Class 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference
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1 Thi Film Ierferece Thi- ierferece Ierferece ewee ligh waves is he reaso ha hi s, such as soap ules, show colorful paers. Phoo credi: Mila Zikova, via Wikipedia Thi- ierferece This is kow as hi- ierferece - ierferece ewee () ligh waves reflecig off he op surface of a wih () waves reflecig from he oom surface. To oai a ice colored paer, he hickess of he has o e comparale o he wavelegh of ligh. Phoo credi: Mila Zikova, via Wikipedia 3 Thi Film Ierferece There will e cosrucive (or desrucive) ierferece if he effecive pah legh differece (PLD) ewee he o. wave (reflecio from op surface of he ) ad he o. wave (reflecio from he oom surface of he ) is a ieger (or a ieger plus a half) muliples of he wavelegh of he i he, where vacuum 4 Effecive PLD due o reflecio a a ierface Whe ligh ravels from a smaller refracive idex medium owards a larger refracive idex medium, reflecio a he oudary occurs alog wih a phase chage ha is equivale o a effecive PLD equal o oe-half of a wavelegh i he. Case : < Effecive PLD due o reflecio a a ierface Whe ligh ravels from a medium wih a larger refracive idex owards oe wih a smaller refracive idex, here is o phase chage ad hece zero effecive PLD upo reflecio. Case : >
2 Wha kid of ierferece? I he figure show elow, he hickess is exacly oe wavelegh, so he wave ha reflecs off he oom surface of he ravels a dow-ad-ack exra disace of waveleghs compared o he wave reflecig off he op surface. () () Wha kid of ierferece? Eve hough he exra disace raveled is a ieger umer of waveleghs, we ca see ha he refleced waves ierfere desrucively. This is ecause he wave reflecig off he oom surface is ivered, which is like a exra half-wavelegh shif. Wha kid of ierferece do we ge ewee he wo refleced waves?. Cosrucive. Desrucive Simulaio 7 8 Thi s a sysemaic approach Le s use a five-sep mehod o aalyze hi s. The asic idea is o deermie he effecive PLD ewee he wave reflecig from he op surface of he ad he wave reflecig from he oom surface. The effecive PLD accous for (a) he exra disace of raveled y he wave ha reflecs from he oom surface, ad ay iversios upo reflecio a he () op ad (c) oom surfaces of he. 9 3 Thi s a sysemaic approach For a wave ha ges ivered whe i reflecs, ha is equivale o a half-wavelegh shif. However, we have hree media, ad hus hree differe waveleghs! Because we re ryig o mach he wave ha goes io he wih he wave oucig off he op, i is he wavelegh i he, λ, ha appears i he equaios. 3 0 Thi s he five-sep mehod Sep Deermie, he shif for he o. wave reflecig from he op surface of he. If >, If <, (This is wha is show i he drawig a righ.) 0 () 3 Thi s he five-sep mehod Sep Deermie he effecive PLD for he o. wave reflecig from he oom surface of he. The we should add his o from he exra disace his wave raveled i compariso o he o. wave. () () If 3 >, This is wha is show i he drawig a righ. If 3 <, 3
3 Thi s he five-sep mehod Sep 3 Fid he (oal) effecive pah-legh differece: Sep 4 Brig i he appropriae ierferece codiio, depedig o he siuaio. For cosrucive ierferece, m For desrucive ierferece, ( m /) Sep 5 Solve he resulig equaio. The equaio geerally coecs he hickess of he o he wavelegh of he ligh i he. vacuum I is ofe useful o rememer ha 3 A example usig he five-sep mehod Whie ligh i air shies o a oil of hickess ha floas o waer. The oil has a idex of refracio of.50, while he refracive idex of waer is.33. Whe lookig sraigh dow a he, he refleced ligh looks orage, ecause he hickess is jus righ o produce compleely cosrucive ierferece for a wavelegh, i air, of 600 m. Wha is he miimum possile hickess of he? 4. Sep Sep Deermie, he shif for he o. wave reflecig from he op surface of he. Which of he followig is a suiale choice for?. Air 0 Oil Sep Sep Deermie, he shif for he o. wave reflecig from he op surface of he. Which of he followig is suiale for?. Air. Oil Waer 5 Waer 6 Sep 3 Sep 3 Deermie, he (oal) effecive pahlegh differece for he wo refleced waves. Which of he followig is a suiale choice for?. Sep 4 Sep 4 Brig i he appropriae ierferece codiio.. m. 3.. ( m/) 7 8 3
4 Sep 4 I his siuaio, we were old ha he hickess was he miimum ecessary o give cosrucive ierferece for a paricular wavelegh, so le s go wih he firs choice.. m Re-arrage o ge: ( m/) This looks like desrucive ierferece, u i is o! ( m/) ( m /) vacuum 600 m ( m /).5 ( m / )(400 m) Sep 5 Fid he ukow asked i he quesio. 9 0 Sep 5 ( m/ )(400 m) To fid he miimum, use he smalles m ha makes sese, which i his case is m = 0 mi (0 / )(400 m) 00 m 00 m mi A soap We make a soap y dippig a loop io soap soluio, ad he hold he loop so i is verical. Why do we ge horizoal ads o he soap? Graviy causes he o e hicker a he oom, wih decreasig hickess as you move up. Differe hickesses correspod o differe colors. A soap As ime goes y, he ges icreasigly hi, wih he op of he firs goig whie/gold, ad he lack (o-reflecive for all colors). Why does he go lack a he op efore poppig? (Use he five sep mehod o aswer his quesio.) A soap Sep Deermie, he shif for he wave reflecig from he op (or fro) surface of he. >, so Sep Deermie, he shif for he wave reflecig from he oom (or ack) surface of he. 3 <, so 3 4 4
5 Sep 3 Deermie differece. A soap, he effecive pah-legh Seps 4-5 Wha happes i he limi ha he hickess,, approaches zero? Whe 0, he effecive pah-legh differece, 0 - / = - /, givig desrucive ierferece. Tha s why he appears lack. 5 5
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