entirely out of the plane of incidence. It thus appears that the . ray or pencil r m is refracted according to some extraordinary law. Axis of Double, Refraction. — If e r be incident in various directions, either on the natural faces of the rhomb, or on faces cut and polished artificially, we shall find that in Iceland spar there is one direction, a x, along which, if the refracted pencil passes, it does not suffer double refraction. In other crystals there are two such directions forming an angle with each other. In the former case the~cTystal is said to have one axis of double refraction, and in the latter case two axes of double refraction. It is found that in some crystals the extraordinary ray is refracted towards the axis a x, while in others it is refracted from that axis. In the first case the axis is called a positive axis of double refraction, and in the second case a negative axis of double refraction. In a great variety of other crystals two axes of double refraction are found, whilst in others stiU innumerable axes of double refraction have been discovered. Among this last-mentioned class analcime is found. i06 OPTICS. On Substances idth Circular Double Refraction. — The following are some of the substances which possess the remarkable property of producing positive, or right- handed circular double refraction, viz., certain specimens of rock crystal, camphor, oil of turpentine ; other sub- stances, such as concentrated syrup of sugar and essential oil of lemon, produce negative, or left-handed circular double refraction. The limits of a work of this nature preclude the possibility of entering fully into the consideration of these curious phenomena. Polarisation of Light. — If a ray of light be reflected from the surface of a body under certain special con- ditions, or transmitted through certain transparent crystals, it suffers a remarkable change in its properties, so that it will no longer be reflected and refracted as before. The effect thus produced upon it has been called polarisation, and the ray or rays of light thus affected are said to be polarised, as it is found that the sides of the ray which lie at right angles to each other posse^ contrary physical properties, while the sides of a ray of common light, whether of the sun, a candle, or any burning or self-luminous body, possess the same physical properties. By way of illustration we may compare a ray of common light to a round rod or wire of uniform polish and uniformly bright, while a ray of polarised light may be compared to a similar wire, two of whose OPTICS. 107 opposite sides are rougli and black, -while the other opposite sides at right angles to these are polished and bright. Thus if a b c d (Fig. 46) be a section of the former, the entire circumference is bright and polished, and if E F G H (Fig. 47) be a section of the latter, the sides a and c will be bright and polished, while the sides b and d will be black and rough. If we cause a ray of common light to fall upon a rhomb of Iceland spar, as in Fig. 45, and examine the two rays, K k and m m, formed by double refraction, we shall find that the rays have difierent properties on different sides ; so that each of them differs from the ray of common light. The two rays, k k and m m, are there- fore said to be polarised, or to be rays of polarised light, because they have sides or poles of different properties, and planes passing through the poles are called ^fowes of polarisation, because they have the same property, and one which no other plane passing through the ray pos- sesses. If we cause the two polarised rays to be again united into one, we obtain light which has exactly the same properties as common light. Polarised light pos- sesses numerous properties, curious, complicated, and useful. If we blacken a plate of glass on one side, so that when used as a reflector no light will be reflected from its second surface, such a plate will therefore reflect light only from the first surface ; and if we cause a ■ polarised ray to fall upon it at an angle of incidence of 54° 35', so that the plate shall make with the ray an angle of 35" 25', and if it be turned round the ray, so as to be presented successively on every side of it, stiU, however, forming the same angle with it, during this operation it will be observed that there is a certain direction of the plane of the angle of incidence at which no reflection wiU take place ; the ray will be 108 OPTICS. absorbed, or extinguished, as it were, by the reflecting surface. The plane of incidence will have this direction in two opposite positions of the reflector. Let the line b d (Fig. 47) represent this position of the plane of incidence : then b and d will be the two opposite sides of the ray, at which the reflector being presented will cause the ray to be extinguished. As the reflection is carried round from either of these positions respectively, so that the plane of the angle of incidence shall turn round the axis of the ray, reflection will begin to take place, and will increase in intensity until the plane of the angle of incidence takes a posi- tion such as a c, at right angles to b d, when the intensity of the reflection will be a maximum. From this it is evident that when the reflector is so presented to the ray that the plane of the angle of in- ; cidence shall coincide with the plane of polarisation, the ray will be reflected with the greatest intensity, and that when the plane of the angle of incidence is at right angles to the plane of polarisation, no reflection takes place, and the ray is extinguished. Angle of Polarisation. — If any other reflecting surface be used instead of glass, like effects would follow ; only that the angle at which it would be necessary to pre- sent the reflecting surface to the ray would be different, each species of reflector having its own particular angle. This angle is called the angle of polarisation. JPolariscopes. — Instruments called polariscopes, adapted for the experimental illustration of the phenomena of polarisation, have been constructed in various forms. For the purpose of elementary explanation, one of the most convenient is represented in Fig. 48. In the figure A B is a brass tube, like that of a telescope, along the axis of which the polarised pencil, or ray, to be OPTICS. 10» Submitted to examination is transmitted; c is a short tube, capable of being inserted, after the manner of telescopic tubes, in the main tube at a. This tube c carries a plane reflector, d, of the blackened glass already described, which is capable of being turned on n^ Fig. 48. pivots, and is supplied with a double scale and index, by which the angle it makes with the axis of the tube can be regulated at pleasure. By turning the tube c round its axis, the plane of the reflector d may be presented successively on every side of the axis of the main tube. In the tube at