INTERFERENCE OF LIGHT AND SOME METHODS OF MEASUREMENT BY THERON BAYNE CHANEY B. S. Knox College, 1921 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS. 1922 URBANA, ILLINOIS ,’ff ■ VO ; ii V I . i f.aQiirsu awoz as-iA thou lo aaicaiiaarfaTKi. il Tnat/!3I>U)2A3W HO ‘ 'r^ ■■- r .*!>' . Vi,' K>’Vr!/7> V.' ^ ‘V . 1- F . ' * A /I • >1 frt H Y3H/i.H>iiWyAH >^i>i!3ifr jw-wi ^ Jl acaaHT eTWatf*i)U^Pr?Sf 3)JT T|0 '.V«dlfJ»in.lll'ff lit no *90 iiHfr4Mf4» flo< Y'fi'javi, if "sill' 10 ioono« 3'PMSciiiMO 3Ht mi ^ . .□& > 'Jf l U ^ gloMlJJI ^>t Art« u 1.. ' \ .• . .. Vi... \ wy 0.5G UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL June -IQ2- I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY r SUPERVISION BY__ T H^'ROI-J n:iAA’'RY ENTITLED^I irr E R FER FM CR -O F Ll Qi i T . S Q::F ;^ I RT HODS . Q E- OFT sure:: "IT BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR 'FHE DEGREE OF RASTFH OF SC I URGE Recommendation concurred in* Committee on Final Examination* •■Required for doctor’s degree but not for master’s 3 A »*¥• i 8iom,iji, HO vTi^ysavrua ./i , jovti jc. .TTAi}aAMi> :mr r, m V A • * tgi -4SAji4^4JS3f.. A* 5A, ^jrcjK.rO^JfA%'JK'L‘'jV|;r: jlh. -ur <> . nOiAx M •- *4^ i . 4 ^‘■-, »; -iv;' * ■' 4 ■ t «' L ^Of U «04r ■^4. ) filUr ^ • ■•^ *»l TABLE OF CONTENTS. The numbers refer to pages. Foreword . I. Historical. II. The Meaning Of The Wave Theory. III. The Experiments Of Young And Fresnel. IV. Interference By Thin Films. Newton's Rings. V. Colors Of Thick Plates. Brewster's Bands. VI. The Michelson Interferometer. VII. Some Actual Experiments Using The Interferometer. 1 . Adjustment of the interferometer. 2. Measurement of uhe wave length of sodium light. 3. Ratio of Lne wave length of uhe D lines. 4. Measurement of i.ne index of refraction. VIII. Some Famous Classical Experiments. IX. Other Types Of Interferometers. 1 . The Fabry-Perot Interferometer. 2. Jamin's Ref ractometer . 3. Lodge's Interferometer. X. Conclusion. \ 3 8 16 22 26 30 33 33 35 36 40 44 48 48 50 53 55 . V r via i y -rftr iii iifii i ifei w ft m h ^ l1 l fn,i« . % >fc- ^ , -^ . - ;» ‘ . -;yg a ' . rfl l ^ o n \f‘ »f r* > 'C^. ■'• . dl. .'• V •S' i Ji * „ t « «*i4ru W wiwbafv ts . *> AU- " ' ^ ^ .V, -1^ ■ .'*''V ■ - ■ r.'. ijTO#;!'- .ni!» 0^'', ; > . ■ t f’j ', ' . . V, ^ • 'I . (Ur*r. i\ajai-^ . *■'. ' , y I. , ■♦-- ,, . _ ■,>p - ' 't .... • ' ■ j 'nn96j^tih9>rnjtf\; :i|, < ^ ^ * ■ ' " i' ' ' .Ui.l..i '■ • , Y i-i[jc'^> .*i'j4aX pilT giUliU 9CiT*i4i*]ttx^4 . , t4 T ^ j, * •' '. *^^i4 Xtf 'air n rt/6oa,^v iu»£ni#I rv*^ vita la- " ?llf.::J./j '« '*.' ' 1*^ .(itiYii a 'i;.j la d^iifKiX. la tifi ..< ■ I- • 1 ' ." -t ' . . I ’ tr" .. ■ ' ..' \^ .ilf 'V f ' ■ «?- . ‘3P 1* lw3>iJw ■ i .niiL f ■ ,;■ yJiOT :..(^o^:a^X4l^l;65“^^ lii,' iWE'^ ,‘ I INTERFERENCE OF LIGHT and SOME METHODS OF MEASUREMEI^T ! I FOREWORD I f In preparing this thesis, the writer has had two objects in | mind. The first one was to enlarge his own knowledge of the sub- ject of interference of light waves. The second one was due to the writer's interest in the field of high school teaching. Ten of the most widely used textbooks in high school Physics were examined lo see how much space was devoted to the subject of interference. Three of the ten made no mention of the subject. Two of them gave two and one half pages to interference, while the rest averaged about two pages. This thesis has been written therefore with the high school student in mind, and this has made it necessary to include considerable detail which might not have been included otherwise. It is hoped that t.his discussion will awaken in a few worthy students a live interest in t,he subject of interference and will encourage them to delve more deeply into this subject, one of the most fasci- nating in the field of Physics. If this hope is realized, the discussion will have justified itself. Digitized by the Internet Archive in 2015 / https://archive.org/details/interferenceofliOOchan INTERFERENCE OF LIGHT and SOME METHODS OF MEASUREMENT This discussion will be considered under four heads as follows: 1 . A brief history of Lne aevdopment of Lne wave theory of llsnt contrasting it with the then prevailing theory of light and including a short explanation of tne theory. 2. A description of une experiments of Young and Fresnel and of other simple methods of producing Interference of light lead- ing up to a description and explanation of the Michelson inter- ferometer. 3. An account of some experiments performed by the writer with the Michelson interferometer together with a aescription of some of the practical applications and some of the classical ex- periments in which this Instrument has been used. 4. A descripLlon or some other well known types of inter- ferometer including some of the most important applications which have been made oi them. I. Historical. There have oeen a number of theories of the nature of light and the mode of its propagation from the time of the ancient Greeks down lo modern times. Some of them were ohe result of much logical reasoning £md withstood attacks from various philosophers for considerable lengths of time. Noteworthy among t,he moaern Lheorles of light was the corpuscular Lheory supported by Sir Isaac Newton. This theory postulated small luminous bodies which ?H0Xj ?o ^it'orisjttisra j ■ iiofi I * Ss TTfe^Kn^;^25ii ijiijp« ' ■ '•V' '’ ■ ,,p- ~ ^sfc «W/l nuftw h€''£ofi|jtfti{o<3 od J,Jflw ijqiftev^i'aii «id'P ^ , :xot'« milrtsXJ ^0 i^dJ fiiu ii^Ti Ji 5ffijR'r '■ > % a/ii Ic, jictiJim XqAii- ' biJ# ‘f V- ‘ , ax^iSi,-jt^4v-,.ca opci'a "io 'itA .,5'' ’ * .U^:(;;.;^io a;»u ^ti ettcUM^iXi.q^ X*i to Wt ^ ■ • ' '.■’V-' .. . <. ft^'»UJ ■wfJO’fiiiriXB/it; .« Ixi#' rfi a ’* '•i ■ ' ' -■ *' ‘ If ^ ,., f .-'H'ixJX to i^jiK-m: •nadio ff - / ■ ■ ' - ■"® 10 f ^ " 12 1 ■ I f I ■ ' J ' ‘ ' ' * j« ' '* %r. ■■ ■' . ■" ^ ' r ^ ’‘- V * '^■v ■';, ”' ■’ if', •■ '•ar I'JS' }J^ •■ !TI 1- -r .u ;', -.■•uiteti •uif.'u. fttomu la ii«#»>3JE(i«.«»^,,»:;ri j,'tl4uii M oc-! ^ ^'ifcA.c'ei'/iim a/tiii,tv oaii:eSy»i4j[«,.i,o«4i,;u|,(,, f«au^i«jo*(n “fKOiai>i*' L> ^^...•: . . j . ■:. , '1 ' ■•. 2 were shot, ouo In every alrection from any luminous object, which, when they struck the retina of tne eye, produced the sensation of sight. By making certain assumptions, this theory explained very satisfactorily the various phenomena which had been observed up to that time. Because of this lact, and also because of the great reputation of Newton as a scientist, this theory held its ground for a much longer time than it could have otherwise. But tae fact that new assumptions had to be made to explain newly observed phenomena with the corpuscular uheory made it more or less unsatisfactory, and the undulatory or wave theory of light as developed by Huyghens was advanced in opposition to the older theory of NewLon. This theory provided very satisfactory explan- ations of various phenomena v/ithout the necessity of making the assumptions which often had to be made with the other theory. For some time, there was considerable controversy over the relative merits of the two theories, and some very famous experiments were performed in an attempt to prove the superiority of one or the other of these theories. Assuming the corpuscular theory to be correct, it became necessary to suppose that lignt traveled faster in a denser med- ium such as glass or water than in a rarer medium such as air. Juso Lne reverse of this was true with ohe wave theory. An ingen- ious experiment by Foucault proven quite conclusively unat llghu traveled with ci sxower velocity in water than in air. The result of this experiment provided strong proof lor the wave theory, but in spite of it, the corpuscular theory remained much in favor long after Newton's time. About a century later, Thomas Young showed Lhe interference of light, and his work together with that of Fresnel was une final blow which completely discredited the » I -,’*^r^’‘‘ ■•''*f-'*» roB nont,aalptiti’ >w»' '■ a- . - . * ■'‘ * * ^ ‘ • , ' ■ %» A « . ,^-vX aiilj * ea uc^^j'w^ io ^'‘ ‘v , fyi^ iimlS At>m: A ', ' - ; V't * V '^‘ -. ' ,f * 9 ,; <)J 6 ^ .aniziiijntJiBB 'nen J'flio* sjjj tjifi a 4 ? yp M »i'Mi vtviiJ •ir'uiUii.noo flit 4ii* t.ta>uo^_i^yi.*w-i*a4p/^'i^ ^^il«t»i:e 9iit ax no/Jf.Tift^jo rtX lusnaVfia «vf« I -r-i.4.v. viO'fWilti.v.K *. . ■f’^6iwl4. ’?a4*.ic .,^-J ttJ'tw ©^*c. dv oj 6jin rw^la-' t*ri^x lK 'i::-T.;,»Jn*»i'j,^a »«e«at , t 4 ,:'y l^.x ,<,xl, 6 *Hx cbJ wU 'lo ' aJrt^^' « '::.-d ¥} . L.i. j(i.-^ itt, »/‘o'-icf vfi'oitwua 9,1; Vx 'XqnuJJa fwiwcti^ • ' '• V V ■’ '•■, ‘ 'i '. ; ''-■ •> ' i- '*** ^ ^ '-O' <.j 'citatix j)nlk('iaA^^ ^;v«'(X •-| .^ir^ o^xw afiy. «xio'o49V|'iw»9xa'*», uxiw BfcXeva^^ ■ a^ 9 .«^x‘"=>v»» 9 ,U ,c.,x Ifcaag 8 te'»X«j?»t.iVj^ ^ vy»*x^' n/.r’' ,8^4/^r «Ai£Oii’T Avtkl' m ,.'..l-‘ 1 . ..r..A a. AHt.'t 7 i It ’* ‘ <■* -.' . .: ' * I! •^- ■ * • . ■ ^ ' • I .H^ !' ‘ Vj. KflB^rV * . \ ^ » *, '^•gft <~ . . f ^ ^ ^ > ^ -■ ‘ .'y; 3 corpuscular tneory. II. The Meaning of The Wave Theory. Before discussing the work of Young and Fresnel, some con- sideraLion must be given oo the meaning of tne wave oheory of light. For our purpose, we may define a wave as a, progressive | I shape or form which is propagated through a medium by tne regular ! periodic vibrations of the particles of wnich the medium is com- | I i posed. Every one is familiar with the waves wnicn travel across | the surface of still water when it is disturbed. Energy is trans- j miuted along the surface of the water oy the waves, but tne water Itself does not move with tnem. Instead, the particles of water execute an oscillating motion as each wave passes by. Waves may also be illustrated oy a i*ope wnich is attached to a fixed body at one end, the other end being held by the hand. If the hand is movea periodically up and down, waves will pass along tne rope from the hand to the fixed end. These waves will be executed in a vertical plane when tne hand is moveu in a vertical line, and tne energy which the waves carry axong may be felt by grasping the rope firmly at tne fixed end. a b c. *%» a BJi bVjSW a ©nllBi) igfta bw ,0Utq^i?^E>o ■ j y^a*j5« X»Taii ilolnw e/u iUiY» Wiiaii'i tl *»no vSaRta ■ ' ‘ ■"• ■'^'Oi ' < JB' r f' ' I ai Xa'xaiX? . JbooTcy^Bjii) ai 4jt /lad* ©iij ,\ie-viiw «iij YO a.'li !16 Onola Aa^jic -it'-’rik' xo fc^XoiiiAq iiJiw ovoo joft keou tXooxi ' ’ ’ - ■ i- ' , ."7/'^ ,^u Aj \u jbXoil sniau ^/r» af^uP ,iicio ©sc its =■/ ^ - ' , . ' '1, 'ff •— ipncXJR !w^4»q XU«r ^.rftob'hiiM ’ ^.•. , ’ .^ ,, ■ *•' ■' . . • -a M *'J lijt.f, Bavtfw GnsctT ,um uaxii ajli oilfcn^ .rfanri ‘ . ^''1 ■ ' ' ■' t, w;^ ts%t ^uoxX XA0ii3*tav d n£ imvor. ejL :?jnaq ciaj ri'<;ia a/ia£^^oX':^^y ^ ciu :xr!x^»i»'Ti3 x^i JXoi '*<3 ^TfVs jtavnv tioXAW - . biiw ii4>, ©oJ( J4i xtnuX'l ©qoa ’ ‘^*1 C'ftj '3x:c In r-tvxi'x, uoXiiW iovAw li-^yA'Vt i)llJ jni*ao*^T r ^ . i I '■'• . 'r 45,':^.^(Xj(tcq »iiT ‘7 'V ** * xo 4wc&nii nwcfl^N, ©I'll , aj6 ,1^ . 0 *U;i3wo’iJ £»©^il«a j)*u', , ' J , . * ' iV ■ , . '’V*' . a oj 9'19X j-tfsX 3nXi^,v‘(ttiii sX oxu 4i!/i^< t / I •* iir f t " ■ -M fiA ,ftv** c ta9v> .nidi' j'« iji}c,i 1o jjowofji iiJW!|£ la’^fleo’ ' J.^ ' -ii-W. ' ■'’X „,,■. >1 'dxivj kt©j#X;' . . . 4 the trough w will now be lm^lealct^ely under the point where the crest was tne preceding instant. But the section b of the rope has not moved forward, but has moved downward. An instant later, the crest a will have come along, and the section of the rope will have moved upward to its original position. Thus the small section of the rope is oscillating in a vertical line which is perpen- dicular to the direction of motion of the wave. The wave is there- I fore advanced by the oscillation of many sections of the rope, \ I each one vibrating in a line perpendicular zo the direction of the | wave motion, and each one passing its motion on to the next sec- tion. It is important to note here that the energy transmitted to the rope by the hand is carried forward wholly by the wave itself, the sections of tne rope retaining their relative positions throughout. The wave theory of light is very aptly illustrated by the analogy of the rope waves given above. Light is a form of energy which is transferred by wave motion just as the energy which is communicated by the hand to the rope was transferred from one end of the rope to the other by the rope waves. But the rope waves have a visible medium by means of which they move forward, which is the rope itself, each section of the rope vibrating period- ically in a line perpendicular to the direction of wave trans- j mission. As far as the eye can tell, there is no such medium by | which light waves may be transferred, but we know that it is transmitted through the air as well as through space in which there is no air. Obviously, if light consists of wave motion, there must be a medium filling all space which will transmit I these waves. Such a medium is assumed to exist, although its ‘ c>T* ■ - rr. *Vir ^ •f, ft - , 4 • ;'/ ^ .'. V f'» ^4? iJnfoq ^ftdbnw t^wJi*/i)^ji8i,t »a »6it IXJlw y ri^wo'ivT ^xU i’l ‘ ,^ . :V-.^ i'» • ' : ' - ■• ■: -,/j « ^ ,6;^ to ^ xieiiooa uei>‘s& ■’ 1 I'/J i) it 1 i ovod »tiid A). joa Mjti $pii .‘^cn- t#Kno4?v^»e #ii;^ 'M jbi .^jfrolo «moo irvM .-i" ' ■ ■■ ’ > "•' ■• ' ^ ■ i> n XXfii^ »i4lxt . rtdi;*lep4 X/^r XsXho , -£itq*iOQ *>/ oittX it/ ’-^UttjBXXXOoc / #t^ '• V04 *^*tOOO x*ii4 4^44 »«s*>ri o.t|f,fr p4 «4 , .*^064/ »y*jK o£ j Td y4x* rtif £rtjt»vfp1. fcoi i*uio o ? JbroaH tfdir oiqjtin «/l? ^pcACt^fHl OVlvTAXo^i li*.':* OdO*t »a4 tc ' , •' ... J 3 r tX4flt X,»t»*r tX "XC \*SCBFiS [ j • 1 ^‘Mine' tii itiol M al Jii^jtj ,i.'Vod/> xi«vij^ eov^w upLQ«/oii41o f r- ' • ’ ■ ' . ,,t^ ' -j EiX iiOiiiW Xsft'iOCO Cm noiJOBI OViV lli ^oiiiw dMO oott t<’» oQ0*» oiW c4 bxui>Jli 044 * folftoo fnyu*t '>44 4V3 . ntjv^svf ©qOT odlX ^ oiiJ ,04 #b*x ! iy ,t ,&*t;;;*-ic 1 t«vc4.V xeii4 flOiJiw lo urunMl \;d niu/boir olcjlOiv < ' -„ , " '-^f. ftrUfiioXv ecfj ta ^i&op ,tX^f,;;X -^4 ' ‘ orv^;iv* =1 v> io i»i.io€'tii!i oxlJ o4 *j3KXLwdit«©45[^9'.r^04XX o oi ^XaoX ♦ * • ' . -'■ ■■'? ^ i’viiXbeifl ji.oi;>* .on «!»*!tori4 ,Xto/ii«o *v? ortX ca oA'f^/4^.X» 3 fji', ■ '* h: jj 4«u** #o?iv 90 diict^ uovow XnglX |loX4w. ^n^lciu iU *9*>qo' XIow a4'*2i4 0/l4i1dS£>ot4/fk44ixlSi^^^ • ^JfV f. K ' A ■* *■ ’ •■' '•' * ■ ■’ \-U’3 ' *' ^ f 8, iftc-XAGr. r v^w J4;iii.i; Yt ,^ifc|fo4YClO ritA pn •fr'l ' % ", ■ 'XiAittfio^ix iiiv iioXxir noiit^o ix^ xeuii 84X liSOCiU^i? ^dfixxe, 0,J /wjmKuoBj^ bX iadXl'Ojs dft Ao 4(J oJioijJ . }'■:■ '%j : \ •>■ ' ■ .-a- ' ’ ■- ’’ ■• * «i- ■ ' ■ )* ar *^( - 5 - existence cannot be proved, and this medium is called the ether. It fills all space not occupied by other forms of matter. It is necessary to assume certain properties for the ether which are quite paradoxical. It must be a perfectly frictionless fluid which will offer less resistance to a body passing through it than the lightest known gas. But when a force is exerted upon a gas and some of the molecules are displaced from their original positions, they do not return uo the original position when the force is re- moved. But in the case of wave motion, the particles must return to their position. Hence the ether must have great elasticity. Indeed, it is often spoken of as an elastic solid with the seem- ingly impossible property of being frictionless as already stated above. This then is the medium by which light energy is trans- ferred as wave motion. As the light wave passes through the ether, each particle executes a periodic vibration perpendicular to the direction of motion of the wave in the same manner as each section of rope in a rope wave. Thus the light wave passes through the ether without the forward motion of the individual particles. This constitutes one of the main points of departure from the corpuscular theory. In this theory, the light energy is carried forward by small particles themselves, the particle actually mov- ing forward in the direction of motion of the light ray. Let us return for a moment to the analogy of the rope waves. Let Figure 2 represent the waves passing along the rope. The X p r j- • »,w «P^ ei nuiftM ««» ' fc«ii» .-(ievciq' i kr., W &*J^^ d'lU^ai .Roi^tota t>V4v lo ni JS*Voffi ' ’\-^ - ‘ ■ ^ 4 r , : .- ^7 Y .'• ■toUtoXe »*»n» overt Joua -iort4t.''oa,i eom^fl ..n,aiW«^‘rt4k§W'«idJ ™ -...OSB ttfj lutw Mi0« oJJsoXo nrt oji Xp, o». "r ... - 1 . 1. - _. , . .1 ^ _'‘‘lli*<^r' oi Kxnoa* a,irt, pj r-a/ M-it . • ■;x» :-rtX rt:).io-itu - oba.^ ev.iw -'^C-iti '.rtJ- « 4 - .rtoXJoa jOvow .eA^'to^ ■■■V /;4 fii.* tiAl 4 yDif;f v >T#» OyM;# ®»IO»»Ay*' \r .■t.atolt^ Uub^imt art* -io i.tlJtw ivuio*ito1 aurt^JBo44w y- OrtiJ ic eoJw^Beca-airt?| Vt^TBo.0 JJS61X art* .V'ct.rtrt'«li5j .?ji :>V',voi lif-jAuJart *..C4iJiv!-.c.v.q hi »na icia.J'iac* 4iftn«£i>^ Wi;i ^ P ' - • t rfl' X./W q iia^nioq.-IrtJ ^iveitt (s»-i fj ^ i« npii^o acHii j^As^l Bvaa ejBii. b ota - bn* q njbio-; otlt iuB ^ • ' ' . . .Axa»«( flcXao..Bva* lo >.»-u,0..,„ ,0 » aa - ir,ee *va4 XXto 31 ,t*(jae!. era, lo Jine okj )A . «9Va» . '*‘ ^sXaw ,aw-A4B^« ,X jjgwX a avaB’-ljo^e IX bm ,mfjui )>■ Xff *>i4 tortX enaat sxriT .Xtl ao'xxxi. .xxxa Ji >iW .,^o*fc%oe Bl m «4 imjpa Bs^aoxib 'a 1 M <» • ' i A. ^ ' vl ,xev#.,x wave. Suppose tiiat we have waves coming from two sources A and B on the surface. They will spread out in all directions as shown in < i Figure 3. Let the waves from both sources have the same wave | i; length, the same amplitude, and j the same velocity. In the figure, | the continuous lines represent wave crests, and the broken lines represent wave troughs. At the point X, two crests from the dif- ferent sources meet. Hence the waves at this point are in the same phase, aind the oscillating particles of the water take up energy from both waves so that its displacement is equal to the sum of the displacements which would be caused by either wave acting alone. Therefore, the crest will be higher here than the crest of either of the Individual waves. Similarly, at the point y, two troughs are together, and the dis- placement of the water particles at this point is equal to the sum of the displacements caused by the two waves acting alone, so that the trough is deeper. Now let us see what happens at the point w where the crest of one wave meets the trough of the other. Prom our definition of phase as applied to rope waves on page 6, it is seen that these I two waves are in opposite phase. Therefore the motion of one of the waves will tend to cause a displacement of the water particles in one direction, while the motion of the other wave will tend to produce a displacement in the opposite direction. The resultant displacement, being the sum of the two displacements of the two waves, will be zero since the motions of the two waves oppose or Figure 3. film -A o»tl»u;s ^ k ^ ^ , , t»v*:4 ^ .',l^s ^&p^U|oa i^.too CO*>i «Xi4j ,c -| ‘ * ■ •■ •> "'‘X r.' •,'-- ^ ^ ■ sa jj n^aj iix . t^itpoX»v’ diii8« r ,1 '•’ • «r; - ;x «ucrni^iioo i%ac.fi rajicin liii 6 oa; .aifd^ab 9vm jA .^L4:i3«cn^ av<>^* itrraa^^iqa*! u.i^, i-vil A4B9nn «-¥J ,x ^j?lcq ^ aiia ,#on*^. aa^^cci aoi.t4iil64ic fjflah uiaAK BtiJ jiiloq Ci^W >*• ■<»♦**» '... , , '/• ./’• I u,’.( .j/^rtj 06 6 t>yan' xi<20<^ itO'!! »jisJ *zoc^¥i eaXsKt>i^jEi^ ^ ■r . ':■ •..■ r- , ;> '^ZtfOW tioiiiM iiiJ "Sc (^>pr» ^ifif .oj X»r.«pt# ^ i^X** wW .iat\cld zTiUoa arc# ■'■ * ■ ' ■ , • ,il^ •' .- " Ij-^ tiGiiX«5c^ a»i4 a/iioyc't^ o>^' ifildq '!*:' '.v* iuKJ ^ tJbxifv ni AflX|JC aXit) Ja eo J[ of 4 * 1^4 aiii iica(!» 5 |tx 7 c?^ $ay4.fr tv;f 044 ic mtf. ■' ■ : ,' - , . -. ■ " ' • ■■; '. « ‘ F- " -’^ii .'iayfriHX# «X rf84#c^*?,«ii4 iiid^ « % ' t* ■ 4flo-rb iJtfiX w J/doq Js enxK^rtj* aoa 8x \l’»i wj|3t‘-‘ l "tc ' *ii;o .-iOfiAo eiw to iliijc*|j oiii ri ., »i.9fLh^ noBn &.J, Ji ,d »54ii; 'CP os to c.^e "lo no'X«ca a/U a'tclaoaHt' /&frr4 a^'iifoqqo' »• ■*. _ >; :. ; ^ j- ji^V4fi'- om %0'' '*XSi K' r >'^'’t'' f' -K ■'* ' : ’^i' ^ t*' ••:ut-;.ir .,. ca Xlfw %VE»< »fOii*fo exi^ to ©4:ixiv ;/tw iOi u' .^. . 1 * , ....'Vi. *ic «ayuw o^x .aJ •as^tivi ’rtSiiX ,nJt rU>^yr c^yj|.f I*- ^ '‘^i " ' ^- * ■\h w ' :'iiv V4iw' V* Jd^iS V^ct^riX hnrcinti MLi^k^x^^ a^.> rci.^AoitMiq <>Ad r«s»xi«j XXjc jkitc^i ,J tv* * v’ jo*tq ■ «Jt Jft3 u ,1 1 x/>dx wpmi' Ic '■" ^ .} ci.vj iQ #AAU'ibl‘io4jrU fthj .n«iir.^^ fc •apt* ou >,«4tcX*;iD/jfto ^E " * . 'H . P?i_.riiirJ«. 'u,. V * B* v. ' • ' *’J pi ftX-i ]bt»YO'it| /iot/itf ., ■ L * ' • ,• ^ JJ»X '<. "i t**»*gXX;"^ taf jBWoilAl^nja t«V U4/JrttnSq^)^ Pldivip/i^' ;:/f T A' r^cv‘4;’ ^fiiiWW>T,Xh dd^xx ' ‘ XUZ u$ ,’x? ^'Xla KP'in^tc ; ^ A4iXe wc/iTiMrE oi*x *'‘^|/ ■6y r. I -«>B0XP p*7.&a j'ik ,t ■^ " im • ■ a . - . ’ y.f ■4t t jk, PXlXs c-dT ' ^ W ■^9qy*^ || fivt v'* ‘ ■. - . Vi-‘'"'i‘V ‘ ’’V ' ..^ '&jt‘t‘ ,j,\ , ' twv.c .-«f ♦,! ’ I 4 s^^^. ,■• ;.-v «^ h^. 9 X ! a show more clearly what took place, let A | I p and B in Fisure 5 represent tne two slits j \ : i; c through which the light passed. The light 1; f ■ p' which passes through A at any instant is ,| .Q in the same phase as that which passes | V f Figure 5. tnrough B at the same instant. Let the s * [> I light from tne two sources meet on the screen XY at the point P, i ; I and suppose that the distance BP which the light which passes ; through B has traveled, is longer than the other path Ap by half ; a wave length. Then these two wave trains will be in opposite | phase at the point P and will therefore interfere with each other, j Assuming that the light is of one single pure color, in other words, monochromatic or of a single wave length, there v/ill be a I I dark band on the screen which is parallel to the slits A and B and which passes tnrough the point P. Now consider the point C. It I lies upon a line which is half way between the slits A and B and which is perpendicular to the plane in which the slits lie. There- \ fore C is equidistant from A and B, and wave trains of light from t these slits will arrive at C in tne same phase, and there will be | 1 reinforcement so that there will be a bright band through this point. By similar reasoning, it can be shown that Lhere will be another dark band at P' which is on the opposite side of C from || P. Now let us consider two more wave trains passing out from A | i and B along tne paths AQ, and BQ, and let BQ be longer than AQ by a whole wave length, or what is the same thing, by an even number j of half wave lengths. Then at this point, the two wave trains will reinforce each other, and there will be a bright band passing through Q. By similar reasoning, it may be shown that there will IVli '■ ''•~;'*ih> * . .1 - c -* K * «J •.'■» <., ■ ■>. ■ -V , '.. '-.*1 ■ ■ “■-^■" v Ij:: •■'" ’ ■ '■ o«j »ftj -’i':r.i*<::e»i ^ iYiJai'? '■‘.m T !*)_ :J- .lii^'^«4(| vHv il^tn# 'Xvjju'c'jfir? - di viifl^ocx riisj^inn^ htn^^JSKi polAvr '' ' ' •'}>tttfi**q xiaiti»« ^jjnJ Gii tieiicta (iftjtje t»xu/ nl xiaiti»« ^jjnJ Gii 'oftue t»xu/ nl '4:^^ *5« ij‘ a^'w-intf 6 *uJ^ 4 [i . .*■ ’ '■ ■ . ':i . ;i^l' '5' ■ ’ S t .} ■'„ :j a.vlu'; iitli J-A vx AO ons i’0*tt '^A^JtX i ' '■ .>' ' ■ *♦ ■' I tv ii. 4«r.; a^^iiiW t?iisiX #jlx ..ai:,# tfr o^iuiXufi >»A^ *j^u^ »' X- ^ TlMtiTO VA- RiSA*’ l-ijinoi hi -ta Agi#^ I h' at oq Ixlw Artin*t.^ «.V,n»» i.jJ nh£» if^o ;!ut^ iiii¥ at itln;i);uB *: /liirAii -iAl .tij ^ iU. .noico' f-mti al^ni-, tnu to oX MnJ gnJtoli&AiH ' ® . '• '.'i'*i| '". '*■> ' ^4 ifv ,t>;3nu»x ivA*» oi .ftXh w ic *%o q^l^AiotTiojonoc ^ U 'tifU\ A Oij^iJCo »al cJ t'U/^'UKl i^..' tioltfih ;;=>PtqjB #jAiA bfJ£i^jPt^£> | • _ .. 7, . . ‘ ‘ ' ’■ “''®' * ' >9 VoPi rnioq Am-o^nt Aoeri^fj a^tiiAm ttu^ * g tae A' 0Ai iu> -#^OsX x**f “iXrA oX »xio4ji*^aV^^ - ••: q-; »(fi Aaiiiw Ai orfCT oJ* aX Abiil»f ,C*fl 'to htx» biTG 4 inonct qaxutelA/jpO' "•Co :^iyrstiTis;f r,!,, . ,..o4rf(i. oujji© «x o 3. avZn^ lit# ' I* ■'■ ^ i, .tia; H3ii/tjbu 6 Ad XXli»' ca^ - Ad ilXir i»yt0fi4* ' moUii' ^.4; jjt laXl^vla .ifliAq-s ‘ ' V *■ , ' A ' isoit D 1<3 iusi's ri>j,xecQqo 'o.ti a£ %£*hS iof.^ ' , • fhmu A4$l't%i\i mi CXl^'4:ftA 40A& c*o‘fSlAlc?x ' ■ . . , J -■ * ^ . u '< ■ , .I'llw ; o.^«fx.r .t Aiiv" aw©4b Od , XA/ri ' \ 0' .il^C'iA^’ . , .'•C >■.. lik ( ' ' ...L ‘ ■ ■ >*> '<'2^1? ■A-,- ■•^' ♦ .* • * ' V ... .. -- .4^r* I'k.r.v^.*^ I. 4 >'|I|>K#j iiki ^rv -fJ.A;iii - 10 - also be a bright band on the opposite side of C at . Thus we 1 will have alternate bands of interference and reinforcement on the screen, and the field will resemble the illustration in ^ Figure 6. These alternate bright and dark bands are called interference i fringes. This phenomenon may perhaps be made somewhat clearer by i I studying the geometry of Figure 7. Let p be a point on x,he screen j p such that the distance AP % I is n half wave lengths greatH ^ er than the distance BP, or j if 1 = the wave length, AP - BP = nj (2) Let the distance MP = x, and let OM = a. Then with P as the cen- ter and with PB as the radius, draw the arc BC . Since in the ac- tual experiment, the slits A ana B are very close Logeuher com- I pared to the distance PB, the arc BC will be approximately a straight line perpendicular to OP. Now AB is perpendicular to OM, so that we have two angles ABC and MOP, which are equal, because the sides of one are perpendicular to the corresponding sides of the other. Since these angles are equal, the two right triangles ABC and MOP are similar to each other. Then we may say EM - AC = M OM “ BC AB since AB is very nearly equal to BC . Let AB = c. AC is the dif- ference between AP and BP which has been shown above in (2) to equal nl/2. Therefore ni EM or ^ ^ OM a c ra ll ll Figure 6 ( 4 ) , • ■ j ,^1 • • ^ » fej» . V J /5 0 'ie> Wjiriv f/^j;;^L:tio ouJ fto '&fWia aoj»iiiom>a<; ft nd ? **■< - V.. ^ tajijaM w¥^i* lif^ti n >"i * * 1 '- , W ' v*»i*4r'-frii4 ,X*u«4iB ao» 5oX5f24 ?^affX2P :^fl4o j i^a X^ .iajUc aoe-v jpnA 3^ :? '■ ' ■* >“ a^sf-sf '. -i"')^' ''2'A : 3;A v-tAj ittaiUi xX^wn vat^v* Isi ?^A ©orda ' ' ^ fl ' ' I , tX ({w/r tu '>V9wi^ ili«/';*da liti^i uAfi U'aiavfr A^/Mta9bVft»pwJ^a;\*rma*ti a»¥& 4 ,i / ; T. " i-:i® .j ^ ^Jep 5 S|^lbi.:saaiKyki^^ 7 - Xi ^ ^ .^' ,/■ ■ >*»«■ Jm a : i -»' ■ f^ifti la *t© 4 T . pa TtX:. - n - and rrom equation (4), I X = f.ni (5) I This equation gives the distance x which any fringe may be from the point M on the screen which lies on the perpendicular bisec- ! tor of AB. Now suppose that in equation (5) n = 0. Then the whole | j right hand side of the equation is equal to zero or x = 0. This \ \ means that the difference in length of the paths AP and BP has j I become zero, auid the point P will now coincide with M. Light waves s I coming from the two sources A and B will therefore be in the same phase when they meet at M, and there will be a bright fringe or band on the screen passing through M. This is called tne central fringe. We have already seen that when the difference in path of the two wave trains is equal to an odd number of half wave lengths, that the waves will be in opposite phase and will therefore cause a dark fringe. Therefore when n in (5) is an odd number, x will be the distance of the nth fringe from the central fringe, and this fringe will be dark. Likewise, if n is an even number, x will be the distance of a bright fringe from the central fringe, and I it will be n fringes from the central one counting both bright and dark fringes. This reasoning holds good for light of a single wave length. Suppose that we have white light, which is made up of the various colors of the rainbow, or more correctly, the spectrum. I From equation (5), it is seen that the distance x is proportional to the wave length 1. Let n be an even number so that P (Fig. 7) will be a bright fringe. Now the wave length of red ll^t is much longer than that of violet light. If we substitute the wave length of red light for 1 in (5), it is seen that the distance x rr»^a n CcJ 9j A ,(,i>( aoniTW' . 'MJm ' 4 ^ 4 | ^ ^ P’ I ::XXAa it ILtitT .y fe*:n.*tOn!s ©rt 4 Xhwu .0 £»J^’r r*» *#ofiaf<«iiXO v4.T oojiiig »J^X«OPiqo hX ©^4 XIX# raw ©rftf i,lx'» % ^ jmSfuifij tfttn JU& ai (^} i4{ n ‘.»*i6io'twjdlT ^ '.i^! .) Mil , X>i’t4in;.o 6,14 ito-*! «^nX«iT il4n ©/U lo ©;;tt 04 «Xb J®4 ©U . . _r 'a ■ • ' ,‘-t;ta|iii n#^ na ax n il ,eaxw« ilJL «4 ©Xii4 ^j, ,«»54nXnl Xi 0 'i 4 aw 6 viix aoii t.HqXnX xc^X’icJ a lo wx^oa^tX)^ *44 ©U I * -.^ , 4ii^*S 4 i*4te4 ^lfX4i©i0p otKO X^'i4r(90 /l^#Ci llXivr,,4X to 4 iijjxx '^f /1 ioojj nbloti T^Inati^'K f^taJ 3 lVo£> fj/wv ^fk ■■• Xi r- ^ V‘ iln^'-j, ,, rr t'f-. ' •’mw tU&O Ic Xli/ 'fC/vl -ii rfoidw 94illw STAil ©a JWiti 0«0<||l|ii€ . ^*X 400 X4*ioq6*l^ it \ »4t 4a, 14 n»pe'^«i »($ : 6oX4aup» roi^ bt netjcuirt n*vo tm h4 tt 4©J .X riJjgirtdX nV6# W-4 oJ^ M'jvti. si . ^ r-. Ic <4a^wr ©vew *^14 wo’b ,0)5flXMt XiiaXid o eb. XIXw . wvtif ©{14 fy4*)4i4»uat; e%- IX .J/ifiXX 4*^iciv lo, 4Ait4 A»(i4 W^bX' ^ t»’£.. t eor^4uK> d04 4art4 n&,*w 4 i #?; #^er“f4^XX. Xmi*S v.^ !L j.,. V, “*. '. .I'ti, ■ V- , ii (r«> f 12 will be greater Lhan it would be if the shorter wave length of violet light were substituted for 1. Hence the fringe will vary in color from the red to the violet of the spectrum, and the violet edge of the fringe will be nearer to the central fringe than the red edge, because the violet wave length is shorter. Therefore for white light, instead of having bright and dark fringes as in the case of monochromatic lighL, we have rainbow colored fringes sep- arated by dark spaces, the inner edge of each fringe being violet and the outer edge being red. The other colors of x.he spectrum whose wave lengths lie between those of the red and violet will also be seen in the fringe, each merging gradually into the other. The explanation of Young's simple experiment here has been dwelt upon at some length, because it furnishes a foundation for understanding other applications of the principle of interf erence . It should be noted from this explanation that in order to produce interf erence, there should be two sources of homogeneous light, the lighL proceeding from each source in exactly uhe same phase. The slits A and B in Figure 4 are considered as sources, so the light which falls upon A and B must come from the same primary source, such as S, so that the waves proceeding from A and B may be exactly alike at any given instant. It should be mentioned here that Grimaldi tried this same experiment about 150 years before the time of Young. He made the mistake of allowing the light to fall directly upon the slits A and B without first passing it through the slit S. Hence the light which passed through A and B was not homogeneous, and he failed to observe true interference of light. In adaition to having homogeneous light, there must also be a difference in path of any two wave trains passing from lo iroa ftXpow;il tu:.iU ' Ill's \f - --I TSi \*t£Y XX4« i^ij yoiisfH ,X to':^ pcijjXtji4)Ciu« oiat? J^Xcfv ' ■ ■ - ■ > '.^ ^ stiialv tuA ,rtui*jJO!f}qu tu?'^'dX ort4’ T wic'c t.z'J v v.rij lA«Ta3irXHiii \fa^ix ,#^Xcrn ►o t9*x9Xo9 9Q(SniM^ gvaX ®w .•XASJ^'C sI imo^Mbn'ok' )r#^X©XV a^/iXi'X- ^vrinX, Xti& \d £oi.*idia((a r>.ij Xo anoXoo ''H’T ,|so^( ^AJtt d Sii^ iifift XaXoX? hua btf'i f\i 4 J, \o 39on} l xXi*i.ih»»T^ ; ' Joao »4X xtX rraa® iat-i»TjX'^ •£qjT‘.i.R a ‘ nc'^ tivlXnlirux}-. n ^ ' .X*iv ^oj:u‘isl’i«^flX lo •XqXodX^iq ‘to?B/it/a«oXii3aJio^/©4 £>JL43<>i4i , - ■•’ ‘ n ' , .,JA3lX •ii>ct*A»^oiaofil :t» a«o*tvott owcr oct Ixfiioiia aiBiiif h ir if eau Jt^X ito^c^' xi£4*f wo*a* ^JlLf>o*2q ‘tfiil^XX I ' ’ ' E ' ^ tf. .Bayxuoti a* tanwliXaAt^ &te ^ n-ii'in ^iX ^ fjfijii A aaiXt- li/iAatT^i t^tLvaa 9:\s iwo’Xl «ao» JKijBi a f^iiA A noqu 43l/iw tfilgXX 4h , « ^ drwi X nc*il sjnXbaBOoiq *ft*jVi'4 «n» aj» Actuu 64 jilitoiih dl ifayl^' ia \i >3 oZk^ >■ . y ^ j •« k * • ' \ 'y*- • ^ . . ,«1G -04 , 6*tO#.x Miicur XmMl*r6 ,X6 ^ftlftrt'*«X40f ifirjaioX-xO t : rfs ^*ti\,li *44 jffXw^X^^ '5 t 4 yjialala 6 iI> 1 BlUata *H .3£ii;o2 icr^ ^ K M 'i' I ncm '{.X*to^4Xi> xx^t *i wttT.tl »liiou4Iw a brw3 a¥ixa.*»^ noqiJ i ■^V> a^c^JiS AaXxUf Aii^tl oon«H ,-3 Jila <^41 ‘ | ^ aocB-^a^fsa^n/, »vn«a^o oi fevX-XJ»1‘ orf; xoa,4aw H ( ' ' ." . ■* ''i'V: ^ We ,cii5XX o^<*»nos«i]»CA ^;AXva*t oJ‘ jsciXiXj;^ nJ A-ffi^XX IcrT ■■S. C' fxin% s9Ai66iv4 eniani owi bX ad^ofcxA '^ ■ ■ ' . '.. . ■ , ,T. ■ ■ .'fT 13 A and B to a point P equal to an even number of half wave lengths for a bright, fringe or to an oda number of half wave lengths for a dark fringe. These are the conditions necessary for Interference Besiaes Sir Thomas Young, the other great physicist whose name is most intimately connected with the principle of interfer- ence in its early development is Fresnel, a Frenchman. Fresnel produced interference fringes in several different ways, two of p which will be ex- plainea here. In the first method described here, he used two plane mir- rors inclined to each other at an angle of nearly E. Figure 3 . 18o degrees, so that they almost lay in the same plane as shown in Figure 8. ON and OM are the two mirrors. S is a source of light in tne form of a narrow slit which is parallel to the dividing line between the two mirrors. The light from S which strikes ON is reflected toward the screen PQ as if it originated at the point B which is really the reflected image of the luminous slit in the mirror ON. Light which strikes OM is also reflected to the screen PQ as if it originated at the point A which is the reflected image of the slit in the mirroi’ OM. It is seen that the light from the two virtual sources A and B, overlaps in the shaded por- tion just the same as the light overlapped from the two slits A and B in Young's experiment. (Fig. 4). Therefore the area DE of the screen covered by these overlapping fields of light will be ^^^>x^’*^^■ vViTi iXiMl 1c. 'rt'Uta.X -noyw fwB o4 Xiitp* ^ jAi<*u h ‘ oi:' E X)ft4 A fc ^■.- : - - - ^ ., ■ ; “' ■■(«? ■' /'■ ■ ft X 1X^4 16’ *TO%ii5ii#£r j5-i»o lie Ow ^o ifw *ic1 ^ >oo'5'3Vi©4.fv.l *icy unoXu H/Hjoii ceoxlT . C'3 w f io Blqionnq »/L^ lU tn ‘fcajoortpeo J»,o« al /*/* . « , ieXJi toTt, • i 5^£'^c»o h^l rl e6/to | i i# X^'ncvAa ft JS>fepi/£fC'n(i { '•ic* >e> . Xx» vOJt»^ .' cl .070»J t’CtiJOil J#utl HlJ Jj2 <>;:/' Xt^ CMf.» Loci/ C>««2tl 'wti c'lfc'i ri- *:, *n>‘/jjK- doje'o . tX/u/Or 1o oXi^iwf *s n' > . Vy Vr--.. iL‘J;\SJ:^ 'i { '< / - » o ♦ * s .e 0'y/;Sjiiy , ^ -*■7 . ' -T- itoLiJi: r,r. ♦fuilQ Oo^u /jX ytaJ 4 jm1X cb p&f / WiiO^ z’ M a owj y,ie kc^Aius k,o '?v'vo-Ti.'ai:5.; ^ ^•.X*^XvXL r^iii r.oXillr S%lh (torj^iiin 6ju.r 15c- Ji\^X ,0'xcmiCi 6 Fv e4.?’fe^"pfd:®«f*o1U'X ,j ‘P'Z ^tim J:. ‘*'/ '-j'^ bii fToO^OIT .-lU I»:r6f»n^4 i^-liuvX /a jii. ai^cnlAJii ouJ It wa»«l' XXiftT fX'^dtxiiw'e ^ivr’^ -Mot»Xlin,.ceXii «X m :|njfe nOjfilw ,WO* 'ttvnxw il I* p . ' ' - ^, , ■ , ” ._,* >':• / ^/«J^(| i»iiJ J«5 li.rfeji iif,,. yisJ v/f..f ‘iti .iiO ao'iTiiTi irX ^o^oa^ai^ j T‘.v •f.a* ^sx* Wr,Mi>rey<3 V Ji^fup 00 'iiwxX i ■ ■ #, ■ pv; ‘ (j • C?f^ 9/ ■ ,vi. lii^vjiUievo aiijiiJ. Oa;^* 1 aC. .', ^•iji eta ••lOiieui .{>■ .-)i-'.)' .tmiU’ijKxxp a'SroiV aiG taUv-l »<- tXlr^Jfl^il aa»il Stuqqa?. ■•5; . vA/,, j, ■ . _:A‘ -* ; ’'-3 14 crossed by interference fringes. In this, as in Young's experiment, we have two sources of light A and B, and we know that the light waves proceeding from these two sources at any given instant are in the same phase, because the sources are images of the real ! source of homogeneous lignt. Various points on tne screen between | D and E are at different distances from A and B, so that at some s I points, bright fringes will appear while at others, there will be \ I dark bands. \ i I Fresnel produced interference in another manner by means of what has since been known as the Fresnel Bi-prism. The bi-prism | is illustrated in Figure 9. It consists of two glass prisms ^ placed together base to base at E. The angles at C and D are very small so ^ that the angle at E is very nearly a straight angle . a Figure 9. Light from a slit S falls upon the back of tne two prisms. That which falls upon the upper prism is refracted downward and proceeds to the screen PQ as if coming from a source Si . That which passes through the j lower prism is refracted upward and proceeds to the screen as if coming from a source 3z . It is seen lihat the diverging beams from these two virtual sources overlap each other as sho?/n in the shad- ed area of the figure, and where these overlapping beams strike the screen, fringes will be formed. These two methods of Fresnel were an advance over Young's experiment, because they provided two sources of light very close together without the aid of any vaHsrs -V c:-4f*r t ' ’..HHbH 6it: .,fr..s .t;u, «■» >•.» ,,„ W A to ftowKoa cwi'::Vv«rt"?K, .j \ ■ ‘. V • • ”■ ■’ '' ' . ■'' Cf ^ f^yli fc^lWi.r,. BC'X'S SAXHjIK' fi&VJtw ' X^tn i>4J lo Nsit'3fca:i aeijwi^ turf no*' ajToX'uV . f 05 ^X 1 -«Aaj|/i®aoLoil; * • •ijoo j£ aiinj c« ,£ 6oa 1 nciT ja v^ia 3 Ot ’ .■ - li. ' *' ••^•xl^ ^QnOfijc J4„fiili4t lAfacuB xxit» a9ar>l*)l ma , efcdAil ' ^ p,, ta4 £>ga ^rCAwtii^ bBJoA*i*tn*% aX. «^Xw ^OwcX ... ■ ,. J. ..... ,.L .. ... . - 'JtV . r* t .. . ' . - ' ', . i' ^ ^ >, J tiL jafoiia £k *»A-nX0*^ei/aa4y dnl^ I &siiJ6 saaea iia'.■ a' '■* :/<- . ,■* ' */' ^ '^1 . L, 11^-;-, *ii e-*yiibeti ' \iin6xj|{i)Xd:ih.oa ffirf- bk;f*VTi«»cy **'^*‘' *^ ^X14^JLU' j&xyWQrib 'i^'rfi '- J h« -J' ' _-■ ■■»‘:,,’j||j|. * ■' ■' . 4^; ■ . . .Si .U/-1J. i*4U. J I, f L«ni«^dc ! t ' li ' 1 ,f V ^ !- HI BtiiovpC'Tq t( Hi0i*a . Ji to » i/jb «g tjftjii .rilXcua ,«ftaMXp5 S>x<>X.J ,?%<5 «Jf «^fc * IT> nj* mro/DL ftfi bti4/%ai i f ■ J I *. V a ' • ''X,^ ' X/’K oiaiTis Im* airr oe a t . : ' ^ IX&i^ .• vi>" ■ •>" ■ — • ,K, A^-*, 4? ;« . ■ — -* V-~4. f OT- ^ .JjiiaXii . ' c t .'*^ )■' ' . L I’ , ‘ *.' ;' ' ' . ^ ^ , eilJ Ac^u Xl»l- W jj>»wcii« j' I ?•' «it^t.n._id»Av Bi,Mor.t.t,J!a;nf 1c sx^ wA* , o •: 'V';>' ’*%lj li A 16 IV. Interference By Thin Filins. j We shall now take up briefly a study of the colors produced \ by very thin films, these colors being formed by Interference of | f light waves. The following experiment will aid in understanding i this phenomenon. Take two pieces of ! optically plane glass which have been carefully cleaned and are free^from dust, and both of which are one or | # two inches wide and four or five in- ches long. Lay one piece on the oth- er and clamp them together loosely at one end. Between the tv/o plates at the opposite end, place a single silk fiber or a bit of tissue paper, and pressthe two plates together firmly. (Pig. 11). Then we have a very thin wedge of air between the two plates. The figure is very much magnified in order to show the principle more clearly. It is seen that the air wedge widens at a constant rate from the top to the bottom. Let S be a source of monochromatic light such as I a sodium flame. Light proceeding from this source will strike the j s glass and some of it will pass clear through both plates, while i some of it will be reflected from each of the four surfaces. In this experiment we are concerned only with the light which is re- flected from the two inner surfaces, AB and AC. Hence there will be two wave trains of light superposed upon one another which are reflected from AB and AC in the direction OP. Now from an inspec- tion of the figure, it is seen that the wave train which is re- I Figure 1 1 . ,’i'T •-s^ ,isiiEap5i^*|i^ ' '*' .-^ ■'■*' ■ ' ,’ *' ■•■.<-‘^- , ,r , >-j t^!>i>Ui,l Btolcft t ' ’«■ .j^ilTaliii u* vt; RI , j iT r ', <^, '■ »«d »V '. i.cri/lw «Lft*Xn x^X>.t)ixrqc nojs / '■Ai-Wo \:tj.iui^i<^6 ^ no «ntt fia.fjxw 'lo riJc4 Tcaoi iw txfal-v oii*iVA/a CW4 r-'\aci., fto •OOi<5 tlio .31K5I RSito ,jcJ titniJ iilheXo fiiir- »r£t ^ cifj afl.’ .|X-eitv^ ,l|S,, ^OJlJrf tg #; nc 4XXW ^ - *»X4iXq ofcjj <»i'W ifiofjQ bnix .,m .. V'.'-F.iu , . X X. «s/ fa/if . efii /!«»/;}•« cl *:X4 ovn.i b« .xiX*?) .i^n ^ ■ . ' ^ ," , ,. ^ t , * .V T.", ' ' V ' x: ■■ oXnXonX'iq firc.*ii« Of ,:Wf>fjo T • • ■.*'^ A i *' "^i~»ii.ioiu. W c 8*^;i ,CA | f ’ * . . * i,-».» ■ ' ' '• *■ ' ' ,'■ '*J J'y ''-' * Gf tiXdi "il .a#* ihonl si /i6 nXjRt# i, at &nimJi avfe* c,9f^ ^:Um c^t,&G;^iotif^ hi sUst« i>o ^ ,it»i5.vn*i! iiitr rtO aXfilq aiiX, s««i*tDiro J ^ ‘f ra rtoi/a ei aalJJ'iX »*7t‘,1» aWI? afUlio -ris-iio ni Er ;. ;■ ■.■■'■^ ■• - .' " ' ' -lad i bfw ,'xr»4i^o dOiSt' eoaclrrlaa iXiw ;8RAdt^ ., I * A ■ -A , |.y-» •i'd! *Cn:C iih KCp.^ 3itj Ct. wl 1 « *J 1 W - ' t ’ •< • I ■Twaiw^fca* II ®« vioiuft «>a©rtiJ ,,a’9^o ;i.oi^» /ujElw aae^i^a-Xzji 'leaj^x: fete fii6 a« ^ XM wjiX fttvldad e/to 1^!^ ^ ►•■».»• ' ' -A ^ V, , ■, irVfcW ‘tifld G Bt &AJ! ' ^ -tic vnu 4.Sj&woad4 adJ *» r •• -6'i aol f iXiafl *ic ‘iftyriud 5|io fi# a6''4tfAftc*l ; » 1 . ■ , ,,A ’ jflT ■ P* ** T . ' ‘i?' «fd &XUC 4 JU aOfQ tA4t eijliot tffiJ dfiitc'uu* stfiAJiuXA-axU ,JnBaQWsctAi vv i?a ;2 ,adJi,A3l Hi5U id eX »la^ lo c«Xi&d<{<},0 , >IX jujij rm<;rcl ,1X6 j« ,i dX JT .^8J^XsXq]C8 plaits oX pik" ». •iX’UA ,<^iqjtAXd •ic.'j; aXu ,Cii:X,.en ns^vi^. ^4 »i»ov4i?'?" ' itX M ,»ie^£;a doua ^^lJXbop: ^xioeXlaai aoaoej^^t' ■ y ' •. ■ , .ii-H’"'* ‘T,’- ■ ^ ' d "'’ ■c -V >^4t>ao * ,»X iGht tol'i'^ ‘^Xi>it ,d to i.ii [a.i.v XX 4 w S t .^taeV 4oXv l./ra • bj? ®cf xrxii(’' n I ' n ^ ' J,. dpm Xvr.fj £'«wPCp*:'vj ItfiA aX4 wd«3 jl^podJ t»cXH 4 ,taXfe oac , . xdq nl 4‘4in3iiy cXdP aotiDa Jen IXIw JX' ,»jjX** aa. doua taitlbBti *£'t*iG's. ^ " v» »■-.'. .1 v Y . - . ,' B1 wcH ,kf' LXJ^ tXfi7 ,ii~XQa^Jl 0VHw 'G Xo 61 (n :,^My f JfrXoq'^dd -fc^j i p^5d4>£ evgft^ 0.' i»^^i I'-fcfrip^xxb'S fUAa-t .„ ity^av ; iJiuE - »0A lao'jt ^iW6Maj'lpa''itXaAJ u ■ tvl •SOaan i\X ■Jij ■ I - 18 - glass which it has Just passed thro\igh and therefore suffers no change in phase. The other wave train has been reflected from a glass surface after passing through the air wedge, so that it has undergone a change in phase of half a period. This change added to that produced by the thickness of the air wedge retards this wave train one whole wave length behind the other one, so that they both emerge from the plate in the same phase and reinforce each other. Now consider a point N (Figure 11) farther down the air wedge where the thickness througii the wedge and back is one whole wave length. Then one wave train will be retarded behind the other by a wave length, but as in the case above, it will also undergo a change of phase of half a period so that it will emerge from the glass one and one half wave lengths behind the first wave train and will thus Interfere with it because it is in op- posite phase. Therefore, we must conclude that where a dark band is seen across the plate that the distance through the wedge and back is at least one wave length or an even number of half wave lengths. Likewise, where a bright band is seen, the distance through the wedge and back will be at least a half wave length or an odd number of half wave lengths. When the light falls perpen- dicularly upon the first plate, the distance through the air wedge may be expressed as d = n«^*l (6) For light which does not fall perpendicularly upon the plate, the above equation is only approximately true. In such a case, the accurate expression Involves a trigonometric function of the angle of Incidence. Equation (6) gives the distance which the wave train travels in passing through the air^ wedge and back again. Clearly then, the thickness t of the wedge is one half 7-’^ i ^ 0*^ f •., '' ^> i iv jjl^: t'p hm r j^> ^Aiiv7 niM PiU ' •t> A;.\^ilil .(><;X*xpq «} Hoii la,,.«»^£Ui( rjX «^i:^rfi» w’ »iit*j^oJ!>m; 0.^ , M/jo *iteuuij pjx 4 j>/v^ioc /l^l^^ji; wv^ir tSotiir ^Jlo ' . i •'■•• •' & i ^,^ic.l;,.>f> v(v t.f.*ik, •»» 'a',w «/ VfAtn fcis toni J«#,^iis ■ '." ■ *«* "•«'» •‘®“-‘-“* «'WS11>'W5W-«i''l'' ■.Sf.'jftWO •»« .WovdOIM. ’^ Uf«. -«i Hosu b,m Sij>(«« *aj. ,/;ju.i6«lo t>lhbi.f,tM »«j"*nejw ,f .. x-»:^*4*-t «'/>v tout .if;s»»x- ,.voo^ <.n-:0 ttrtJ la- i.i JJJO >v*iW rif)(f ^ vt.'nn tijj iinXxiou ea^^x >uj. -.ti ni .;j XX X/ ffXlw e>» j'Uxxij «ijxix iijtn b^ a tn£ ;f»*»i •*im/ttkrMt ,«»«« , ,4 xn«cj (tiiax-id « ■ HtMi» ■ ; WxirojUrf*'; »i»i«|i»^ » } dJy»i.X' BViw ^ Jac».t 4r id Xix» jiaaw asU f' '***'‘’''* “•'^' fasix *aj r».!« ..*x;.tsnvV*v*w iXxili u'^ak^-oho'^i •< f . m . ^ . ' ■ . 'T ., _ |8;t ¥iix Aoci4,y.x*;Aij,ife' ‘ i- ■•>■ . , -IL,,?' ^ti#ligri<4X6 ,©4 /"xK J t " '■' *" t »,)*.' J M s. - ,6.Vlr, B% n«fiu, tX'iJ»Xi>»jXt<»q.»*q' X141,\3pn aooi. xioWi' Id^X nll ■vrtd ,*w.v «. xsix'.x «: ,w»« tx*«»4wi(w.^r^V^ •wwX’l c ficjjoflx^x oi'itfWtidicijxxij « aevXaynX; '•'/I, . scj.-ia ,*/j «0i^XS' W‘h>?t'i^'xwf.i.l . ^ ^ ••• .a.., W ■■■ I ^ . ■•.• J.lu‘;_l- .•.. i . . .. . .la-, .T ff'.^V. ■ '* • "4,f k-' « . vVi, .VC ‘'•' ■ 'f?. i ,*t.ii'Hl r-, , '*% .. ., ,. t t r > Ik of this distance or - 19 - t (7) In equation (7), 1 is the wave length, and when n is an even num- ber, the expression gives the thickness of the wedge at a point where interference takes place. When N is odd, t will be deter- mined ror a point where reinforcement takes place. Since the air wedge widens at a constant rate, it is evident that tnere will be a number of points between the top and the bottom of the wedge where interference and reinforcement will alternately take place, n for any particular fringe will be its number from the top of the wedge down counting both dark and bright fringes. Thus for the first, second, third, etc., bright fringes, n will be equal ^0 U 3, 5, etc., and for the first, second, third, etc., dark fringes, n will be equal to 0, 2, 4, 6, etc. This experiment is not very hard to perform, and the fringes may be easily seen with the naked eye if the eye is in such a position as to receive the light reflected from the plates. The experiment is very inter- esting and very instructive. It has been assumed thus far that in this experiment, light of only one color is used as tne light rrom the sodium flame. Suppose that white light is allowed to fall upon the plates. Then a series of rainbow colored fringes will be seen separated by dark bands or fringes. Let us consiaer one of the bright fringes for which n in equation (7) will be an odd number. Then for this particular fringe, n is a constant, and 1 is the only variable. The thickness t will therefore be proportional to 1. Since the fringe has width, it follows that t will be greater at the bot- tom edge of the fringe than at the top. Therefore the wave length iij't (t) X-' -d »■'. v<»^ cs . J iie>« fui 6s^4rfrt>/l» tuts ,AJ^it£ av«v «/ X. ,HT) r:(3diiwpe M i& ertJ^lo ^ntnjtiti^ s»vX^(ioXicfkjiclnl**i a Vn^w I «a Xii5T ^a^tivm ix’ xx*^ ^ri^xacca ^ ■ l ^ »li t ( F|-.J(fl ' ^ fc soijcd «na fjocr eAj'Tj^ewcjsa aXnl^.lo.^n««liwi5 jii 4 ^ Ij ^1l;iX‘ralAli»'t 5 aa 9 0P»^Via^ai'^»?9A« { f- If' '^- J K -L QCJ eHJ ao-n ^t^Kua.afi .’o a.Xjt» <,*nt,i n«XuoIi>j«(i, vnii\ol,n 1 I • * • . , , i*i> - ' fi I V Set tuxff .•»^X'(t «‘ilJ}J^a iM H'U't ‘Tt^ At^jr4J0S' cvcft XiUfi* .0 liX« ft Jifsi-i ,...,^ ,i.no3«*. . „ ■ W‘‘-:jV 'i-| ..oJb ,t>ttaj ,bnga«6 ,i«m »iU id inn ..Site ‘,i f* ' o* ‘.^Oi Jogstiiiqse sirtT . > ;< , ,■ . 6 i«» Xuup« ai iXlWH? 1184a tl.Viv 6d ataol^tl *nj .none., cx b4^: tfar ■•«W, •fi.8W- «4 t* «ol««c« . 4(*« e^a.«i, u n« WJ •S> ~ ,. ; *4 -' -•iicui ii JftOBi.j^ ax ‘X^Xoay;#Ac^^ j| >■' : '..C4 ooqK 0/ vWoXia bi Jaeil ^ \£C Xj ^o aaX-iaa ,.^iax-a JaiX'id.'anj le sop i* 0 X«itt.» BJI isj; ^>ll i*t '? £,tc ^ Xixa (TJ . neXJauf. aX «-riaiaw''5p!l''OrJ K\'- '*’“'’ ■''■ *■’ ^^wiWose'Kj' M •noto'jeftX XiX« x'/eaaftsfojiiji .01, J XXX»V ^4 II 1?^' 20 of tne light which is seen at the bottom edge of the fringe must be longer than that of the light at the top edge of the fringe. It will be observed that the lower edge of the fringe is red while I the upper edge is violet. This furnishes proof therefore that the I red end of the spectrum has longer wave length than the violet ? \ ^ I end. Another way of showing this is to Interpose a piece of red | 1 glass between the source of white light and the plates. Thus only t I red light will fall upon the plates and only red fringes will be seen with dark bands between each two. Tae number of fringes, both bright and dark, should be counted, and their distance apart should be observed. Now interppose a piece of blue or green glass between the source and the plates. Blue fringes will now be seen, I [ or green ones as the case may be, and it will be observed that | they are closer together, and that there are more of them than j for red light. This shows then, that the wave length of either the blue or the green light is shorter than that of the red. j With this simple piece of apparatus and by use of equation (7), the wave length of monochromatic light may be roughly ap- proximated. Let tne plates be illuminated with yellow light from a sodium flame. Count the nuxriber of fringes from the top to the bottom of the plates, both dark and bright ones. This will give n of equation (7). Then with a micrometer microscope, measure the | thickness of the base of one air wedge. This will be t. We may | substitute ohese observed values in tne equation and solve for 1, tne wave lengtn. Let us suppose txiat the number of fringes counted is 24, and that tne thickness of tne wedge was found to 1 be .0035 millimeter. Substituoing ohese values in equation ^7), 24 1 .0035 = =61 i we have ■ I-': ► t n liana »S(U-Jt siiif 1c « 3 Jie fttiJsti'tnj ii it»»« ti riaf.:w i • ti ,. -nt ■•ti ‘lyw «*♦ Jiliil »-li Sc iJMlj «W'.^t4acj£:' « j4kt^C\’J>a*x ' tf •;. , Vv .ch»r? x^,>avi^ dj'xW, inp^ei sin^ -Ueitr 6 jk* ,u«4»fi*.co‘'i«'6XiK:ite '10 ftjJia Uo ^o«iq *i ^ccq ji^nl' no'* ,'=-v«T^iao Sjti^ojS^ ova tu.xtr *XIJ fin* | !■ • t^fl LU> Ji liir «4 j rox.^ at#rl,r J;d fir.4 ^vjA'ixstiqs 'to •Xqjrjta hld^ riJX?^ h ^A« olfrx.ft.cn4t)cnoA lo xi^^eX ifiV ’, (^5, , ;J. i:oit Jfija£ woxxat; xtil* bai'anzowxxx 6ri »9ia.Cil »;Si iad .bstiaixi^:^ a . ip c.’ qoi (1C71 a^x^s tc -wdono brij imjoO ..BaX^ aiiXbi’k^’’*' £ iiiiJia r.rx pat dtod $itJ ,j,lo. «pi| bW" 11 .‘•dosapuia, i»-o».cioiB d >,ix» nPi? . coXitoW' sfeSi x^ *'>• . w -n-j- XXXw .t.yfH::*- »,,ou i'fed .nism>x Wdw^fii. Vx 'k? 1^‘i.cv S.VCX to* »:,fce aiiainfoXitt aifcp ■4 1 il ‘ ‘'* •••*' ai^iixiadne vsMvm^' " -. . • oHi'm ."m 21 1 = = ,000583 millimeter which is a fairly close value for t-he wave length of sodium light | considering the crudity of the apparatus. | Considerable space has been given to the explanation of this 1 simple piece of apparatus, because iu furnishes the explanation | !i to many phenomena which we see everyday. A very simple experiment | I! which any one can do is as follows: Take a. piece of wire and bend j it into a small loop with a handle at one side. Dip the wire into | a prepared soap solution, and on taking out, a soap film will be stretched across the wire loop. At first, the film will be of uni- form thickness throughout, but if held vertically, tne liquid in the film will run down to the base, so that the thickness of the film will increase toward tne bottom. Thus we have a wedge of the soap solution instead of a wedge of air, and light will be re- flected from both surfaces of Lhe film causing interference to take place. White light thus reflected will be seen as very beau- tiful colors varying from the red to the violet end of the spec- trum. As the liquid of the film is constantly draining to the bottom, the positions of the colors will be changing continuously wnich adds much to the beauty of the effect. As the top of the film gets thinner and. thinner, it will eventually become black. V/hen the black area appears, the film is so thin that it soon | breaks. In fact, it la so thin that the distance through it and back is practically zero, so that there is no retardation of one i wave train behind the other. But one wave train is reflected from a denser medium than that through which it has passed, so that it suffers a change of phase of half a period. The other wave train does not suffer this phase change, because it is.. ref lected from | auftiit ^c iu>Ao^X avrv ^r;j ‘ic.,. »>U«v\«6eiB xt3£8l " - ■'- • •/ * Vr ' - . . ’ .'(v^ - ' - , c^i,tfiuaiqxfc Mii c4 fxo04' ^XV4H •• «u..n ,5o«4¥^^ -^. »o i*4» ta^ll f.ii« ,n£i Ic o,'i6e«' « to 0-- owv:ol-u.i,a 3flX««*o *in *ivf -10 *-M*»c vn.v ».* f,..^, .4 .o4w^«'»sd* »d3^ nidd^oA B£ Ji, 3ott t*,- cd «£, d,«!(d > .-c-,;. bojWtB, w 'at.ni *v«r^ -Ji .-Odi, oa ^,b.ea«.,-t,»it 3/ l;ii| - 22 - a rarer medium. Hence the two wave trains are in opposite phase and therefore interfere with each other thus producing the dark region on uhe film. i Thus far, the fringes v/hich we have discussed which are pro- ' duced by thin films, have been straight fringes extending across i the fiela of the film. A very simple experiment will show frimges produced in the same way which are circular. Take a piece of clean ; plate glass and lay iz where light from the sky (not direct sun- | light) will be reflected from it. Lay a thin piece of glass such as a microscopic cover glass upon the plate and then press down upon the center of t,he cover glass with the point of a needle or a pin. A very slight pressure is all that is needed to produce circular colored fringes with the pin point as the common center of the circles. If there are slight irregularities in the surface of me glass, the fringes may nou be truly circular, but they will be closed curves. Sir Isaac Newton made a very complete study of such fringes, and they are therefore known as Newton's rings. He produced these rings by lay- ^ ing a convex lens, (Fig. 12) which had a very long radius of curvature, upon a plate of glass. The lens touched tne glass plate at the point I C. Now the lens diverges away from the plate at all points from the center out to the edge. Thus we have what might be termed a circular air wedge. The loci of all points on the curved surface of the lens, which are equidistant from the plate, are circles. Let light from a source S fall upon the plane side of the lens. Some of it will pass through and will be reflected at the point P Figure 1 2 . Tf -aSi ^ ■■; .- _ '--■: f >tliic,Qtjo sn ‘tniu-i i trvii« owjr“«/ii •wttu I* ■ V -- ■ '‘- 4i ol- artist) •ttJ :^±z»nPoti(i (^iiiU-^BtLSo t>rwi; ^ . .aillj txtj fuy 001^6'^ , siA ti^idw\U^uQUi>tkt.b »« 0tii ,‘ijsl mlt/iT *•5^ai^1 »,»rtt xXi* Jncmi-mix* A .aXtt'^rij.jo ointi .rij V.*U> 10 ei»la -.;loT .T4Xl>s-jJa M/I ilalitaK {.flf tguia *rU irjt' I/^jHAoi'i -mi tiunl»^icn) \ts um «pi^ fo^xx owdu ‘n x$i bm Ba^' 'i,mq 'Ji :.■ Adi-e ,^WiXa ipoxq nX/la a aon^ ^ Jae»ilu^ md IXi»^(4xi^^X iwofc n»At Daa ^ 4.taXq ndi rorj;^ M^.C2i ^•voo oioAoto*toX« iv «i> R ■ ^0 BiX^tfT to Jdiqci n:iw a««J5 *l/nVQO ?ihj *■ , jj "* -. . . ’'“ fluxi^C'tq oj ^96oor) :i J’AiU i'i:- n/ ^^MRa«^q, jri^lxn ^ v»*®T A’ J»*i“ rtOAJ*aoo buJ am va.’ ajtw Wi TUiriJOn^^ ito£;l%jr. ni «4 0iliiiiXw£i»^*il o*tu4^ tiJnXoq^ iooX, ©4^ . ttt'X.P'ii 4 .'u;: ,ei).Xq ■ oliiX',, #Ji4' lo '^ ,. .^m Ic oWb »n«£q «»ii4 Ao^^Xiii 4$ S^.JAi«s nm ijp?'0o4:i^o0 :iJ. *' X ' A - ■' nrrflriilllilllffaBia on the convex surface of the lens. Part of the light will also pass on to the plateand will be reflected at the point 0 of the plate. Both wave trains will be reflected in the direction OQ,, As in figure 11, one wave train will travel a, greater distance than the other, and if uhis distance is such as to cause the tv/o waves to emerge from the lens at L in opposite phase, they will interfere with each other thus causing darkness. Now there will be a large number of pairs of points as 0 and P for which uhe dis- tance between each pair will be the same, and xhese points will all lie in a circle about C as the center. Hence there will be a dark ring caused by interference at all these points. Let us con- sider two points further out on the lens and plate such as M and N. Here the distance bety/een M ana N will be such that the two wave trains will emerge from the plane surface of the lens at F in Lne same phase and will therefore reinforce each other. Like- wise, we will have a circle of such points about C as a center where reinforcement will take place so that there will be a bright circular fringe. From tne center out to the edge then, there will be a number of bright and dark circular fringes. At the center, where the lens touches the plate, there will be a dark spot. This corresponds to the dark area seen in the thinnest part of the soap film just before if breaks. The rings nearer the center will be wider fhan those nearer the edge. This is due to the fact that as we get farther away from the center, the thickness of the wedge increases at a more rapid rate so that the points where inter- ference and reinforcement take place are closer together tnus making the rings narrower. Since the wave length of light at the red end of the spectrum is longer than at the violet end, the distance between uhe lens and the plate which will produce rein- ttiA stl^« 6-4iJ \o ,«*;ir>iL6»ifT.lo »i;45l»j>}B:.icaVi3oo 1 ■ ,. ' . \ - , ■' ' - . ' lo c JsXc.: usT Jtf '^Dojoali^'t tia lliyr no *ji© tic i>©j^©j:ta*i wd IX tw zata'U nei^t^3 a iXiw tUA*i>Si eno ,ff oifj mi ahiiMt, ot aa iiaua (\i^»on»j«lb ^sin., ^-ladav " Ui* t^iii •JiM^qo al SM enSl «/«> oo^iWsiaae'bJ aoUw *x3 iIX» woM .eeanafTaJb ^inmio s^isUf anetiWnX 3^ -LZia ddw ild’X/iv ^ol ^ W!A 0 pja a^uXoQ ic lo -t*aau/Ct j «r.. a*?/tieq di^ajlj ihU dd iiooa nedn^sd . *’ Jr ikl /-a* ‘•'sarii aw?#H D dxicdA, aiu^la ax -xjc>i BZ' ^^,1 .a^nicq <>iiAdJ £Xx ja ■^d h^Hiti$o W K aa douQ .-^o suq zfHij-un 94iUod owj ^ Of * 4 *ia JadJ 4U 51?# Hi ^ at>ti4dEZJb 5a um.£ ait? la Aoa-'iua mnaXq a;W iia-a >^aia i4i:# i,i!l4^|Viilv#^ _ .iwiwo iioa^ lltru t>m »«Axlq a/SiAf — r- - *w*«a*.«*i »««xiq ©4^ ci •xa5xi»^£> ^ u j^cda aJnXoa Hotxfi to_eXando 4 >vari XXi#^^,;«axw .. ' i' *« 45 ;J.-s5Jn4 a «d iX4* evsdj oa •ewiXq «j.ax tXJ* Xnon»bio4«t'^^i,64)»-4; ,*wit» .•»flo ,n; oX «no l»Xn»b »iw Bciq ,««Biq4 ^ .rxesaut, -ni.T ‘.na^Xnl 'laXao'jia Aoisij tijJa. Wn«diiufji V fX^ .5dqa ii-iai. a’ei0 “3^ -Oval ono£» fcjciflq ^Ui*5«i.n5 x;a o5«^ f»ibcia*r*^^ ■ ]U ♦ ■ ' ** '■ i.. . '■ Si - fbifX a ’l,- “'■'“ ■^'•^‘' “»*•': ?•’?• »»«fX ?o4nX»-« 6,U[ ^ .'.JSi,«i^^9va» *|» «i«a wp- 3jadS.;. ' I, '' *ii) ,ir.a *s»^X oi , I‘V‘-. ' ■» , 24 forcement of red light waves must be greater than for violet waves. Therefore the outer edge of each ring will be red and the inner edge will be violet with the other colors of uhe spectrum blending from one to the other betv/een. It is Interesting to note the ef- fect of monochromatic light in producing Newton's rings. Red glass may be Interposed in the beam of light coming from the source, so j that only red rings will be seen. Then if the red glass is removed \ i and blue glass is interposed, blue rings will be seen which have | shrunk toward the center and are not as wide as the red rings. This is due to the snorter wave length of the blue light. The number of rings which can be seen using white light is very small compared to the number wnich may be seen when mono- chromatic light is used. This is due to tue fact that the red out- side edge of one fringe tends to overlap the blue or violet inner edge of ohe next fringe which produces indistinctness . This over- lapping increases as we come closer to the edge of the lens , and as a result, the outer rings disappear entirely. With monochro- matic light, this overlapping is impossible, so that more rings will be seen. In his study of these rings, Newton found that the radii of the different rings for a given angle of incidence were proportional to the square root of the numbers 1, 2, 3, 4, . Tnus the radius of the fourth ring is twice the radius of the first ring, and the radius of the ninth ring is three times the radius of the firsu ring. It should be emphasized that in all cases of interference produced by thin films, the character of the fringes varies greatly with the angle of incidence of the light falling upon the film and also with the index of refraction of the material of the film. Newton found the way in which the radii of the rings varied with the angle of incidence to a great degree V Y v o ^ 4 - - . ^ ’ n !.febvA» ft>iolv Tt/i i»xri> •tojtf^ng 6.w^«a n^£iJo.‘^<^L';o3 ara ionl b©S .»B/Un *» ‘«w>XaeJf 3nio^’5o»i£i nX\ Jd^.r f>x^isrncn4©0l|^ ^ *>6 ,»ont.o6 aaj muni BxUteeo jilsil nifir rJf fc©aoq;nc^nj: liu v/.w b»)Ycj}:»n ii«aanX» Wn arfi ix ^te/l!? .n#»i ^no Hiw asnXn ban ^Xco ouil^ »VA4 naaa ad IXXir e.oain auid ,baao.n*J^X al sciiXa ai/id'bfus? I ,e^Zn bdn •rfcf as eMw as jon ©ns bnr *i.©di;»o ©it!/ finsao^t tornxiu .Jix^xi acid «rfJ >0 rix^icwj’ ov w naXnoas' tirtfj fiX d/i^UX tairta ^rjlw, n»vs nrJ n/s& iStoJfjw t^l't Ic n^diwB ,^iiT t» -oacjfl najlff fnjoa ©d ualiiw n©aiR4/rf ej bci-aqaioa - iiu bin ©j\4 imij joai »aJ ej , mi Xii|ix nsnnx ^vi fy^no MiX:^ ,,u qsXifivb bi «bn©^ ©arrXnt #n^ib -%^C .acdii^onidblhFli ^aoxboncj HaXfiw djcan ifdy lo ^ , ‘inax ahj tto 03A9 dilJ OT ni»r;oXxi laod sw ts aofldaWx ^xxi^ -cniiooccs .^Xwnf.tiio n©»<|ei«aift a^VfX^'i nei«c adJ .dX^fftn s asr-X'i enoa’ 4urf;^ ca «6xixviac>v^llea t(i o6i/^»a ,f'-itJ^®£ »V4:af* tiJi aXitsuo" ■ ' '*' ^ ' » ' 1 JJ ■ .du^l ^rtO)i iiJ rt JitSvrf^irqyks jp;-^ (0 , , • ~ / vao ,Biru.(3 ,»bn«-i«-i»j«>,«,uft, ac XXaa art '.aaJuV « 'ao4w«8 S'-f'ig ir ^>taXq H3*iiO‘ulX »i ijoi/tw Iq !«!«•*», ' ? f -•>§X‘ifr-i lo #4 j 0l .tt*«»£U^5i0'n hf^4^oi'lki iu i£6 '^i t .aric'xx avAv otU.lo ^fjo iz^not^nMH . - -if j.A- ' BfciiiT'T ./ «fliaJi©4 *^ofl avoB .^* 1 ,; iicl-»c*i, 'Uii4i -lo i< •iwijj ,di;Aiq toA ?iu*i TTf-i WJiesvajwjf ai j/l cv». •ianxi* ox ^v.«ui 4< XfiSa-, *« .iwi’;,eM5a|Fx^C^M „ -»i ta n«»« al SOX’? JiX^Xoo - « 0 ('.,i« ,»no"!»'ix-riT ,t^ito'tlXfi'a^%^^ .bJltiX .ftajJXaarcrji' xsl bay-iasdo otl IU«\ anotaui*. a I A'ioXoo 6il^ cJ ^(S XXlw AQitin lo ' :li/w i^T aJri^XX !>®Xo«>XUn t<« .«7 b'« 6 aa«%'W ‘ ^ c;i4i ,i,no gCnUb .^lylo fxCo^BRi Xcq« v’d v>i •^x«„x ^XO aox IP'.Wa ..anox auj ra ad IXXi Wot'.Xa^CV a .. , ■ .p . : iT-% • ft xaoj U»**«iXu«.» oaxiiy W.Wia,W‘.B,.Xa oeJu^a^J oo,, " g-**,;.tU3X.X XadaaXtci b«ui ^a+tiwitw -^d ia.auao a{^-,Xrx »o «i-| A 1^0i> ®H . &*ti. ” - ; Ki^mOQ A fe/U \t) fcJoIq ^ fjw «rt»a trM» ^u-w*! ta a"3» j 'xo i» no X t xit »^illte'6B^4.;Uog;^XXl t-Uw^niJ \;p ^ 3i14 r;:c%'i J4ata , , .^ U":e^/a4t - 26 - opposite side, such as at point A, produced the rings by trans- mission. Since Lhese two systems or rings were complementary to each other, Arago predicted tnat uniform Illumination would re- sult ir the field were viewed by reflectea and transmitted light at the same olme. His predictions were fully verified by the ac- tual experiment. Nature produces for us many very beautiful color effects due to interference from thin films. One of the most common ex- amples is seen where there is a film of oil on the surface of water. Some of the light is reflected from the top surface of the oil film, while pan of ii. is reflected from the lower surface, or the surface of the water. The oil film varies in thickness from place to place, so that difierent colors are reinforced at differ- ent parts 01 the film. If a very small drop of oil is placed care- fully on the surface of very quiet water, it will spread out in the form of a circular film, being tnickest at the center and gradually getting thinner towards the edges. It will thus pro- duce Newton's rings quite perfectly. Usually however, the oil is distributed over the surface quite irregularly, so thax, there is no regularity of color arrangement. Another example of this type of interference is often seen upon the surface of highly polished steel which has been exposed to the air for a few days so that a thin film of oxide has been formed upon it. The light is reflected from the surface of tnw film and also from the surface of the steel underneath, so that Interference is produced. V. Colors Of Thick Plates. Brewster's Bands. Before taking up the theory of x-ne Interferometer, it will aid in understanding it to consider briefly interference produced v-i t»afc6o'i't ,A inix:<( «fi iioue tJttoqqo «'T •■aJTP OJ iiwn»v*£^ctJi on»- ajAin- 10 uneja^o c.»‘ o«#Kj tloote. .noiaalB ***t f-JwtK nOijariamXXl irto^inu J*uj fiatsib^iii oj)a art.- 4U uliia SIM anoi.i,lfco„^,»Xfi .4>iJ J ojoeno loxott Xjjlwa*^,» -toi Boouto-iq 1 »IW lo eM» ;•(«■» i Jiiiu ceil ooAonBlioiiU^M.Blii lo *o«iniB djW • fi n*^r; i/x /; B,prto Hi »aooi»l»oij-j lo "utx ajii,, i» il^xo -tadiortA- '^. DSSoqin oatii* laoja f,Sil*xXi>q ^XdSXrt lo JOalva irinnoqa , woo aiia ■>bXm io Bin lUsii e jAlj oa av»l> »«1 « nol il* bHj pi ‘ ^ . " A ' ' ' ' •ni t* *is.iiuo „ad con X.*jjoXln ai mU uc^U.aene l T" •* *' .1 ' Swifi to .dfddOftdbm loaiB eU4 lo aoBiiwa VnJ liool oaX«4n« nXil J ., - «■ ^■^' F A * ■ ’ ■ 1 I •■• ■'* - :■ . assail ioXdT„.J0 a/jcfioo UX" J1 .,H»4»aoi*»,.»iii »fl, lo viosdi sdj’qq anxjUS SooloB T’ »X*>^ isPiBcoe flJ i-'i nt tiia i ! ' .•' ' ,\d .:-Mrr» - 27 - by tnlck plates. Sir David Brewster first made a study of this phase of the subject of interference in 1815. He used a device, the essential parts of which are shown in Figure 14. It con- sisted of a straight tuoe which was blackened on the inside . Figure 14. One end of the tube was closed except for a small opening 0, through which light could be admit- ted. At the other end of the tube were placed two glass plates of equal thickness. The plates were placed very close together, and one plate A was set so as to be at right angles to the tube. The plate B was inclined at a small angle to A, This angle could be varied by means of a micrometer screw. When a beam of light passed through 0, by looking in at the other end of the tube, Brewster observed interference fringes. The explanation of these fringes is more easily seen by referring to Fig- ure 15. Light coming from the direction Shown by Lhe arrows passes through to the lower surface of the plate A, is re- flected back to the upper surface, and is again reflected downward passing out from A and directly through the plate B to ^he eye. A second wave train D passes di- rectly througii A on into B, is reflected from the lower surface of B to the upper surface, thence back again and out to Lhe eye. Now it is clear that if the two incident wave trains are in the same phase and are parallel to each other, and if both plates are parallel to each other and have the same thickness, then the length of path for both wave trains is exactly the same, and they arrive at the eye in exactly the same phase causing reinforcement. ■_4ir ^ ^ • V f u: •^&^S14* gr/it 1C ic ,4iofiiir r;, 4i^»ie<:'x«Jt^«ift«.:*9/w;/ rflCo 4X ,* r ni m>c?ta teru >' | f - - , ‘- / ri>JiS ». . . .v tIMU« i*tiit j a iQ>\fceJci'« ^ ^ * ' *’* . ■ ■ 1 ' .iJ-f/«oXs idiiu lo toft anCTr * ^ ! » ♦r' iS*V«- ❖a t>lu^x> it^Ll ifo/ilw n3i/t*xilJ ,Ct, ^rui^t^c A iwl 4&iyoxe -' 16 Be^u-lQ rn#i^ cw4 |j§oAi^v t dri4 t'lc> i>n» ertt^ ^‘A.-f.fce^ • tifiM 0 • , riC *• ■ • t. ^ il ■ , ’ • ' <^.' ' ‘. t' ■ iC .^<8i* •(« o# tktm i!!}-m • r » m • ,»43lc onb v'te «r^u: .;u >;¥■ .. * CJ ^ ^^^^,.'7'^T^l» '‘ r mJ\f fl ■■ ■- ■■ 1 UCi < XA^Xt Xo c 0 \l Mn/L^rta i^tf X>«i*tAV ‘ V,' ,tr(ix4 #^j lo Ib;*^ ^♦^^>0' 4ti rU ijtitru^^X \o ,0 - !J '■ *' *■• jfJ ‘ ‘ ^ ■ ’ 0- , S"5siH c4 ^ erw woil '3^n;rt,co 4T^ «'u P I'bx aiCo*:a*' ortu \u nacfta *•> V b '.' i . ^ l?t^ CX je>GC Ic 06al»Vjfr. aowbX -©rf^ " * ■r ^ '• • ^ : i>r»# mia &4 3i3iii/*in 40&xt ,e‘ etJ.'S'i’ i r'v-i ‘ •<■ i ■• ' '■■■ .., w'';'#i t . , » im bni cn4 adS# 7J5©ro aX 4/*wcTf ^ ©•ifi /iabRa 04 Xalinvia oof jbfw J ' /r ' ‘ * 1 ■ I ' ' ‘ * . ■ ' ' . • ^ '4# ' •' IC 1 ' '' •1 #. »' »fi4 r#:'fi.t , t’#«^AttiiA4 t$ti 3 &^xi t>'n^ 7Ci|40 rtoAa o‘4 .■ xXa ^it4 iJOil lit anl^ax «vjm c.^ob tot rtxac lo; ■ / ,-v ■ ■„(> ^ .'^ ' , ' •' . , ^ ', MX‘^***^ '^ 6/>/jrX gftxM - jni ©it! 4/i 9 * - 26 - But If the plate B is inclined to A at a small angle, the thick- ness of glass through which the wave trains pass in the plate B is slightly greater than in A. The path followed in tne reflec- tions between the surfaces for the wave train D is therefore a little greater than for the reflections of the wave train C in the plate A. Therefore, the wave train D is retarded behind C, and they are thus in a condition to produce interference. Between two ! such plates, there may be several different combinations of re- flected wave trains, all of which will produce Interference. Fig- B I 1 r. -I . . ure 16 shov/s a few of tne com- binations which may take place. In Figure 15, the wave trains pass between the two plates Figure 16 only once. In Figure 16, the two sets of wave trains, A and B, pass between the plates three times, while the sex, C passes between the plates five times. Each of these different combinations will produce a system of fringes, and if conditions are right, these different systems may be seen at the same time. Brewster’s bands may be very easily seen by setting up a simple apparatus such as is shown in Figure 17. Take two small plates of glass and lay them, one on top of tne other, on a dark surface. Prop up a piece of ground glass at one side of the plates and at an angle of about 45 degrees with the surface of the table. The ground glass diffuses the light which passes through it from a sodium flame. With the eye in the position indicated so as to see •rljr iX^tod .* .^»>^a «,j .uoniXoiii* uX 5 > u ■ •' '■ * ■ , 'ISf .1 ttl ^woX.Cc1 li^tq OfiT ,A iJ? fied^i *ic>^|ifi»x^ XX»fli^Xli' b1 If-' ® 16." A si-tl nXAH^. »>v^ ©if.? oetS^ni'ix ©iijr jr:|t6*rjr®o tirtci^ * ■ » ,v . - ^ •- u..i: ■ \ ST,. ^ _ ^ xil s? TtiauJ. 9ftJ X<-' ^ol„r»x(W' V . ’ - -> * ' ' ■ ' \ '^-^*1-.. ■ ■ ^ ‘ ■•‘f '-■ "■ ln>^ «U ii G r^XB^sJ av* < '‘?y , , A ct4i ©uiJj>onq' o.r ncLUhato » ni i©dJ '" * * .' ib*^( "f)*i lo uno^j^aiOcoo tatdvi^ «k4 a XIXX **o 4 i < Xx.r*‘ .aftijai',# ©vAr -fcO^ *J,*i 4 i: S«rC(>^ 4 lQ «iU hui*n4ic BMfe: ■ f r^. ,4100 ©.rt*l£ra BBiftXrj Wfjj AU«W.Jr ©#d _ . . .'1 ' ' .', . ^ ■’ jOcj io qo\/ nc tnoi^awkn./ Lt.i. Jl*iab li rto I » * Xii aaBlii frwc‘Ji} >0 ^o^XC a qi/ ^ JA tr^A ew»TfiXq * txx ©X^t'a^ano -* - -i2»- *’ ?•’ 'f\ Ji' .Tt ^.1 I0 tAOijl»iiie Bii^ iixisr cl^ diixjrfH lo ^i3f^^ nii^ A too*;* v?l« 4 iJ 5 i 4 ' 0 ‘{Xtf €«?coAf 0iW f^AB Od- oti oa,?js44JX<| , f*4i ^o/ti^i , t«iv**jk>& -to ^iiwic | ,jio/t6 CO B»nk44o 'w,0 10 jn-fw mgil rii-ht .jij Of„>o cj -tc'' eoo el««i najte ., Osarj tff ’’ ^ofiiwaxTot •>iiJ enfa,T»4;»i5 5X ittniaw/ Au4Arii 4I ^ Vcrlx^ 1 ^ - £> ^ cl> »4‘ . 'iv a #»dfl5^aiiA;a£t4 ;ioVi ■ ' . , 7 ' ' i r.iiit OiU) I ii;r 4 ..q*7'^ C e»n*? ,?0!T4lt et»iftp9 a \;a £>«XP.niiUwiXi noaij V. ' ■ ' '' ■ / ’’f** '-^ ^ m ftX inwaa -*f44X ^s,j; .rio^^a f'f ‘ *i«Xq 1^1 "i-Onicq, /£rf Jr<»j.x(j «8^.i .'•'X*.«t '"W 11 .4^ 1 ,,, '.v4 <>ilSf,.'^0 f>ffO oii S - 7a ♦>‘i/aJi84i. 4.i.jSic_!*'4fi3 YJSXaiCsw 7^,' 2Sl’ *'■'^**’^•1 ixiXi/olJTBq aiiij .tiiitO t>fii! -i^Owu * ^(jorae'uaio «jjjio aeaXg laom b : « «x?d Oeaili, oami, »f;o xjniji* lo, sjnioq xu'’i» aa't*4»^4;-''lo ila t .:■ .ft nuoO/ioo lo. icaosxtt. a ,!£i6doou ,a«9'n»olrtO''oBfiOai>«ov O.Brfb aS'WJT BOW, Xq •*4 ,;#:■ fti’.V - 30 - VI. The Michelson Interferometer. Some very accurate measurements have been and can be made by the simple methods of producing interference already described, but the instruments of greatest precision which are based upon the principle of interference are known as interferometers. The best known and most widely used interferometer is that devised by Professor A. A. Michelson of the University of Chicago. It was originally designed by him for use in a very famous experiment to determine the ether drag or drift, which he and Morley per- formed, an account of which was published in 1886. The most com- mon form of this in- Figure 18. strument is shown in Figure 18. Suppose that we have a source of monochromatic light S, say a sodium flame, passing through a lens L which renders the rays of light parallel. These rays strike a glass plate M at an angle of forty five degrees and are transmitted through it to the half silvered surface AB. Here half of the light is reflected to the mirror P which is heavily silvered on the front surface. This light is then reflected directly back to M and is transmitted through to the eye. The other half of the light passes through the half silver film to the mirror 0 which also reflects the light directly back to M where the half silvered film reflects it to the eye. Thus the eye receives wave trains which have passed over ^ , ■ ■ - T.i. ^ r I ^ ‘’V^ . . .,- ' . ' . ' :. - ti tU -5^t!>u MO ^r*ii‘ V^#v .tciorj -.v^'‘ 1 rL '■ " ’ ' B' ■• ,- .c . ' ' ^ ( ;■& ^ ,»»l.4'JVt..»0 tAi*-!!* *0fl«*3/|6jiii' a/ij(ol(,?,o^,I lo :«M^Wl.B^.•ix<^*i» «riJ * . ' * t* *' t tiolM tiOito|.0b*;i^ jQ&^ffo^3 lX.l3yr.crulot;xioii: lo ^9tns#i JB rt^jLioi/W ^ifiiiux odtf Anohnon ftDlilw aa ^ ■ s. rJ5 ;?-» It ajr-Xq daaXj^ tfiil, oaf j>^,.pi^j£ A AJ" ib lX«d «fiT oX* itaiq'ilitf . ., ■* if '■ ^ fifcXl ?iiw liXo^Xl^n Qa^ '/.olA¥f C ^i^<'Ufli^QA^l‘Cj fiXYl -it'vXXij' iXM^^it^i I fc. * r (1 At iJoon«^ jsan Xh»^bv;:x& ^0114, 'll oi J f *tevo i>e«3£q ^vAA,M^tUa!^9AJ,AnM<»v»w uavXo^e^ avo awrilt laviX ai<4 . "' i? : J.MWV « ' ~' - 31 - two different paths, one from M to P and back, the other from M to 0 and back. These paths will hereafter be designated as MPM and MOM. Prom the figure, it is seen that any ray of light from S which is reflected by the half silvered film up to P ana back again to the eye must pass through the glass plate M three dif- ferent times. Also any ray which passes through to 0 and back and is then reflected to the eye, passes through M only once. Hence the ray MPM passes through three times as much glass as the ray MOM, and this will mean a large aifference in the optical path of the two rays of light. To compensate for this, another plate of glass C, known as the compensator, is placed in the path of the ray from M to 0 and back. This plate is not silvered on either side, but it is cut from the same piece of worked glass that M is cut from, hence it has the same thickness. It is set on the sup- port in the same angle as M, so that the ray MOM travels through exactly the same thickness of glass as the ray MPM. The mirror P is rigidly mounted on a heavy steel slide which is made to slide along very accurately grouaid steel ways by means of a long screw having a pitch of one millimeter. To the end of this screw is attached a steel disk of four or five centimeters diameter, its edge being marked off into lOO equal divisions. Thus, when the screw has made one complete turn, the mirror P has moved either forward or backward a distance of one millimeter. By means of the graduations on the disk, the screw may be made to turn through ,0l of a turn thus moving the mirror .01 of a millimeter. The screw may be turned quite rapidly by a small crank at the ena. But in addition to uhls, there is attached to the screw as an axis a worm wheel in the teeth of which a worm screw can be en- gaged at will. By turning the worm screw by means of a milled « *v » 4 ’.rvfvrv » C w ii laon)^ »jtjo ,f.il^f,fj c-w^ \ ■gv ■ ' .,.■ c»4 - arilr/q /iLS*dt tsttnni. tiotda i*^ tn« ea/A' ’.««4 #& 4 cj#xl»-t «X %a*i ©4iJ‘ qmfrQ oT .drfaiX lo owJ 1 'Xd * ni :v»ofiiq si yanoqui^o ajij tss^ i:T»oml ,0 «a«X3, ■ -- ■ ' ' ‘ l^v; ■ ’ ro b^9vli* JCQ ^-4- iq aliif .ao#a ^ 0*o4 Ji'c'xl ^cl If 4*/xU un#X3 1c ©a »4q lijiv iic't'S 4||3 ei /j-1 jiltcI ,.®|yx& M3i;a 9ij4 AO ai 41 .©«»mtatx<4 0®^* aoao^i .woil^irwo I ,433 x;c*uW-. AX©v«n4 MOW -Xi^* ^9 ejj eaAa aii4 aX 4»ioq t *icqrUffl .'aJiM x^n. eijil ca4i.t, G«©nMo4iiJ 9jn£« oiid |l4^oMpco '1‘ ' ]»mXQ 04 cNtw ,ai itoixiw X«?*#4a flo bfi^mica Mi v.'^j£ffc sfloX m la auaaa, toayctjj X'^ay anolot ' ... f * ;-- ■ , ui »ri6© aiiU to dna 'bno oT ^'iaa-&j»iIiiiB. #no *^o >"aniVMi -f 4»4i .''fJt/iaiii tw^ -ao 'IKOI 1c Jiaii) ico4a 4 X)ftU0644^^ • *. ' * I ASH Bi?... ,i-iiat, .(UK'iatllu inuy^ cc ( crni.llf Jwj.'m ajXBO aj^», Tsajie tuvto «iw ^ non^i«. ejU tj^jqeoo *nc Silii .sica ftiJ To c."j>Oi!' \a .’tuiontl^ln »no Itf vowialM a bTowXoao ic*hta^a'i ^ ▼ B xmrj oj «^j«s no ba-um ©a '4 .itaiii' ^jioi'4^Vji'xa iiT .mvt. Jiiiaj u ic fiv. icni* «tfir gAivooi A'u;4 4^1ct io. ©fii ji. iibi 3 « ’a xtf xi.f>Xqfin o4iiip Jt>®n»a/4 ©o.x-a^^M'yoM lia Hfi w«»iOK oiij 04 ttX *^f»A4 , fillip o4 noid'i&X^ niT4i;X< **■ -O'. OC O..C ao-.o. m'o* A tfairt* it.^tUo*l adi nl X«,orf»* irtow A ai'A*' tBXX*n*B *0 >«d»rtj - 't*. rj<|U40*i4J a»n^j«ib exfj niit» .o'jcXwrt&dl .'x^JWfiiiii'X^. utw. ,i'^>ai>tTiXXXXcc^ (U tna ai**wXo gwerit^a m.T su, i^ ; .;,a««:. wcJ y:A«. •xaiaiMixtia -•rwifni lo ©q^J ttXaj ,ffot;tc>^ sroI 0 /i o^onj XailX c« ,/ioi^iX;.fioo Jnt*j;«»*ui%aeju 16 c.^nw,*o>*:AnX »^0JB'Wtl^ eJjilq Ii*oi^-xt>v vu. uoXaw Bn9n:>e^ W' -wJtj?tXia ni 9iij ^#3 iJtHfu a-Tii aworfoo a-a^rtT ;.1i feciilup •< V- jj , .. s' .i;»r»r JiT \;i»wf‘ ao^i*tt ©i»X o« Jri!»|ii , -*rcnati«xnX itoeXado/fi a^ixi i »rid ^--inPwoH aj nAiiiiUlamin^q txauotcax^ooa fl Xma G bwnle yau iibui w/i ialx» i»vix« es, floMi sSiWeifi »«** »«j aJoa i«a’l»djoliloJ“ j Sj ^icj li ll^Xa »i,i 0 (u«ia Ulw OJl nt »' Id #il>;^'’(JA intvl ,(Xiw 1« fcojp*x'i«i duX ,tjijisji>xfci!v«':4ec, Jt/i - dj 'diliMdi .XtoXd.U./ioo, « JjlUouiOKi »J/JW ^ xlji* ^^'bv ^ax Jui*. .X e-jds; ■: ,5^ <5^, uo *ddXio*«J>v*ai>9w -ixa, aa^ijla tXASJs*., j 0.1 »|u. x« o'rtd 14 -..oq-jtH,. tfd £Xiw <»dj jud latHi(i,yj:'xtni s»ai!iX-*,l ,JS*oj;iritef^ ■ ixiu.dXfcg>,q.tdq , Jdi*4v. Sdod,**,' ti li ii'ti '. .A pj - 33 - Again, if the two mirrors are unequal distances from AB, then the rays of ligho will converge from all points of tne mirrors as they come nearer the eye, and the paths of the different rays will therefore be of unequal lengths, ana there will be interf erence , this time in tne form of circular fringes. Thus we may see ver- tical, horizontal, or circular fringes depending upon the relative positions of the two mirrors 0 and P. Let us consider for a moment a particular bright fringe seen in the field. We know that for this fringe, the paths traveled by the two rays of light MOM and MPM are such that the rays reinforce each other. Now if the mirror P is moved forward a very small dis- tance, the length of the path I£PM has been so changed that tne wave train passing over it now interferes with Lne wave train passing over the path MOM, and we have a dark band where there was a brighL one before. But the bright fringe has not disappeared. It has simply moved across the field a snort distance. Thus, as the mirror P moves forward or backward, the fringes are seen to move across the field. If they are circular fringes, they will expand from the center if P is moving away from M, and will con- tract toward the center if P moves towards M. This fact is made use of in many experiments done with the interferometer some of which will now be described VII. Some Actual Experiments Using The Interferometer. A few experiments as actually performed with the interfer- ometer will be described here. 1 . Adjustment of the interferometer: In the more common ex- periments performed with the Michelson instrument, a sodium flame is generally used as the source of monochromatic light. A convenient method of producing such a flame is to take a square 1 ' » «wi> -.^AM bo^ n*o(»irU, xcirpew, ^ c*! Sill lit' ', niiiA’ ' 1 .. , A . V .^ij a« -MevOk «iU i*V*ni<»q UA coot »W«»& Uiw , III. ax« J*«-Si»nifc it, ntUBT, «dJ b/i^ ,e^8 o^. i^t'n»n,eco« ,^rCl^1vlel*JhJnl^^ci‘ X^iw -Rnorii^ 4jn« Xjufponj- . -nov 8# KWitT ,8®snXil •sajfuo'^io aXii.^ > i ij »a 4 (JOQI; ?&rJXl)ittQ*X>-co^;X'xl n*iiit-nXo nc tv. ■f ■ r .'inJi 0 ancTiXfK o»ri anoi^laco jtfrea tt3nX*3fl fi^jQ n^IifuU^ 0 firr a id it»&X»^Too ax; doi ' B " ^ pri^px^ uiu sf^ij *ic^‘^snJ wtJinl or ,£)£64^:!'iiiypj. »^xr*j y^iJ j^uj ^,t^u »n^ fiOM ^rtaXI • '•V _ - - ■ ' , ' ■ ' -CXB XiC4^b ^19 V ^ iil <1 tv'i/tir. «uJ li mcK ,*jtnA46 Ht^iif 04- J*1AJ hl>3a.‘,rfp Cl r,£iBli e*.ti 1o 0X14 . M :rn4 ; a-j^dw bnm S18U a e.vbiui .VW 41«< sfUMA*! * t ”• - . _ .. .r. .ii:u ,oxifiT .6oii#3aiXr j^oxia a c^XiiS. b8oio 9 i^ovoin \Xq«ir hedi*iti^ ^ oi* eoB ao^ciii ©ri,t f ^aiirio'l ct»vo« ^ *xo*i%t« t)iX4t I f 1^ - . . . .. '*■' ■ '■•;'■ *''■■ Udm .X^iis t Q^ffM U .fcXfeil'oiX.t eaci^'evoiiirij -ftco rxXw £»^, ,« fflQirt j^.xvoit Bi 1 ,1:i ^ 9 f 4aal rx/W .«,, ^ it «ti>40«o <*di bijsto^ • ,4 ' ' ^ *r *■ * j »i!i^ Jo«ci9li»4Ai 4J44 xlti^ t^ech' \nAdi nl \o.Bmj v*» .* -iirtiaai •.-< • . . . ' fS^'V ' ^ fc4K^^ 9[iS Mu Iv^h^mcVioq illBy.iBii R« fi4noi«Xibqjto.‘0^ ' •« i-ocjico.i-ictfi ,ni 1c 4no®4BXjfMj ST' ^ .■ ' , ‘ST' mx r■^X^tt,h.m.,imaurSip^ petituscitl •Uf uHw topnaUoq iJnauI-xt^^ .^Xii4£ aiifRiio-iauoncin ifi jipraiee »£W .a bmu x«ew» 3- ftl- 6.B,*r> -Mt pQ f. oj al .a411 iff ■^*^ol^l®v■BOb.'■A'« " ’* ^ ' " ' ■.^ftabbapeaa^ «ii* ..iX l'AmT f - 34 - piece of filter paper and roll it into a tube just large enough to slip over the tube of a Bunsen burner. Wrap the paper tube with ordinary grocer's twine so that it, will hold its shape and then soak the uube in a solution of common salt. After soaking, it is allowed to dry. It may then be slipped over the Bunsen burner so that the edge of the paper projects a small distance above the mouth of the burner. When the burner is lighted, the paper burns, and the salt causes the flame to be a bright yellow which is the sodium flame. A paper tube made in this way will produce a sodium flame for several hours. Now set, up a convex lens between the flame and the plate M of the interferometer, placing the flame so that it will be in the focal point of the lens. (Figure 18). Wave trains coming from the flame will thus be rendered parallel by the lens and will strike the mirror M in parallel lines. By means of a small piece of wax, stick a pin to the lens, so that the point projects down into the path of the light coming from the flame. The mirrors 0 and P should be as nearly as possible the same distance from M, The dis- tance of 0 from M may be roughly measured by means of a meter stick, and P may be moved by means of the screw until it is the same distance from M. Then by placing the eye in the position shown in Figure 18, four images of the pin will be seen as shown in Figure I9. Two of the Images will be quite plain, and two will be dim. By means of the two adjusting screws at the back of 0, it may be moved through a small angle so that the dim images of t,he pin will coincide exactly with the darker im- ages. When this coincidence takes place, the fringes will appear. Then by a few adjustments of the screws, they may be made circu- Figure I9. yK. '''''':W^ ooiw^eifc iX#4i4:iaiu •tot40Q ertJ tl uv^d n^dA wullc^iioa ”| .edJ,4X rfoidJ^roXXo^ JAbMC fl.od 0vV&m«X\ e/U,0t.8**io r, 4WXF.OII .. Afti^LcKj iii« 0 XfrJv>d 0ilbX Z0Vf(OO C woH ■w pi *d iiiw Ji .>oj: > e«tfn .•»»j«wi«i.,*j,a.-j«.ho«. ♦rfj mo-i doxod!. »nJ*-.J. «v^» wUsiT!) .»n.i »„u^4o Joioq, jt«p<,j ', _«Xi*xi» XiiJ» i>rjt yiaX a,..' ^a xpXlMeq fctnsJnat »d «uaj xxi» pliiXt ,.'j>» Io .#i»iq XXiW» 9 lo st«f#.-.l .8«niX XsXUvn i.t Hi lo-iutiii' opi,- wi.' tif.l iwot- si ^ooioK} Jnioq ojU iartijja .8n»X ,,.p4 oi nXi ,-wiot ,et ♦•u?3X'5 nX nwQdfc mJ XXX«, ifH^X o/ij lo on'T r.J «C^ lo ’ifTiioj-, L*u XlXf £,rr ,nlJi;Xq >'■ .V y«i XX ,0 lo Jlood jij finiiiAtlM c^' ‘ ’i’'^^' v ,',3 , ? j . . ^ . -• ^TJ . . , ’H 0? 0X3^^ XX««i« ^'n^uoirt;^ x«V0tt 00 V y^t ; lo^A-^-iXb Xi^i*^rfWQAlco XlJ^^atqudJ . if.«=>qc0.XX'i» 0fU ,itoaIq ^^Ol4•ivXoAX5>O^BX4^t..OD 'X(> ny^# Ttsi^ to inefflenneBwlI' ,S' ~ * ' ■■ - ■ '’-*’ ■ '■ jl ' i tf ! * , liMJagf* .r^to.ui<.iiea iitei^iu ai tf fl^anol »v*» «iit ■\l ^ ' tpOOOOOo. “^0 J il jxialnd 'tRa;oiJnf»\uo x4t ei; or £n«wnoi • <■ ' p. rvBif oXo/iii VAC ftJrq »A*y ^snrdo ca ronoH ,A.t4»ci omaa novo &oii/4 r' . ' i ' , ■ ■• . V ,. ^ 6VPr %tr.(i R to rormjfciii jr liovofli ^ nonn/ia c.iii^ ^a^SaoI nonnioi .wfrnott £>aa ♦M»a f'-ow rt«6e oaj lo eAurai Votf .d/ajjei odi ^iwco ^^mUoh 9ihi aAlmfC. .tX^cfXc bnawnot b^von , J-rilJ ^Aa €0/ ioj .rsiV to 'JXerli ©a 4 aX JnXoq 'n^yl^^& ^^sGq.tiQXtiy,^^ ®a 4 fvA '• ^ .oXoil #Ai/ eaonor XiecnKO ov«4 ft^Aint ck>J i»fiw AO 8 A 0 i/ii/; 6 **n?; hrnt iavcfl erii tonnX® ©Ai dolflw dfii/r^cT •C‘^ t«:iYXh dji* t« JSeiiqxix^.a» ©onr.Tiiifc Hldl? .wrnoiir&di Ic lar/i 4^ ~vn 3niwo4XPt , *£lai r oiU v.) A4^AaX ovAr oAXfiovXa .-OOt 0 £>5)fcAftA raario& oaT .raax'l rajjCi>o« a ';noi i^evn&cdpirnw-^^ nr .i-»voB ,o •jotijiB'»iw KeiAr A'suctO-r' BnaiBaj^cBo tU BOfleJaift iiw t| , '^V ;•:<•■ ■ ■>* ^'i ,« ,(W«X0» &•;/,« *£t# .' ' ■■ - 36 - The fifth column gives 1 in Angstrom Units. D 2 D N 1 (2D/N) 1 .002950 .005900 100 .00005900 5900 .002963 .005926 loo .00005926 5926 .002935 .005870 100 .00005870 5870 .002946 .005892 loo .00005892 5892 .002945 .005890 loo .00005890 5890 The average of these results is 5895.6 Angstrom units. Sodium light consists of waves of two slightly different lengths. The wave length of tne shorter sodium waves is generally given as 5890.22 Angstrom units, and for the otner component, the wave length is 5896.13 Angstrom units. Thus it is seen that the value obtained above agrees very closely* with the generally accepted values. In order to get accurate results in this experiment, care must be taken that all lost motion of the screw is taken up be- fore counting of the fringes is begun. Any lost motion will in- troduce considerable error. This is not a difficult experiment to do once the interferometer is adjusted so that the fringes are sharp. It is however rather tedious, and is very tiring to the eyes. 3. Ratio of the wave length of the D lines. The fact was brought out above that sodium light is com- posed of two different wave lengths. When sodium light is allowed to pass through the slit of a spectroscope, the prism refracts these two different wave lengths through slightly difierent an- gles, so that two yellow lines are seen. These lines are known as the D lines, the one having the longer wave lengtn being the Di line, and the other the Da line. Let the wave length of the tri jt eo vXli^; m» to;^^ •’ » jj (tncas) X ooeeoobov ':‘Si-woo. &stocoo. ^^ 65 ^ 000 . olseoooo. •fe** V* or;t Oot oof* 00* ' a 2 V* Tfor •’*(f .'. ■f^c'teoa. ..I dS€iOO. \0V^00v^ .' ' *\jr ' fieeeoti,,. o^aeoo. -■f^ • oa^sioo. ■,*H- ‘.s c&ssoo. 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IX 111 & eX i<) 40^^oe ft jxoufe" Jirti .n«:aS'i'X oiU ii^vo^ija '■ i-i ' . • <»v»;o «» .ssnuea frij « .taxUdo'^a »«ljC*(»'t nj ttmiw wo#. 4«v;n/.J'll ^UOliliO-lq All^i4l®X.iWV«II, • ■ [£* ' V';'i * ^ 111 ©ono-’i© .lit) oiu »ti!>noir T:&i:ijfo nX to ,XeijpiO b*i» VXM^' -cO^i# rJsneX uVAtf •no xo t*feonol ortl »T®dl ton## ol - , ■ ■ ... * " ' I 'Ai *^ ,. , ' ' '* ei lui Juh .jtiidnei ttxu'H nor^^*'. lo eu<^ tiiim' Bbtbfit ^M!’nX^l ic ft; vb njocf ujL ;r oon©nexil6 iid^ ^o^’k^vc* aft. 'liu ovo« XJXw jop mm ’m ,w*i\ ts, ©rU iwoonee mir ni: ■ ' ■ f?l € oit©^ ;#l%t j> ©ai" nedf ,;i»a*.'o pjlf iififu ©rid v: r f * ■ '4] Jiip lo ^0u ©r.c ,4n<.^«wjoqbft; nood a'iuf iltfeqi j] , }tiyj «n* o« iltJXdir « lip;l y^a j«t oodJo edJ nc t;anl^‘,©v^ f ‘«‘«^-ad- *ooeq« e le Vx#/Ts.ia? odj IX icxaj n«ii% .jo* 'rorflJo o/U Ip * *r$*r* ■ •^dXn't 5dj , ^0 nX pidV4« to Bioa itjlou 'iol Sijix 044 < ^ * ' •’* ■':'-i| ' ) . K© i^i 4’i^vS -“jIji C’BlPrtXflajiXi x|e4ftlqcoo . J»o ©fvo ottL'JiOod , q^eqctisell^ 2 ‘ f T . X.'XuKBici 'rviai'^e Oil! Xo Jon tt JpS , 4fta nojWo cdl ftaotjed 1^,/] ,/i0©t 00 y\sF, la bX&& dlod nti» ,^i>x#4c ^ • JO fiftii^oe ©np pprft wOW-HliOKaiXfe Ml *W jtr , j. 46 «/pi^ e IXjfijl aAlj^^l/ico k!0j4 J)ftp tc lUpq 111 aon©o:©Xtl®Si|j/ V \ f ^ftX lad?* .R’&/tc qtjtjfu i iiit (jJto .‘xo^noup, 044 lo ^ ’ ■ * * « .*.#1 41 6V£P. q« 3 floX lo uO 0 t. bodli»4rrop nX eoneiolt^ 4 » 'oAlt , r, 1 1 H' ’'■fts^. .*«J - 38 - would contain 1000.5 of the shorter ones. Let N be the number of Di waves of length li contained in the difference of path. The difference of path will then be equal to Nli . Let N + .5 be the number of Dz waves of length Is. contained in the same path dif- ference. Then the path difference is also equal to (N -+■ .5)12. . Therefore we may write Nil = (N + .5)12 (9) But to produce any given difference of path, we have seen that the mirror P moves through only half that aistance. Then Dividing through by Iz , we have Nil IN .5) 21z = 2 And dividing through by N/2 gives I 2 “ N { 11 } which gives the ratio of the wave lengths of the two D lines of sodium light. In the actual manipulation of the experiment, the difference in path is made zero by moving the mirror P to a position where it is the same distance from M that 0 is. The two sets of fringes are then coincident and brightest. Then move P slowly either forward or backward, until the fringes disappear or are dimmest, counting the fringes which cross the field during the movement. The number counted will give the value which must be substituted for N in the equation above to give the value of the ratio li / Iz . The following results were observed: N 497 li / Iz 1 .001006 >- - ■ J.'. *f*\> ‘ '. •- - ’■■’ ■ ■:• ■' • ' "re 'ie^ftwre 4 ‘rt 4 - na^ejc/iB no ^ • • . A * ,.?'’"c‘ . .. . ’ * ^. *^*^ G. i- yifU . -XK ov tid ivjiU iiXXw io • ta i)OWciw;> 4 t lCvf.«©VJW, jtf: .. zXiQ, . *!• p) otf X«;^o o«4.«- of awlt J . ■ -' V'tI ^ * V «Jinr ft*? >f7clo?»©4y ^ [v- ,’ ■ J #• V? ) - iXK ■■, ■ . , •'^' ^V','^ ' **'''* tM.CMiU nwtfvori ’ '■ ' V. . . .. H ^ , , . s. NX^fl. ftili 0fc>j*xa *ioxrfiv fistafi/nl »juj ^i^i^flrujou ■ " ' ■■ ‘ ■ v^’ ‘ .iojiiX.-^iAV'dilJ ft 7 X^ xxXfc L^;JrjL;od ‘tftoiax'fl, , itfloiaVvou ' eii> - . ■ ■ ' V -, ■ ■ ’ . ■^,„ ' V.'JZd. i -?® ..•■•'*B>?'' •W 3 » WMf fii- a sot i»juA«adJui'*^.i ‘ ,.v '=^ V V .■;- . “ *.X \ 4 :X o;U i' ' i',i I'i/' rc ^ )j , / ‘ _ 5001004 ; m ■ 'Vt'’': , \.i •■•jagr rTsagT***.^^ ^ a i i ,i' U 1' - 39 - N li/ Iz 504 1 .000991 490 1 .001020 489 1 .001022 493 1 .OOIOI 4 506 1 .000988 487 1 .001026 498 1 .001004 499 1 .001002 491 1.001018 The mecin value of these results gives li / Iz = 1.0010091. If we take the wave length of the Di line as 5896.18 and of the Dz line as 5890 . 22 , we have _ 5896. 1 8 _ , oninini lx “ 5890.22 “ .ouiuiui These lwo results vary from each other by one part in one million. A study of the separate readings however does not show this close agreement. This discloses the fact that there are some diffi- culties in making the experiment. The chief difficulty is in the inability of the eye to tell when the fringes are dimmest, in other v/ords, when there is least visibility. This is shown in the marked variation in the values of N. Another difficulty lies in the fact that as the position of lowest visibility approaches, the fringes become so dim that they are exceedingly difficult to I i k count. Hence the desirability of taking a large number of read- ings by which the errors in some v;ill counteract the errors in others. The value of the interferometer in spectroscopic work is not so clearly demonstrated by this experiment as it is by the Inversion of this process. If, when light passes through the ^ • I l-V ' ■-.-■'S., V. - * * ' '\v.; -^' ?.," ■ dev « af ’ SloTOO. I • ^ t: . '^OOUIOJ « it viX' jovial «.ti1j8**: Q88rt;^ lo a»a«^ iieeii 0 »>^c u^ e^l tC '•Ja 4 c aiU.wSi'^ «C?GfOO.f a a U- 0 VJ 5 ii W uS-S.oeS^'i^ .••'iU'B «/Hj at 9{\v Id xi'jtio ae^\ 9^XjLr^fil ow/^daiilT vaoXd ai/lt w»rojj, io. 1^ , -iVi.-b ftaolt'.i'ta Joat oii^ *6ft«oiaii6 gtiir/ .t^nneJiga xfi, ei VXijitriif* <^ifV .^(xtrlnttnxe. t>/U icrt; aet JXj£j ' '* ’.. i ' '*J 4 ■f]' -. ^ , . ,v*;..»i!i^ti -i# xi«i OX oiij; to ' > f * nt tx. ■is?!’ .v»ii/tj£siy #,B>(t' »-te4i' I»di ,r(K!^» i«&ro •K-fti V.^ll,q£l^J6 .t, 1«r iisuitaw *iU iji »H? iJXXfifW ;xic.* 4 j. » 4 '|.- jwii ; eii .'tpj/vi|b £ijjo|_b«®o*a ^do.. jsrtx, ■ix. «y oaooftd s*^oi’n%dJ ,r‘-"«*- Is .•i»^!-'w^fi ejji*x .« ,p«3U.3 tu '->1 h-'w-we »iii. i^'ioXri$oo' iUw VdiDo ni ika-i'iB ant aoirf*^%d eani ■y:.^ ■ V.; , . ■ « . .£ . '■y^ ^ ** ***^ •*•«’»■ oit%a^ ^ ,, 6 ax W«Uq\'o'axi>mtfe ,■^I. IS.:-- . . * ^ '•■ jitf* ■^n, s 'I'S - 40 - interferometer, this change in the visibility of the fringes oc- curs with the change in path difference, then we may be sure that the source is composed of waves of difierent wave lengths. Thus, the Interferometer is of great value in spectroscopic work in analyzing the various lines of the spectrum into their components. Some of the lines are much more complex than ohe soaium line, and are made up of a number of different wave lengtns. But Michelson, with his interferometer and with a machine of his own design called the harmonic analyzer, has done some very noted work in separating lines of the spectrum into their components, which could not be separated by the best of grating spectroscopes. His harmonic analyzer is a machine which automatically draws what are known as "visibility curves" for the various spectral lines as they are seen through tne interferometer. A study of these curves shows the composite character of the lines, buo it takes one expert in the method to get the full meaning from the curves. The method is more fully described in Michelson 's book entitled Light Waves And Their Uses. The Michelson interferometer however is not so well adapted to spectral analysis work as the Fabry- Perot interferometer which will be described farther on, and its advantages in this kind of work will be then pointed out. 4. Measurement of the index of refraction. We have already seen that the fringes formed by two different wave lengths overlap each other for a certain path difference. If the source is white lighx., we have all colors of the spectrum, or all the wave lengths from the longest to the shortest. The fringes formed by all these different wave lengths will coincide when the path difference is zero, but when the mirror P is moved in either airection, the shortest wave lengths soon gain half a r. */t^' ® ] -»o ».iA 'ij \,^t^ta^}y iiSa dl »ij|4jKlo j imii> OQ a»l^t,y$^>{^.■l■ttti tlst>^ii jt^Xci^Qqi #no& /^o r>e^C£t ^^t)V aicoQ eofci) ted, oirt'owT;iK^^«ilj5^Xi:«o J I . driX4'tw » I ^ noaotj;flKKj o4 Pi <»U'IX ^eri^, sa «xX 3ittl«*iri£q»o f f' ' . alK .b=»*4^oaan«e*Wfe i-. ;dj tw je'yeqe.Ji Ti#dJ nX .fceiJiJjis Xood B^r.o^4it>doi4 d^SvX^aaeb t*'irU^ | {/^ jrx<>e o« Jaii tJ ' ■■'' j ' jfl ^ ' ■ ’ fiAfl ,flfc fci*5il'Xo|%h 9Q /ii% daXdt t»^«Jro*X)ef^id^rri Xoiefe ii L **• ■ • ■ ' .' • ' ' ’ '• . \.TM' lii . ' ■. {E:. [^ « - uUo b&.?rtf‘f^.'*, r**tai ra>- ?. „* f _ '"“'• . v .. n I * •* ■ ' ' V ] ,\JUQ fa^..£3Xci^ rjedX XXlw ji»jcw 3to i*ntA UlAyt £il ee^i^i3iav|)i> ■‘. . . ' ‘ " , ■■"^.. ' -.• . *t6 jikhal oiU lo Xcfti>#(|*4i/na<^ g ' *' ' ’Ji ’ • ' I cwx jt 7.>iisno1 aejSniii mtf n* u e*ioXc?o IX« «Vfc/t b# ^.udsil eJXdir «x e6nvSi»od^ i, ^4^ 64. irto2x*flX a/WatreX aviiir c'i3iOAio6 XXX^ ad^aneX ^caiaSliL eeaiW xxa t6 ^ • -7 n . iV ''r' Ai. . ,, ■ s ,#/^_Vvto &l <5 isyiftX(r< iBiU rteilw 4ud ' ,0'ife-ji aX ^ iXsil n|e^ ‘men F4i{^artaX #ri,w * , , ’ . ‘•"" '> ' : .v**.- „ 7 i . ' I ., ‘i. .• . - 41 - fringe over “Ohe longest, and the fringes disappear entirely. This will happen when the mirror is moved a very small fraction of a millimeter. The appearance or white light fringes therefore fur- nishes a very accurate means of telling when there is no differ- ence of path, or when MPM and MOM are equal. Let the interfer- ometer be adjusted for white light fringes. Nov/ if a glass plate is placed in the path MPM, the effect is to increase the path as if the mirror P had been moved away from M, and the fringes will vanish. Now if the mirror is moved toward M, the path will be shortened, and when x-he decrease in path thus caused is equal to the increase previously caused by the glass plate, the white light fringes will reappear. Now the velocity of light through glass is slower than it is through air. If the velocity in glass is V2 , and in air Vi , the velocity in glass is V2./ Vitimes Vx . This decrease in velocity corresponds to an optical path of Vi/ Vitimes the thickness of the glass. This ratio Vi / V2. is called the index of refraction or the glass, and it may be desig- nated as m. Then Ir bhe thickness of the glass is t, the optical path through the glass is mt. If the glass were not in the path, the light would travel through a distance t in air which fills the space occupied by the glass. Therefore, the difference in path D caused by the glass is D = mt - t and solving ror m, we have m = ( 12 ) In rhe manipulation of tnis experiment, the interferometer is first adjusted for white light fringes. This is done by setting the mirror P as nearly as possible the same distance from M as ■A . V ■ - u - h if ^ti-T licie^iJoX 0«cr •©^reJt'xT •A a4.nr ilftai t iov b bbvm &i "' '■ .' ■' St 0-^'i Crt USViW ,V/»i.XiOJ lo'srfiGtf 'f'tOV' ij‘ fcSffiiiit -'1'^‘5'tfcft fii ®itJ :J fa ii*. JiOiS K^Ji..j3SyJlf »S0 ;^iU^ o0Clj> /| ofeeXB 4i IX eJiiiw :^b- oX #iix ,\eiU- it 0-1 X4Afi>f 4i £n»nwiiv ftGiV rfjijiq- •aao' n»diir>5fia ^boftoa’io.Xa orf,/ ^d 1 .ajfa> J Sf*/c^iVaaq ..^j • ' ,'i • - 'ft iU lacier au^ 11, .■sxi''ii3uo*sii^ Bi Jtx }mdi lowolo »X o^^4-X24 *^1 ' ; S' ’>, ,'-' -•■ ■»\'' . • Tf -V V f .f -V \ A * .t^.k 4 ^ - «. ^ ^ •. . ._ . f ' <■“ ■ . tX lr Jd^lX ' ' ' ‘ ...A Ri ♦om'ioVilb aiiJ* vd ImiqutiQor^aqB BA^ ■ ' ^ , adjust bhe mirror 0 by means of i-he adjusting screws so that the fringes are as dis- tinct as tney may be made. Now substitute white light for the sodium light, and with a slight turn or two of the worm gear wheel, bhe fringes should appear. Now mount the glass plate for which m is to be found in the path MPM, so that it just covers half of the field. The fringes will therefore disappear over tnat half of the field covered by the glass. Now move the mirror for- ward slowly, and when the distance moved, has shortened the opti- cal path as much as tne glass has increased it, the fringes will appear again, but this time in ihe half of the field of view covered by the glass. The distance through which the mirror has moved may be read irom the circular scale, which gives the value of D in equation (12). The thickness of tne glass, t, may be measured accurately by means of a micrometer caliper, or better, by means of a spherometer which is graduated to thousandths of a millimeter. These values substituted in (l2) gives the value of m. Two sets of observations are given here, one for a micro- scopic cover glass which was .1675 millimeter thick, and the other for an interferometer plate which was 2.1536 millimeters thick. The values of D are also given in millimeters. For the microscopic cover glass: .0904 .1675 1 .539 .0979 .1675 1 .584 .950 . 1675 1 .567 .951 .1675 1 .567 *;^cln*,siy-7s fivyijiir UffUr ^‘.C7X«1 anoh .3 6 ac«fjJt« »4W " tiiU mdT . >: it. xfJlvr ■ A ■ = ■ W. ■ * * y * * ^fttb i« i>Hi 9 fi 4 wa4 ofe awi**:o« tjciJai/Lbn 1.0 arsMuii ' '3 ^ •aJ' lol 9iXjlk, 0Ju^I^kiMja woH .isi^ vd ^aat ^6»/i4 sjb. 4c>al4 ,'•■■■ & , . V ■' ® ‘ . *Ui6a ««dw •di '10 6 t(j 'io a-u^J ^fui ,JUattX:^Jti&c!a •xcl ^jiiiti ocaia #a^ w<>a .«!i;91(qa biuotia af^a/uni «riu \Xb«rt» , j • ' ■rm^yoo iJJ; oe ,|£SK £Wa^ «iii nX :>auo’i a f.piiih 4 waxiA4sii fxfji aAd«f £>ixm % vXiwJitf ‘~>L ’'J- .. ta ■1 j ') -.»'■ “ XU# cyaai ii sijU DfiAl^ M .'ionn aa lUisq / jUu • ' '' .■' ” . ,** «iviiv lo iXjlolt f iu' to \ sj ^ iiliU Xud ft*‘H nfc'ini.u 944^ doXd# ^o/vax';.: »4t .a«#sl3 «aj tji AxU^ avYXa dcXd^ , >Xx$o« »4X «d 'yma &«v(/f: ^ VO t-Ka t4 .Qdiila oa^ lo Am /iaoXiIj wif*^ , (?♦ ) aoliTxuxpo aX v^l lo ' ■ ■ - ’ \ 'Sff ,»tA4Xt»4 '10 ,'i^aXoo I’JJsiPO'XoXm xj lo axwiooi xof xXo4a'«iroott*3t/iri5^fa .^4 Ic. 6ai6|taiiooiJ4 q 4- doinw ho 3 we}on:‘ii(^A enaow oxjXav &ftj SI -YXjj ^STi A ni xnJiX^Xaiiii/c' %oi/Xsr 6i»i£T .^flriwaXXXia ;,,/^i,. ifc'.w „ -OloXai a * :i ftXiO ^iKiod rt'^viv »ji4 Uv /}4oa^„o,if7 - •ff . ' *■ 0/4J f/CUs ,iit>Xil4 'i94 >k;iXXl^; ^ ^ , «-wrtf /laiar bU^Lh »xoYtt4 oXi^OO® inoXoiaiiXXxi' .X bMW doXiW r X#i^ 'i?*Y*>£i6'irtfeoiiU IV .4i04«£XXXX.i ni AoYXa* ofiXa a lo *■ */ , j‘^ • r- «i 'X ,:ttfe«Xs loYoy ffi 4 4 ]L - > -^8^. f'» >1 1 .►.i ^ • * AJ.I , 1 TBf. 4 « ^ :X'V ' l> ;- ^r.; - ■' ; '■.i . ’■.v', . /*■)^0^0. . . , „ ^vtso. .• ♦*( • •■. ^ »'''.v oc<5. j D - 43 - D + t m - t .0912 .1675 1 .545 .0933 .1675 1 .558 .0954 .1675 1 .570 .0993 .1675 1 .593 .0907 .1675 1 .542 .0910 .1675 1 .544 The variation in these results is rather large. This may be due in part to the fact that the glass was nox, of uniform thickness througnout which would produce considerable variation in the readings. Another precaution wnich is necessary t,o observe is to see that when the white light fringes reappear, that they be brought to ohe same position in tne rield. On their reappearance, they are apt to be dimmer and smaller than they were before the glass plate was placed in bhe path. After some practice, they can usually be brought very nearly to the same position. Another precaution to prevent error is to see that tne plate is perfect- ly parallel to the mirror P. If it is inclined to it at a small angle, the thickness of glass through which the lignt passes will be greater ohan the measured thickness which is used in tne equa- tion . The results for tne interferometer plate, which was made of very fine glass ana whose surfaces were accurately parallel, show much greater accuracy. D t m = 1.1995 2.1536 1 .556 1 . 1998 2.1536 1 .557 1.1930 2.1556 1 .553 f \1 KG J ^ Q 'C C»C. I if , 1" eec. i * i ^ * ‘■'.'V ■'7 ^pj;* t-e.t Ofci. ^4 «liit .OS^I afAjae-x ®eVi«^ ni fSbi^aln^v ^xi!P ^ 4*.'..- _ ^ ’" ' . ■ : ' - S':] OafJrto/JiJ anoiiw; 1c ,a« ,rtj Jocl^Uj oj'^^jiy.ni «4(J lU noJJjit^^v i.Xei»i»6x«noa «oi,i>ci0 6t«c« K *fdS Juo«n^o-idJ VJ ai •W*.I0 .>1 tiM^wiS « .,'rilm(.noJi.a«,.., ,.,,/orJl ..^tae. tsflj , 4 jjj .I(i /iwiir BniHSce I , !i ' ' nX«M PC ...-X«i-;,:j pi „oHUop „^aa .4 OJ Wa^io-io C3X snol*ii v-i-^ fiea x)a>. ,»^t3Pariq -aoa •.-v.fli .3 Jh<; oju ni if»«o«tq ■'»» eJeX(.a ox len* arn»!fs^Jiox fe-w &ixX 'ic'i eiew saoxinr /xfiA afe cs \;rJ4v X, s < >• 1 , . ^ - «i tj. r't^mutiOB /iowa I res. f ?eax r dee>7 ^ ate> .7 J . s li 1,.. — ■ gm^ ' ■ Mfil . I,‘ ' »'v. :ik^i 44 D t D4- t ‘ - t 1J901 2.1536 1.552 1.1959 2.1536 1 .555 1.1996 2.1536 1.557 1.2016 2.1536 1.558 1 .2007 2.1536 1.558 1.1973 2.1536 1.555 1.1989 2 . 1536 1.556 I 1 cent of variation between the largest and the smallest m given above is .38 of 1 These results are very con- sistent, so the mean result should give a very close value of m for this particular plate. This method has been used to measure the index of refraction of various liquids and gases, and to show the change in m of a gas under varying pressures. The gas or liquid may be placed in a tuoe with glass ends, and the tube is then placed so that the ray MPM must pass through the tube. This causes a displacement of the white light fringes in the same way as the glass plate, and the calculations are very similar. VIII. Some Famous Classical Experiments. Consider again the equation D + t m ^ and solve it for t. Then t = D (13) m - 1 This equation suggests a method of using the interferometer for measuring tne thickness or transparent substances. The procedure is similar in every way to thao given above for determining ra, but in this case, m is a known quantity, and t is the unknown. Since with the interferometer we are dealing with light waves V — ti sc‘e. I -y> rec^ ecc.r 9c2.f f 4 .'ICl.S -,n .' es«^Ai’T- sttJ Jm #*»81 aI .,y ‘.6 >060,'i»ii wr ILa __ ^ ' a !., • -uA. VJ»v eni. •••rft .»: I tc ;;. «\ii&Uv • • ' - k -.0 «ul,=v a»oia r««v -. evii Wi-« •■«. ;l*/’««.-i casj, ;./u of , tef ■r ji ,9islq 'iMlL{ul3*tAqltliis CJ f-wii, ne.»t( JU 54 KoAJtNA aiiiT^, *? ' hr "A '.0 a ni Ajywjia .aj muie. t, : tao .o^aej. imi eb^upU-^^W Isc ' y*Mbi 9J ,04! t^pn ,0 cas-'wiT .aa-ivosam soitniw^iajS&u '•>UJ ^WU M Jxoair, CBM «i atUitf •«U,Z,«i .i.6ne obajc^ A»Jtw t pSe Jf®«»wlqBlb A o jaoao «i.dT . aa,? »ai muaioJ •sll'jeuii MSB -vW lii B... . -_ 4 . ■ ' '■■■«*- tu- .oMXq ASiOij tc v«'ai»o .vu ,.i swi-a J= ^ i '.,-',y f.| ' f* ricl 'if.-offio-ral-i^jai o,u s,uai. u botiJ^m o «Va*a3ua n^iiaupi ‘eli '* a'itlooe-iq aaT .Baoficj BOVS ana-, j to «l9eniioj(iy »aj " - 'J . ' Lff -■ *► n*?l.evcon \5«w ni ^'I£ * d . ,. , , . ^ ^ 0W ^d^ Airiw ©oitxs^ 4 ' ' - 45 - : wnich have a very small length indeed, this method lends itself admirably to the measurement of very thin plates, such as the film of silver on a mirror or a soap film. j E. S. Johonnot, in an issue of the Philosophical Magazine | j of 1899, reported the results of an experiment in which he measured | i the thickness or the black spot of a soap film. He found that one i I soap film placed in the path of one of the interfering wave trains | if producea no appreciable displacement of Lhe rringes. He therefore | constructed a frame by means of which he could place as many as i I fifty soap films in a row in one path, and this produced a dis- placemtfnt of half a fringe. Johoniiot calculated that when the film was Lhin enough to show the black spot, that it musu not be composed of more than two layers of molecules. Therefore he took his measurement of ohe thickness to be the upper limit to the dis- tance between the molecules of the substance. He showed the thick- nesa of Lhe film at its thinnest part to be aoout six millionths of a millimeter. Mlchelson has made very good use of one interferometer in I measuring very small angles which could noL be measured in any other way. He has also used iL oo measure the coefficient of ex- pansion of substances which could not be obtained in large enough bodies to make their expansion appreciable by any other method. The Interferometer has also been used in connection with a very delicate balance by which Lhe gravitational force exerted by a large lead belli upon a small one could be measured. The force to be measured was about one twenty millionth of the weight of the small lead ball, a force which could not be measured by an or- dinary balance even when a microscope was usea in connection with it. The interferometer has also been used to test the accuracy of • V -T i ' 'Tl ^ 'U.'' ■ * . ^',7 v' .■.' ' , vi Hi' fir.J ek ctooB ^t^BJstq Jnitu ^'x»v lo •^n^>m«^a»®4fif» ■i:(i ' r'-' C,-'.*^ ' " , ' , ' ■ ^ ' \ 1 ? • I - \$ - ^ ^ - ' K.' ^ ■** '.V ' .®rit A 'XO ‘50'iiiil 4 ,^avxxn . [ 'ic «;;cAi ctl \konMido^,a’'}^i' I 'm j» - . ' ' . .*;*•. . ^ ^ — JM. *■ ; tf.rMV ^ , t»f:u i)iU< 0 'i .aXi*i (iBos h ’\cs XO^Xcf &itJ" oao lo ni o.po«Xg^ a^io'i^aaJ *!; .e» 3 /!i'xf ^ 0 ,. ^ "■ ' - - ” 6«^e 041^^1 ^Xuc* .-i* foaoiiJSo^irf afii^' w t a.. ^ i... . ... ’^ . . - ''i.; , _, ? ^Xx> ^ t>BOiito*iq 0ii4?^ itfie ,4iJ^,q aao Di «iri,.- a«^ii'-qjio«^S 0 flX «#n»r -^. Jcmr(oji 0 i , *»r 4 a^ ixi^^ f ;y m ^on 4BUBL .Jciji} A-iAitJ ^o/iR va^ ;t^pn 0 ’/Ujla r '^'■’ • . . • ' , '!r^ 'X 1 ^ «rt «ioi 5 -iwit . 3 #^^i^^Xa<^s ' 1 © <*-tow lo ^, . 0 iXi,» 4 ^ 0*1 JimXi 7 oqQii Biii »a Ov^ aeen 3 J. 6 Xjsj fcfeWCiiR iJR.a-,AJs! 4 f 4 ^a it 44 if aalupaXoR ♦.^ita.TXiOXXXitl 3 XiR ^ilOQB ap Uii II' .•i©^««f44Xiifif A to I.. V- 43 i- ^p'AiRAi i&o^ v/tAv^ khetu ' ■ ‘ - ■'* i^™' \C06 nl bo^fig,a eg tfatt fciuoe -.tfJiilw. «els«i •‘xXfaaii^w^jy^ i./,i -Xd xo irtRXaXtleou eij^ •‘’iaxiotn irX ,04lA >uvn y^w aaj^-a^ nX.XkanX.flJdo od ^on Z>X*^co .at? d|xa^h^ 3 Ljte^^^^^ i 4 'iax[h« t» »ig*X» 6 lttqii atitariiK* X 1 BV ‘.a- iHtw jjox Joojuiog s:l pam, fpaeet pyXe; xd bM«foxiV gi,,c ! ewmXeJtWJolf^S ?V eft^ol »ft> , i»wn»i»«efc 4« 6/uoe-^g i Jtef a;; e. nci^* _ eig tc .«,-,g 50 #/•;»« :: wm - JjJ«o /^,-^io aa.'jT^U, X»*uitiXt,^ai^'ftd doo.'iiXgop; 4<0Xja« *»Q*xci. XX3d,-,X)AaX ■■XX4ai|;' iiJi.g «^- ■'Mi ^ *sw 5 te[^ 53 aj^ ','Mf^,,rnntfigrtifa a re yta:a t >«e=i 3 fc}.-...'ixffl^ -a-*^ T'f!- - x«A' , I-Vio n...'.i"' ■ 46 - very fine screws sucii as Lhose used in dividing engines with which fine diffraction gratings are ruled. Such a screw must be very accurately turned. | S Aside from these valuable uses which Michelson has made of I the interf eromex,er , he has performed what may be termed some very | r I startling experiments with it. He has measured the diameter of the s ! great star Betelgeuse disclosing the fact that it is a heavenly body the size of which is beyond the power of the most vivid | i imagination to conceive. One of Michelson* s most famous experi- ! ments is that in which he determined the length of the standard meter in Paris in terms of the v/ave lengths of the red, blue, and 1 green spectral lines of cadmium. By an ingenious modification of the interferometer, he succeeded in getting very accurate and consistent results. The readings were taken by Michelson and tv/o other observers, and at v/ide intervals of time from each other, which makes the very consistent results which they obtained even more convincing. They found that the number of light waves in a 1 standard meter was, for the red cadmium line, 1,553,163.5, for the green, 1,966,249.7, and for the blue, 2,083,372.1. They found that the absolute accuracy was about one part in two million. One of the most important and interesting problems which many eminent scientists have attempted to solve is that of the | s "ether drift". It was pointed out in the early part of this dis- cussion that there must be a medium by which light waves may be transmitted through space. This medium is known as the ether and it is characterized as an elastic solid. The problem of the "ether drift" is the question of whether the ether is carried along through space with the earth as it moves through its or- bit about the sun, or whether the ether remains stationary with 'V ■*" - - ^nJbtvlh ri beaw « 0 oiJw et^ now, ’ e»cf \WLv*i e*ui xi 6 ^ ■**■:». ‘ * - *■ .iidMiJ w vXe^^niiotMi 1c 8Eiiv<;os|w4^UI iioirJN «8 rjj elcxsuXflv oa^fii ©MaA 4.- XC' f^^.-ni»A#a- 8 «ii £i^XW s^nftr.WqX 0 - V4,;ii*via«4 45 «i **-1 »d/;3rJ»(/|oojt|2 ^RtfoaXfX^G I' tfiviv jrcc« ©ft^ ime^wd ei *Jo ©siBr’ fUiBicjiX c^»t.^* %^iOuXedoil< U *>J(jQ .cyX 6 »Di?o^ CJ irol;^afjJt|patti n j ? h»uibnMCi^ ac \o (U:sti9l olu - hvnhin*>3W‘ . ,»CU' ,©«Xd jtc.'i -.‘iJ Jo '.fiJiinaX ^.vcvr ©xu lo nR»ifi ^ al^'^-^t^t. r. *^, m te .iu»iWx*i) ^10 Xi,^iooq«* i' fc^iA hi ^at^©o-xus ©rl. «7?> (>iu fluaXtt/ioilf ^d n©7Uj 8^frl^£©•^ ©d2, .JAV?08rtdti- . . , . . . .■ ' ^ V \tr ,S ,'i<»d:it; Jiv^r^ ac^rl lo ©JbXv ;uifiVqfli9do *fa4Jo . ,<»/^ ^,,5;: riolji. ajxufiri Ja^aiiaco vi^y o At' ■ .f ’ a at «o 7 f« 'io luaoaw *«a j*,aj fcmo» Y«nT- •aai'Mivndo.wfs o t ,*>/*iX , f/ii& •J/JX'.X'iociiai jaoift' Wicf^ .|. •*aM JX'j 1 v“ fcX ©rXoft ox >ojq^©^^4t tiXfl.X4f»oto^' -oxt cijsj ^0 x*i*q \£nj^v 9dX di J^o btiJn/oq a^iw^iX ^**41l*xJ>, ‘i©jrf 4 ©¥r^ &*ti yaa it,ovT^w ,TjistX siolitx ^d r-x;XX5«m «z,‘ 04 ' //wljX rjpXoijt^» '* '® ^ 5i' v.'^yir f»iij ea'fiwcijji fifljji^e® aXxi? j>i^XrJ6'Xo«^^3rio<; . ttol^»ijso ti nbr.Jo odJ ncXXrftfp Axix a.x' •"'xlitl .qe^ Tit Mi iwcs|> aWicWM' ««, Mw *^» Ml* eoi^« iiJiw xhenoxxixa ir.fi^&mi^ 'if*dXe\^/5X^:>i8iiX©Ww .mi#, .tim - 47 - respect to the earth. It was In an effort to solve this problem that Michelson invented the interferometer. In performing this experiment, he had the collaboration of Morley, and the results of their experiment were published in the Philosophical Magazine j in 1887. An interferometer was built on a rather large scale. It I was mounted on a stone which was abouL four feet square and one . j foot thick, and this stone was mounted on a block of wood which was floated in a tank containing thirteen tons of mercury. This rendered the instrument free from all minor vibrations and made it possible to turn the interferometer through an angle of ninety degrees without getting it out of adjustment. Light coming from the source was divided by a half silvered mirror into two beams at right angles to each other, and these beams were reflected back and forth several times between a series of mirrors mounted at the four corners of the stone. By this large number of reflec- tions, the beams were made to travel over a path of about ninety feet. The beams were finally brought together again and reflected into a telescope where they were in a condition x.o interfere, and interference fringes were produced. Michelson predicted that if the ether did not move with the earth through its orbit, there would be a displacement of half a fringe when the interferometer was rotated through ninety degrees. The instrument was set so that one of tne beams of light was in the direction of motion of the earth in its orbit, and the other beam was at right angles to this motion. Then when the interferometer was turned through an angle of ninety degrees, tne two beams were Interchanged with respect to the motion of the earth. If the ether were stationary, this would cause a retardation of one beam behind tne other so erio® ^ JioiTo n^ ^1 J siisv ^'rJitnclneq 'ol \n«4o^.oai»l'Te^^^^ 644 £«4n©vM ^ i^yXueh-^ X>n^.^^4*i*xc« If .'t«i4i»nQ6o*^’5o ^{?oX . fi J1C bQ^motx •4w^«^o4o biiti »jtoiii4 Wttol* .^ti^'SUei£ If, OOQ4 rt3©4^X4J 2Mtfni^4rtoo^:iiia;^ li, lU iiift to^^C‘i4^^a^v-^Ciit^fc liij, oo'xl a«*n oflS i#Wi^T -4 •(C^iTaXa 1c #15X141 n/i rt^c'trit i^4©ttc'jtm©4ihi .%xU a*ui4' oJ %)l^dX«f^W (4©*il ^filcao v'diiX^X . «/T©tj.’x.|,»x,As Iw jpo i^i 1 — -* - ■ *' * ^ ' ■ '* '/t *1 ■^f o cwJ'oinl tM-u* i,B-»vx^e i Urt j. x,o DeWvii o»* so-itfea >i Er: a friiPxfj if'ro doxio o^ E^XiSai *■ - , V. * ■' ^ tij ' .^. -. f-prfm-Oi. -«lu.'!<:Ja to o»i,|0 * ooftwiad „oi, X^novea « Jk "’ '^A.bIs ' < Ic 'iOoRwis ©^"XJiI aXilJ” V ,^f:0JB »44 e'ten’io®' •1(4 .\;w©iiij £ »:oy^ XiAVrst o7 •wbqi ©^av dd4 ,BftGi4 fcew'uaXi©*! Liiil *io44#2jC^ 4il3uc*ui a*t«w eiltf ©dHdT lir^ .s-ot-ov-iu ci ticXJii.noo « nX .ie» odoab»lii t..^. ■ ■ ' ‘ 3s "■ ..■"i'if s*' * li :act!v- J>o„-6iXm,q noolartois .beot,|.o.„j aa'crti'.t’* ,: ••n ij ,JXcBci»t-eJni ano n*.!v *sni-it » tjt«ri io Jw,MooX•» J-s aBW.'inao tkOti- mt, ifeU \.U - 48 - as to cause the displacement of fringes. The observations were taken at different times covering a period of a year so as to make sure that the motion of the earth was not in any way affected by file attraction of any other heavenly body. The predicted dis- placement of the fringes however was not observed. The natural conclusion to draw from the results is that the ether moves along with the earth in its orbital motion, but there have been some i other hypotheses suggested to explain the negative results ob- | tained. One of them is based upon the theory of relativity which ! I assumes that a body in motion is shortened if its length lies in the direction of motion. If this theory is true, the beam of light lying in the direction of motion of the earth’s motion would travel over a shorter path because of the shortening of the apparatus in that direction which would account for the results which Michelson and Morley obtained without discrediting the theory of the ether drift. Michelson has been working on the problem during the last year M921), and it is hoped that the results obtained from his more recent work will throw consider- able light upon the whole subject of the theory of relativity. IX. Other Types Of Interferometers. The Fabry-Perot. Next to the Michelson interferometer, the most widely used instrument is t-he Fabry-Perot interferometer. It is very simple and consists essentially of two plates of glass, each one being half silvered on one surface. The plates A and B (Fig. 20 ) are A mounted on a support so that their silvered surfaces are facing each Qj other. We shall first suppose that 5 ' P. o the two plates are not exactly Figure 2o parallel to each other. Let S be ^, - .r?B> iTiol Jf vrrMUp- *«? . ^<-2s« C.t C« -«ct i. '# >u,-*-% ' 1 “s . TH ^Oo vfnf!-. ma^rtAA. i » .. . v " 'tl' a 8"b»‘%y«yvii«* jaU 4M4 ui .Miuaa, .44 Mfi-h ► »«(<<■ Va«j anaaPina V.- ■;■• .,4 . viJa^j.a ..a,- niaxq*. «j Wieajjspi aaaftr-jS^jikvi^ * t’-* *to. O-oe^iJ ttoqif i M ivit-naX-Wi IX f^aftaliortti ux xit,ifj^>a «/ 'i^d' I 4 ^ / ?U . fro/)J*rr0 lo rtOX.it • fill > .Y^k> _ -jj— 1^ * . ’ . ? ’ ■ ^ . 'fli ^ twi«B rf'rtaaw fitj '*■•- ;'i.lJ-:K 1,. otiiib-,tbia^i Rl^aixt^^ «.u l* aAiW4ieu» n«4^ciSa a sfi-f 'iftt xrijcasi 6lx)o« >fox^'no>4f.«ai&,4.nd4;i4 t« 4a»iUM» ijia.irtf M4' .r.i -,-j.^T^/,S ertt '.»ia4-i»<«MA*4n|t ,;r^aa ‘ t ' A.. ' ' -^il .■ . . fL .' ■ - » aV***^' '. -/ ' *i } t t'.'l T.ttil b — I* -a... _ . . .'flBJfliffl^*” <■* l>‘ *'V' Ji^ nj jjtijj-^.e :r*itj^q^a, .V, rw Jbo^jri^OA,^ '^ ■ I ^' ■ ‘a ' ’'>^'^tJ. fv f>*t& «e^A»Vxw» .* ■ ^ ^ . a •* jj' ' i ‘ " , G i.^- -I® i*-^ yMp uoaa. « ■4 p .f>ir - ar . ' ^ • **** '. I. ,.>>».«. , . ■ . iH,' .' , * ' J^'w, *>:. . If iXiH ^ Win ,*t J0*y nQ 'Ut^'n » ■■ • “ -Ml ’ -V \' ■ . " . T1.1 ^ I I ■ '" * C ^ ^ ' " ^ , ■ ^ ^ ■ ’.*!* ' 1 . . ^ -'S ''-f.;‘K’' ' *-.E ,0 ’if umirt a •j« , .t;4,x%’ jb^j* ^miie*tmntti wi B .k ... #• - ... ' J . .. w'.'i ‘'h^ ■': ' r f .f .la 00 .^f,>i Idhin •/5ki^ iftM., ,14 t«iU4-^i.a*4hX 6 tiiO 00 SMifp^: t> iiSiAi e -a'30fi« .’ ftfjif I'noov^ f-tiz-iJ «v«. •rfT«-.«: c« 'Bnfl .I,-(J.,14 „d4 » ir ft^plrrWni't.f CfliJiliops i. nt 4no^o't»ii4 '•■»«» j^^^,X«a;i»'^^.itn4't>n ,,T>v <1^ veUtf n*,« , X»ried'*q .#ij|§i*4o_i:q :«^ , ( WO )' jp!, Mw' i-i <;irt- .,dJ»Jjza-:to *d X/lt ■ i{v.jj \5'4i»x#-^4 j P'' 7^ ij.nr'V r^’To *'a^' '^ 6 ' , k;X ifili*: X 00 teaH ''^ '?^Cv '. •# ^ fi)t' writ ■. - . ■ <■■'> ‘'W ,. - . 'irtO rioxxvw, 50 - fringes become very dim or else disappear entirely. For this reason, it is very difficult to determine the position of the mirror P for which the visibility of Lhe fringes is lowest. But with ohe Fabry-Perot Instrument, as just pointed out, the dark space between the fringes is very wide compared to those of the Michelson interferometer. Therefore when light of two different wave lengtns is used ana the shorter one has gained half a fringe over the longer one, the fringes of the shorier wave lengtn stand out very clearly in ohe spaces between i.he fringes of the otner wave lengtn. Hence the value of N in equation OU, page 38, can be much more accuTcttely detex-mined with ohe Fabry-Perot interferometer . In using thia instrument, the light is generally passed through a prism first, and only light from one line of the spec- trum tnus produced is allowed to pass tnrough the plates, which makes the light as nearly monochromatic as possible. The adjust- ments necessary to see the fringes are however very tedious, and it requires considerable practice and patience to become accus- tomed to the instrument. 2. Jamin's Refractometer . The interferometer devised by Jamin was made especially to measure the index of refraction of gases and liquids, and is therefore most commonly spoken of as the refrac- tometer. It is based upon the principle of interference by thick plates as explained on page 26. Two plates of PlEure 21 . M ^ , . fil4v» -O*^ «I0 Jt life V> ftgg^t * '' p' liny 10 .>;j‘ ‘ili.'0.rilJtij " V * I ,. .. ' ^i"' ■* ' ‘ i' ’ ^ Kruo fcli? H#*/C^i „ul {:* , 3 ^^»^rfLn Ja/^ 4(1^05'^ «. '■^*C”«; ^‘•‘ ,,>® ''ns . . xf' “ r ^ • If* rt M ix^ imnik:k *t#rf*t'Cji‘« C0v‘rrvwX ■ — *' -^'' ' -■ t:''V,- .f "" — ■ fc* ♦ ' i' ■ . _ - ' — . t* ■ - '^, i',- 0aJ .0 (i^ '-•♦■^ '- ' -i ' _ * i ■ . i H» ' £- ■■ M. I t^ . / sQ ^x u»iviv*ii ai J045XX i'ltj rti ^ ^ apt 113; r •^> 1 ^.':* t>(ix *ft «iX;^ertC coni JiicjtXl i«^A*txV wwinqii*^ ' ' ,, - . . a . . . ' .rtl L^. Li^M<^*ia3 B%sn cj hftiroxiA ^Of!noi)iftnoof k u ^ . ‘ ' ' ', 1 ... _ -»^ /■ m . i .. ,-<' f*'. ' V '■ ‘ '•■ ^ ‘' W-" .- ^ i^ '^' ’ ■■ '*ii' ■ l/w *’ 4 ' • • •-.r* w-w * ,».v-.i . ,C3 .»*vw* i».-. ' • ,-\f;"'m\ ,_ . o.t •iUJit.t^iinv -r-i.,, AR» r„!,:,^t, t*oi»,£, ::»j.«,..*^sJu.4.Ti tniL^.il'ra ■ :.....,. .'■ . .... ";., . i. '' '.■‘.■.*ls; .01 i^iiA i^C>Ii/pJtt t}M *iga>:3 cto.f 16 x ?jXnOn: 30 P JBAS ^‘*Tfj'*.e,*f*»r *4 ^ -.aivxion •' Aj <*■£.' ip ht>;rtOQa yBni?-.a''4X J’i . la ^i:|l&ninq ♦<13 OCy^ y 1.^0 V 1^. - K ' :■ ,'/■'% X S.Si c’ / ■i- f a. ^ ’ 'll' - 51 - parallel surface glass of equal thickness, usually about one cen- timeter, are mounted parallel to each other on an optical bench as shown by AB ana CD in Figure 21 . The plates are mounted ver- tically, so bhat in the diagram, they are shown as perpendicular to the plane of tne paper. Each plate is silvered on its oack surface. Light from a source S passes through a lens which causes a parallel pencil of rays or v/ave trains to fall upon the plate^ AB at 0 at an angle of forty rive degrees. Part of this light is reflected from the front surface over to the point P at the front surface of the second plate. It is here transmitted to the back surface where it is reflected downward at Q and emerges from the plate at R. A second part of the light from S upon striking AB at 0 is transmitted to the back surface where it is reflected at M to N of uhe front surface and thence to R on CD where it is re- flected again. Thus the beam from S is divided into two beams as they pass through and between tne plates only to be reunited a- gain as tney leave the second plate at R. Now if AB and CD are rigorously parallel to one another, the paths or the two beams will be equal to each other, and tne beams will emerge at R in the same phase and therefore in condition to reinforce each other. In this case, the field of view will be uniformly ill-uminated, provided the plates are perfectly plane. But, suppose that the plate CD is inclined to AB by a very small angle. Then the path of the wave train OPQR will be slightly different from that of OMNR, and they will emerge at R in opposite phase causing inter- ference fringes to appear in the field of view. The plate CD is mounted in such a way that it can be controlled by two screws, one of which moves it about a vertical axis while the other moves it about a horizontal axis. These screws are graduated so that -MPT. Bil’i’ , JW b‘U,l3i» c*i4» ,,.>vx3«aA nl aJl i:o i)u’t^P-l’fO tti f ■^j.«‘<; 9iw »»o px«f r,p |1,1C0H '«. *1.^^ H • f . ‘ 1 ''■ ■! ■ ', ■ '* ;‘y ynH'fifV ^'< 1/'*^ t*vii xv^oi ^^.1 4 Bit-1 ia i»^ *i^,’c »9ii'Vf]uia ^r.o*5l «4tJi *lo4* , trt V” .,^Ot o# boJ,;ls«p-i.),,^^,.i JI .»iti, * ' * V i . .a ■ . . ‘ ". |i i ^O'lX 4M3*1#J0« L^'- ,4 '•4-.. h § i. i ..... «^ ‘ . '■' * ■-■^. '- . - .w'J^ ► ^tfii. *iJtt rXft^ H- ii .it’j^^J ^f A.,K 4 ji " . ‘', ' . '* t • «»V' v-:^.«i'i O i ji .-i riaiipi ao iio .n c??. ores . r/-' «^o4 o^ni b&£Zyi-b a£ ^ «\oni' «>:-ia »rfi ;nia3;jfloo*a Siiv ^v#>aXi ^•-' W-p4«^.tb:;-,'KJ«f ,i« ;-£*.Mr.p^ »;,o Oi "di K JU, -*S'!friv». Xliv OI.'B?a uOi biu< .It Vft^O ^ii 4 'O-uJ^^ .i4Xi>r,«o .ni vn«Viti»^4i;j^4 «V ti.iu !dio<(*y,« ;j;S >a,,XT JJOrtV'q bip- nojplq;^ ,jjj«q Pi., .*J;wii,;_jtjA»i vH,/i’;,^ gx -aj Ic tfsi»3.^acv^ Jjto-jfl-rtlti fX3jJaiXpi,^rf: ■''t^iat s<^i8uao pnp/itj .93i'so5#iOvnl ’;J.4 « jypiii'EjpS^pO* .^i flO>3»XaX«.^»v'^ Jf«oj3«, .rXf.a^voB-x^^a !»; «■ a l' -1 . - 52 - the angle through which the plate moves can he read directly from the Instrument. If the instrument is adjusted so that the fringes are seen, and a piece of glass is uhen placed between the plates | and in the path of only one of the beams, this beam will be re- j i tarded by the glass, and ohe fringes will be displaced a certain j amount as the result. Jamin made use of this fact to measure the 1 j J index of refraction of various gases. He placed a tube contain- ing a gas, the index of refraction of which he wished to deter- mine, in the path of one of the beams, say OP, (Fig. 21) which retarded that beam a certain amount behind the beam NR thus causing a displacement of the fringes. Now by putting a piece of glass of the proper thickness in tne path of the beam NR, it could be retarded an equal amount, so that the fringes would be returned to their original position, or if tube and glass are placed in position at the same instant, the fringes would not be displaced at all. Then, the index of refraction or the glass be- ing knov/n, the retardation which it causes can be calculated. This will be equal to the retardation caused by the gas in the tube, and from this fact, los index of refraction may be deter- mined. The glass used (G in Fig. 21) is known as the compensa- tor. It is evident that for different gases, the compensator would have to be of different thicknesses. It would be a very tedious process to try one piece oi glass after another until | one of the right thickness was found. Jamin' s original compen- sator consisted of a single piece of glass mounted upon a vertical axis. By turning the plate on its axis through an angle, the thickness through which the light passes could be varied as rf ■ •? ^..., ■ - V' ,Li :>.' -- '7 ;. 5v x*6(iri s '* ■ -ttli .<» v.« ,aoc«, 5d |5 , H« ag^ g,u . K#.r.o«. g ^ ^ -■i »s»jt;j..-.p «ifi»j.,r Tjc .iir.jji.j-ii g,jg *ii 'j : v.,4i .*K 5- ni :iiU a» ■■4. V-?^ 'j’ut uftjBXa } -44 e.«af ,0 flox,«ai4, »t .,<.aT^ ';it* .taggfgou.o »(J nkj e»,x,«g- a xigj-.y Kk sn.} in ^iU y^ii otit illkJNi. ^ ' .4 -' • *tl -.^a>a,qi,fa6. gif’;: gWu^rt * X I ) S „i’ S) bu«« a4«ta I0jj>fi9(j«g6 -grt,. ,*.oax,a Jn.rrsnxi, ■-:mv a. t.g i>^o# .» .ntuif iwa.-rfi. * l ' K ' ^'*- ■ ^ *7 ■ '■ t’ J ^ ^’Tl ^ ^ \ II ■.. it i iT^ «« >1 1 8 oXcgi, .t'rtyij'I te» iauhi^oitUt ‘i/tj^-i <>rtJ*l'?|oao 34 5^' T'’ ‘ -ifia IX.. - * ■ . ' •'■ ' '.' ^ -"I 60 ^Xq ^l^iU'u i> (?^JiU€no^» , ^ - V' ->', . ' ’ S- ■' • KiXjft X«:.ij*:rvx^A nor^i/ Wmiboi , ^ '. *, > I r:‘ s • *'' I *HK y .• 44X ;rd g.t^anXfl'WJ x« £.3r*l« . ^ t 1 f' ’ ' !~ Ji tii 1'^. "J. 1'’ ,'.'>ak- 1 1'.' , , I : .^'.t£- 3> ; ti'. - 53 - much as desired. A better form or compensator is illustrated in Figure 22, It consists ol* two very slender prisms whose angles are equal, and which are placed one upon the other so that their edges are opposite each otner. In such a position, they form a parallel plate, and by means of a screw, one prism may be slid along the otner thus varying the thickness of the plate at will. Such a compensator can be calibrated for the various relative positions of the two plates, and when calibrated, it is very use- ful in making experiments with the Jamin refractometer . 3. Lodge's Interferometer. The principle of the Lodge interferometer is easily under- stood by a study of Fig- ure 23. Three glass plates AB, C, and D are used and set up as shown. The plates C and D are in- clined to AB at an angle of forty five degrees. The plate AB is half sil- vered on the surface next Figure 23. to ohe source of light S. C and D are heavily silvered on their front surfaces. Light from the source S strikes the half mirror AB at P. Part of ix. is re- flected and passes along the sides of a triangle between AB, D, and C as shown by the arrows. The ouner part is transmitted transmit ued through AB at P and passes around the same triangle but in tae opposite direction. Both wave trains, after passing around i,he triangle in opposite directions, emerge in the same direction at 0 in a condition to produce interf erence . The fringes r-': . ■ ', . -:ic -- ■!™i ■,'« , . ,t y> B«>i il* L •J»'.n»Xe ,tH»v C1KJ X« JUrtu uj rrij, o,_^ toiiaiq .,4 rtc-i«iir. ** ,XJ<«t3i^v ,H * i?‘i jv* « •^c^ ,'no{JXo«} t: iioi/^ .-ibwb jir- ■ 'aJiaoaqo, in4i«riai,» i i Wj.8, »a t«» •ii’tS eno ,.»no« # W .o^JaXi I»XX*'5i^Ji .XXIw M tfjrx\ V'.? f? tl ib6firtlUx> K»4Kt .!;«« ,ti *i;i:.S, ti»XJteo(3| . ' ■ Ik ^ •• •j, ^ ^ r,’ ' , -^•. iXJ«a« -t. \M,..„t *84 u ohllo^tn *»f^S ■ ‘ '■.vj'..,.. r o* Xpij^^c #* t^OSh ' *-. C"' 4'^i!w 6»«i/ a fiKUi ,0 ,64 «*4T .rtfo4n eA qjj ,tna ' -ni. ♦‘iii :; 0 f^^ikXri |s*,*M:4i4£ rta 4* ftA C4 . fvi'i *)o ->^4 llail i ai M<’-i -^ilT || J' ■ ' a ’wfc, ii»t^ \^nn-jv r rr V'"^ . •'.:i ' ^ I > .4 3 ^(i ! ' ' ' fi V, f y-'v' * - M i'4 ... *^^ a. y 0 U iU 41C XU vAi^- iX p ’^ . ^s*il it'vi,.t ' . ^ *o«l4ua "ft i' ' ^*"‘ •- ••! .^>4 gi TO'iit'a^ U«d #UJ P’ ■ r T ■' 'a '' '^' ■ ,.ti .,-. .B«**x«s-.jjX(ca(ii-j, ,i J^JXJ gjjj, ,a#c'*«, ,414' i^d*'nif080S(aa I . . " .V .rV: ’ . ■ J ' S'" f rtL ,8 ■ ■ . -. •Ji^ins torn % tfa 0A li«?4xstn^Ti/ ^a^frtiQ M».i'u> ,anifi,aa, rtSc«.’3.ftoXXoEr;X4 WlaoiKio anx ni-iul:| , ,t.»*^, aij? nX aaTaau , iiX!oijoaiX.b e/Xsoqijc tiX ‘*j;8£y^lj arfx •l.«f'» . 4 _ I _- . ► 'J-. . .“ ,. 5 l ( '■.* - 54 - are seen by the eye through a very small opening such as a pinhole, or elseby means of a telescope. When C ana D are exactly the same distance from the half silvered surface of AB, the reflected im- age of C will appear to Lhe eye lo coincide with D. Now if C is moved forward a very small distance, there will be a virtual air wedge between the image of C and the actual surface of D. Inter- ference is thus caused in exactly the same manner as with the Michelson interferometer, and the fringes formed will be either circular, vertical, or horizontal depending upon the angle be tween the two mirrors C and D. Lodge used his interferometer in an experiment to determine if ohere is an ether drift. He mount- ed the instrument betweentwo circular steel plates of large diam- eter which were whirling as rapidly as they could be made to whirl without Hying to pieces. If the ether was given a motion by tne spinning disks. Lodge predicted that there would be a dis- placement of the fringes seen in his interferometer, because the velocity of the light would be accelerated in one path and re- tarded in the other by the moving ether. But after all spurious effects were done away with, there was no displacement of the fringes observed. The conclusion was that, there was no drag of the ether along with the moving body, at least in tne case where such a small moving body was used. There are still other types of interferometers which might be described here, but Lhey are all based upon principles very similar to t.hose already described here, and none of them is as widely used as the Fabry-Perot and Michelson instruments. One interferometer manufactured by Ph. Pellin of Paris is known as the Fizeau instrument. It makes use of i-ne principle of Newton's rings, and is principally used as a dilatometer. Another inter- li -r - Jr . < d* ■ V •^.TrT-vjv ACA’’ , ^ ,,,, [ Y 46 i/o , atiosetijitf « »Vu 4 a ^ Tt'.- ! . -bXIt'j :c ^>o•x»vJiK ?io 4 : - -j .c>K,<: an* »bioiUi>^ «j ,<» oJ -j«.»(j^. xXi« 3 P tic /Cca-Xv « «:J Ul«-.. ■J.lj.,.. 0 --S 3 &t*. -.^InS .3 '.0 •iia 4Jm> 0 lo 'nfWj*e J .vJ-» tvrtjun .»J» »Ol!iUats;K» nl tagta, ai eo^-ioi; _ • ■ J baTUiw fc.u.,ol 8 rtJ t.ra, .. 04 »Xj.v jiiJ >eZi>^u6 X'.1 :,.■ fu.,> ,Q tJ; SK .Jll'ifc '.xia;* A*. Di wnv 4 . '!! -lAsi^re t^i) n/i ■, ,li.: J f * » I***. . 4 - Ow *-/)®nJt*n>qxd=, n/i -t it, ic «»»,i:i,; n t Jt iaJ.'on3s'e«3iw.«*-.*sc aricca ,jiv bajsXi e'Kt w^u,j jiaraixli '^iiJ »f“ . if4©a?i'«.V..ctnX ai.i rl flees -ic mixj iist'ri ®d i)Xi/on^ dd^x axij'^i^ X£v \ts.;U' :i. .n* snXt^ow t>irj *idxUo nl [ . •ai '.q'4u«<-!,.-i,,«ii, ,4.v *.|,.*s ,m/» ^4B4, eiiesvlie*! aieori«f' ^ i rr f..,w unefl# jw .,•./» flcXatfXittoe eaf . yWe'!^^ ,, _ 4 '.-.-...e oSBi) j,..,» o£ ioaex 3 „ J^Jv<;* ».it 4 < 1 #' ' r :'-,,iV’ ' I ' ' . w^lku cjiilVCift* iS J . ■■ ^ ■ k r£- f iloXiiw u'iej«rao-ptTr^j/fX 1 -iXqX rriiq /♦fl.-u XX« »n^ . . '». ,,W , «« f BtiiU :r- t5.4> m/6/v< iX 9 l*xc*i ■V . - , W. -In .. *X '■ ’$ . . .• ' « i' rt.’"? ' >\ ^•••,. , , , 01 . .^1 . - ■-. ' ’■> . . •■ a 4 ft. r ‘ >’. '■■■■* — ,.-. -' ...-r.ai -.la.. l: - - .. »'!&«*», 9 (niMx\ I Liin ji,-Lj^*i|isd . V' i ' "■ - 55 - ferometer due to Lummer and Gehrke is similar in principle to the Fabry-Perot instrument except that the multiple reflections are made to take place between the two surfaces of a single plate of glass rather trian between adjacent surfaces of two separate plates. X. Conclusion. Books might be written upon the subject of interference and its applications and measurement without going over the same material twice. It is hoped that what has been presented here will acquaint the reader with the elementary principles and applications of the interference oi light, and that a desire may be kindled in him to explore furtner this interesting field of Science. For further reading on the subject, the following books are recommended: Michelson - Light Waves And Their Uses. Maclaurin - Light . For the more theoretical aspects of the subject, the following are good: Edser - Light For Students. Preston - The Theory Of Light. Wood - Physical Optics. For directions as to performing various experiments in inter- ference, see - Clay - Treatise On Practical Light. Mann - Applied Optics. The original v/orks of Young and Fresnel are very interesting for the light which they throw upon the history of interference and of the wave theory of light . » • I ■i i rtriiiBia w ) I H I .lAmfciaa ■/' ■ ,*. inW: ■ ■' ^ i ■»“ <.: ..f .„n ja- .. '?■ WtM rf s*i •'■ ' .J . •' '>■. 'E'.::,! ■ t %f 4 'ij|Tde(ro 60 a S;6eo, % 'icd? ittiysV **v. . S.tl»!ii:o-! ij„- , J-Jt.il, „,. io.,ja*a»a j»4i-.,»-toii' ' •'^rfJSii - gl'iiar^K' .. - L' .•‘fi :'« ' .''i-S5.. }'i,i VajV.)(qU t ' V .'S '(j-- ■■ tQf: u,rf 3 ia. . ■^ij)’*».iT <»a? . j i«»t> !'^' 4 ^ -v, 4 J^bq 1 •“. -•j -j ;i «>tf«;aw ajjimc ,«.i ■•'(if ', ' .atfXJ^C ifoJXqil* . flfllS^^^ .-.C^ Uti,y ' 6 '>* tnc.uXji w|i|a . 'V ' .^' ■ ■' i!*’ ■’ " - 'I, - ' ■tm r. •. • ■* * < * i -to ';>^{.>6j:ljd -fevAy* 'nU »i.r '*r' T— - '• - 56 - I wish to acknowledge ray indebtedness to Dr. W, F* Schulz of the Department of Physics of the University of Illinois for many valuable suggestions given and for his interest in the work of preparing tnis thesis; also to Professor A. P. Carman, head of the department, v/ho suggested the topic and gave me much en- couragement during the progress of the work. FINIS *”C ' • ■■ ■*'^»lll|a'''''*".'r' ■ n-‘ *• "i -i . C ' ■. ,'ti :■ i^l^' - ' v7,. 'J ». • y --'■[■"fir.' *.■■■:. v'i^. j^'*^'itf"■;.,£ '^'-■ cK*ih 9 ~ \'«. V ^ 4^' * Jr ■ ■'•• \ • N 1 fEtT >4 • ^ 1 -'^r* vf,t t *v 7 -,^ ' / ‘T^-' ‘''^y^*- . V I /I V' ■ ''.i' . ■".,?5