! " # $ %'&)(* * + * ,.-0/2143657/98;:</98=/#3?>#/!/A@B/9>957CEDF/!-0GIHJ/!K4LML NO/#P*GQ5RC=L :SGJ8T-0GIHJ/!1436HJL KUHJ/#P*C;V0K41W5=571U30XY57-0/ DFG H /9:<8;L 365RZ0VB[\C;/#30P?1430X]V^GJ8;5_LJ:`57-0/ DFG H /9:<8;L 365 GJKUL 30XaL 30/bV^GO5=-cGO30PcLJ5=-0/#8 V^GO8;57C GJKUL 30XdGdP01W@B/98=/93e5fV^GQ57-g[EGJ30Ph8=/9>#L i!j?14301U30Xk57-?/#i 5=L V?8=LMP0Z0>#/lGO3h1U3657/#8m:</#8;/#30>9/ V^GQ5=57/98=3gn oqpsr.tmu vkwsx y0z { |}z`~R z x y0 \ m~R x hx"~ m~Fy0z ^ z ^z`~R z z = z By ,.-0/98=/ 14C GJ3 GJKU5=/#8=30GO571WH / D G LJ:TC=V0KU1U5=5=1430XlL 3?/ C;14X 3^GOK.143657Ll5 DFL L 8ai]LJ8=/ j6 P01WHM14C=1UL 3 LJ:0GJi]V?K41U5=Z0P0/On 3b:SGJ>A5 DF/s-^G H /FGJK48;/ GJP? T/#30>9L Z03657/98=/9P!143657/98;:</98=/#3?>#/sLJ:?5=-014C Ne143?P 143*L Z?8E578;/ GO5=i]/9365 LJ: 57-?/Yj0K4LML i 1430XaLJ:sK4/930C=/9C#[gLJ8R eZ^GJ8;5=/#8} DFGIHJ/ai GO5=> -0143?X0n ,.-0/98=/ j6 aGJ8;87GJ30XJ1430XT5=-^GO5 5=-0/.V^GO5=- KU/#30XO57-!57-?8=L Z0XJ-a5=-0/.i]GO57> -01U30X K G J/#8 DFGJC"-^GJKU: G D G H /9K4/930XJ57- GO30P]D 1W57-]5=-0/TC=GJi /TV0-^GOC=/T> -0GJ30X /ELJ:g GQ5F57-?/E8;/9¡^/9>9571UL 3 :<8;L i 57-0/ :<8;L 365 C=Z08m:SGJ>#/ GO30P!57-^GQ5"GO5 5=-0/.j^GJ> N2LJ:^57-?/.i GO5=> -0143?XRK G /98 ¢Sj\/#>#GJZ0C;/.143Y/ GO> - >#GJC=/ 5=-0/ 8=/9¡0/#>95=14L 3aDFGJC :<8=L i£GO3]L V 5714>#GJK4KW bi]L 8;/.P0/#3?C=/_i]/9P014Z0i ¤¥D¦/E>9L Z0KUP >#GJ30>9/#K^57-0/ 8;/9¡^/9>957/9PcC;14X 3^GOK§n ¨ /2GO8=/ X L 1U30X!57LaK4LML N]GO5_C=/AH /#8=GJK P01U@©/#8;/#365_1430Cm5 GJ3?>#/#C LJ:¥57-?14C./9@©/#>A5 n oqpsr.t p ªe~Fy?z ^ Az ^z¥~R z« A ¬ m~R sz¥ ¯®¥°S± ² ³µ´ ¶!· ¸T¹Bº©»`¼^½ ¹Bº\»g¾B¿ À ¶2Ág¹ Â?½IÁB¹\¾ ,.-0/ >9L i i]L 3?/#C;5 C=1U5=Z^GO5=14L 3q1U3qD -014> - D¦/ C=/9/b1U3657/#8m:</#8;/#30>9/b/A@B/9>95=C_1UC 143 L 14K©L 3q57-0/ C;Z08;:SGJ>9/2LO: V0Z?P0P0K4/9C#[¬L 8 143 5=-0143fC=L6GOVfÃ^KUi]C.LJ8_C;-0/#/A57CELJ: i]GO5=/#8=14GJKgC;Z0> -*GJC_i 14> GeÄ [ Å ÆÈÇÊɵËAÌ ÍFÎBÏ7ÐIÉ Ñ ÍmÎgÒ§ËAÇ!ÉSÍmÒ ÓQÏAÔ ÕTÒµÖQÍFÎgÏ7×AÍsÒµÖ¯Í;ËAاРÙ#Ú¯ÛÜÒ§Í.ÉSÛÞÝAǯÛàßOÔ;Ï Ç#ÒµáÞÐAâsãQËAØ Í}ä¯ÏAÌFåQáàÍ9æeÖ¯Í çË è Í;ɧ֯Ô}ÛéاɬÛÞÓOØ Ï7Í Ð ç É;Ò§æAÖ¯ÏAÍ Ç Ô}Ë9Ï áàË9áàҵگ֯اË9É0گɵÝAÍmÖ Í;ÇFÖ¯ÛÞÍ Ç¦Ö¯ÒµÛÞÖ¯Ì.ÛÞÇ ÉSÍ;ßQáÜè6áÞÌ Ç¯Ë É¬Ë èOËAÚ¯Ì Ó¯ÛéÒ¬ÔmÏ ØµÍ=ÏAÏ É^áÞÛÞê Éµß¯Í Ò§É¬ÒµË ÖOèOÏ Í=Ò¬ÏAҧɵ֯РÛÞÉ\ÒµØ Ô}Ï ËAÇOÇOÉSÉ<Ì Ò§ÛÜÛéҧɵÚIɵҵÛàÍË9ǦǯÏAÇË"ç Í}äIصÍmå¯ëQáéÏ Í;ÇOÔ}ÒµÏ ÛÞÒµËAÛÞËAÇQÇê ÛÜÒ?ÎBÏ9ÉeÍ;ǯËAÚ¯Ý9Ö çÒµË ÉµÏ ÒµÛéÉ<èìÐ Ö¯ÛéÉ áàÍ=ɵÉMÝAÛàèíÒµÍ ç ÉSÚOç ÔmÔ}Í=ɵɵËAØ É èìË9Ø?ÏAç ÓOË9ÚIÒ?Ï ÔmÍmÇ#ÒµÚQصÐ9âMÆ Ò0ÎBÏ9ç ÉMîgÖ¯Ë9Ì Ï9É6ï¬Ë9Ú¯Ç¯Ý ð<ñ òAò ó ô§ñ=õ9öA÷9ø Î ÖQË ç Û ç ÌsÚQÔ ÖTÒ§Ë.èìËAØ Ô}Í Ò§Ö¯Í"ÎgÏ7×AÍ Ò§Ö¯ÍmË9صÐEÓQÏAÔ ÕEÛàÇ#ÒµË èWÏ7×AËAÚQØ;âBÆÈÇ Ï.áÞÍ;Ô Ò§Ú¯Ø§Í ÒµË.Ò§Ö¯Í ùË è?Ë Î Ð9ÏAÖQá Ï úIÒ Ë Ö¯ÔmÍ ÛàÍmÎgÒ<Ð ÏAÛàÉgÇ áéÏ ñ;Òµõ9Í;û¯ØBñ Òµæ Ë.ÍmÇ#ÔmÒµÏAÛàáàÒµá6áÞÍ ÛÞÇ#ç2ÒµÍmügصý.èìÍmاþí ÿ ÍmÇO Ô} "Í ÿ!^ "ê # Ö¯ Ím ÇE Ò< Ω =ÿI Ë þ $¥ Ç ý Ú¯ áéÏ Ò§ Ûà Ë9 ÇQ Émæ æAèìÖQاÍgËAÌ ÉSÒ§Ï Òµ Û Í % ç ÍmاҧÍmÖ¯Ç#Íg'Ò å¯&`صÛÞاÇQÛàÝ9ÔmÛàÛàå¯ÇQáÞÉ;Í æ Ô}Ë9ÛàÇQÔmÛ ç ͦÍ;ÛÜÒ§Ö¯ÍmØ åJÍmصèìÍ;Ô}ÒµáÞÐ ËAØ ×AÍ;صРÇQÍ;Ï Ø§áÞÐ Ûà)Ç (¥ÛÞاÍ;Ô Ò§ÛàË9Çeæ ÒµÖQÍmç ÛÞ+Ø *<ËAÛÞÇ9Ò ,Í %JÍ=Ô Ò§É Ûéç É .Ï -©ËAÌsÓQÛàÇQÏ ÒµÛÞËAÇ Ë è0ÒµÖQ Í / ËAÒµÛÞËAÇQÉ¥ÓOÍ;áàË9ǯÝAÛÞÇ¯Ý ÒµËEÍ;Ï9Ô Öeâ ê $¥ÇIèìËAصҵÚQÇQÏ Ò§ÍmáÞÐAæOï¬ËAگǯÝ_ÎBÏ9É Ç¯Ë Ò Ï.ÝAË Ë ç Ô}Ë9ÌF̦گǯÛéÔmÏ ÒµËAØ=æ Ï Ç ÍmاÌ.Ï Ç¯ÇR×AË9Ç ÍmáÞÌ Ö¯ËAáà2Ò 1¦Î صËAÒµÍ ËAè0ÖQÛàÌ ê Í"ÎBÏ9É ËAÇQÍ Ë è0ÒµÖ¯Í¦Ì Ë9ÉSÒ¥ÏAÔ}Ú¯ÒµÍ"Ì ÍmÇ Î ÖQË Ím×9ÍmØ áàÛÞ×AÍ.ç ç 0 æIÓ¯ÚIÒ ÖOÏ ç ÒµÖ¯Í Ì 0 ÛéÉ<èìË9ØSÒ§Ú¯Ç¯Í Ë ÓOÍ Ò§Ë#ËFèWÏAØ ÛàÇ 0 Ï ç ×7ÏAÇQÔ}Í ËAè Ö¯ÛéÉ Ô}Ë9Ç#ÒµÍmÌ åJËAØ Ï Ø§ÛàÍ=Émâ?îgÖ¯ÍmÐEáàË Ë9ÕAÍ ç ËAÇYÖ¯ÛÞÌ Î ÛàÒµÖ Ï9É<Ò§ËAǯÛéÉSÖQÌFÍ;Ç#ÒsÓ¯ÚIÒ Ô}ËAÚQá ç ÇQË ÒsèìË9áàáÞË Î Ö¯ÛéÉsÓJËAá ç ɵåOÍ=Ô}Ú¯áéÏ Ò§ÛàË9ÇQÉmæ^ÏAÇ ç ÒµÖ ÚQÉFÏ Ì.ÏAÉ§É Ë è?Ö¯ÛÞÉ ÌFË#É<Ò ÛÞÌ åOË9ØSÒ Ï Ç#ÒgÒµÖ¯Ë9Ú¯ÝAÖ#Ò§ÉgاÍmÌ.ÏAÛàÇ¯Í ç Ó¯ÚQصÛÞÍ ç Ï Ç ç èìË9صÝ9Ë ÒSÒ§ÍmÇTÛàÇEÒµÖQÍ 2 ý , "3m4þ 5 ý 6 7 þí ÿ 8 " 9: ;3, 5mþ< æ^Ú¯Ç#Ò§ÛàáBÏ áÞÏ ÒµÍ;ØsÝAÍ;ǯÍmØ Ï Ò§ÛàË9Ç2Ó Ð!ÉSáÞË Î ç ÍmÝ9صÍ;Í;É"ÏAصاÛà×9Í ç Ï ÒsÒµÖ¯Í Ø§Í ç ÛÞɧÔ}Ë ×9ÍmØ§Ð Ë è Ö¯ÛéÉ =?>A@I B
Interference - the oil film
air oil
h
water
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C D=?>A@ <BAE The phase change in the reflection in air from the upper surface of the oil is π; the phase change on reflection at the oil-water interface is 0. F=?>A@ <B takes G= Iplace H Constructive interference when the total phase difference between a Jray reflected from the surface of the oil "and K a ray which LB Nhas M passed into the oil and been reflected from the water is an integer multiple of 2π. Given that the phase changes on reflection differ Tby S π for the two rays, this requires the path length in oil to be an odd half-integer multiple of the wavelength in the oil. The film is observed at near-normal incidence, so we may take the geometrical path length in the oil to be 2h.We therefore seek a B Z a ]_b B [1Z \ .]_^`U λ WVYX >ASLU. WVYX > c \ ]_^ wavelength λ in air which satisfies 2 h p> 2 n oil Oilfilm.mcd 1 21/03/99 16:35 dV
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¢ Ä ¤ /9 MZ0GJK 57L > [ n yAy:@ [ n 0[ nm> i]1U>#8;L 30C#[ LJ8 i G K 1Ui G]:<LJ8 GJ148ED G H /9K4/930XJ57-?C2LJ: P?[ B ["n y?[ n :P!i 14>#8;L 30C ,.-?14CFD 1UK4KBXJ1UH /RGÊ /#KUK4LIDh:<8=143?X /Jn z 3 57-?/ LJ57-0/98 -^GJ3?Pg[^G!57-01U> Ne30/#C;C_LO: Q?nmMA>AMÊi 14>98=L 3?C D 14K4K©X 1UHJ/ >AS ¢ VYX Ä ¤ /9 MZ0GJKF57 L >M<n B G[ Q Nn @ G[ Q n h>MG[ Q?mn P*i 14>98=L 3?C#[ L 8! GJ148bD G H /9K4/930XJ57-?C]LJd: P <n B MM [ B mn QAM G[ Q? n yAP?[ Q?n hM [?X 1UHM143?XaGai 51 KM5=Z08=/ LJ:¥ /9K4KUL¯D GJ30Pfj0KUZ0/Jn z 30>#/_57-0/_Ã^K4i)j©/9>#L i /#CsH /#8m ]5=-0143B[e5=-0/#8;/T1UC¦30L2V0-^GJC;/TC;-01U:È5FGJC¦G28=/9C=Z0KW5FLO:g57-0/ 5=-014> Ne30/9C=C#[ KU/ G HM1430X L 30KU 5=-0/YC=-01W:È5RLJ: j\/95 D¦/#/93 5=-0/Ê:<8;L 365 GJ30P j^GO> N 8;/9¡^/9>9571UL 3g[ X 1WHM1430XaGYi 14301Ui!Z0i LJ:`8=/9¡0/#>95=1UHM1U5 ] "57-0/ Ã^KUi GJV0V\/ GJ8;C.P^GJ8;Nq143 8=/A¡^/#>A571UL 3gn ,.-0/¦C7GJi /"V0-0/#3?L i]/93^GELM>#>9Z08¥1432G_C;L6GJV2Ã0K4if'n _/#8;/¦57-?/sÃ^KU i HÜCg57-?14> Ne30/#C;C HOGJ8=1U/#C GJC 5=-0/YD GO5=/#8 P08=GJ1430C LJZ?5 n J X GJ143 57-?/ P?1U@©/#8=/930>#/a1U3l5=-0/aV0-^GJC;/]> -0GJ30X /9C21UCR L 3 8;/9¡^/9>9571UL 3c:<8;L i 57-0/Ê:<8;L 365 GJ3?P*j^GJ> N C=Z08m:SGJ>#/9C#[gC;L 57-0/2Ã^K4i 14CEP^GJ8;Nfj6 8=/A¡^/#>A5714LJ3 j0Z 5Ej?8=14XJ-e5 1U3q578=GJ30C=i 14C;C=1UL 3 D -0/#3 57-0/ Ã^KUi j\/#>9L i]/9C.H /#8m 57-01U3gn ®`°S± ² ³µ´ 2 ± \j± 7?± Q ´ ^³F°µ?± 62° M'± A z :">#LJZ08=C;/J[BD¦/!P0L 30LO5 GJKWD G MCRL j0C;/#8mH /aG]Ã^KUi GO5R30LJ8=i]GJK`1U30>#1UP0/#3?>#/Jn J CTD¦/#KUK GJC L 1UKBÃ^KUi]C9[?57-0/ X /9L i /9578m LJ:`57-0/ C=1W57Z^GQ5714LJ3f-?/#8=/ 1UC_1Ui]V\L 8m5 GJ365.1U3 5=-0/bP0/#C;>#8=1UV?571UL 30C LJ:¥57-?)/ 1U> -0/#KUC=L 3 GJ30 P C¬GJj08m e `/98=LJ5_14365=/#8;:</98=L i /95=/#8;C#[0D -01U> - D¦/2C;-^GJK4KB/#30>9L Z03657/98 C;-0L 8;5=KU Jn :g57-?/TK41UX -65"14Cs1430>914P0/9365 GO5FGJ3 GJ30X KU / Ä 143qGbi]/9P014Z?i LJ: 8;/9:<87GO>9571WH /_1430P?"/ K C GJ30PÊD 1W57-!GE8=/9:<8=GJ>95=1UHJ/F143?P0"/ K c [O57-0/93Ê57-0/ c Ä L 3YGTC;K GJj2LJ:¬i]GO57/98=1 GOK6LJ:057-?14> Ne30/#C;G / =?>A@ mn > ¤ 7 t [ V^GO5=-qK4/930XJ5=- P01W@B/98=/#3?>#/Rj\/95 D¦/#/93fV0GO57-0C J GJ3?P J ¢<C=/9/TÃ^X Z08; 1UC ¡ U c ¢ £ ¢ ¤ X ¤)¢ ¥ ¦¤ i c Ä £p¢ § k ¨_L¯D £p¢ ¤ U ¤)¢ ¥ U© «ª >#L C 2¢ ¤ GJ3?Pg[^Z0C=1U30X ¬ 30/9tK HÜC_K4G D 5=-^GO5 ¤ U c C;143 7¢ "¤ ® c Ä C;143 7¢ Ä =?>A@I¯ P
Interference - a film at non-normal incidence
d n1
n2
A θ2
θ1
D
B C
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Interference Fringes - Newton's Rings Side view Radius R Air film
Lens
P
t
Glass plate
Top view
Lens P
r
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1
21/03/99 16:10
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