1B24 Waves Optics and Acoustics Lecture 28 of 33 (UCL)

Page 1

! " $# % ! &(' )+*-,/.102.1)3,54 .768,9*;: <=,9>@?2?=A ,CB :D)".3?!EF: G 69*-H@IJ*KH@'L<=? >M<=,/HM'L)+,5GNEO,5G1,5'PIC,RQL0 B-HM<2H@.1H@?=' ? E : 4 SP>@HT)+UPB-,V)+*P,WS;:D)3*X>M,5'PYD)+*ZBPHM[\,5G1,5'PIC,5.969*P,5G1,W]_^-,CB QL0 )+*-,`Y=,C?=4 ,C)+GN0a? Eb)+*P, .N0_.N)+,C4Xc &('edXH@IJ*P,C>@.1?='gfh.ji/HM'L)+,5GNEO,5G1?=4$,j)+,CGk6 ,W*;: <=,WI5?='L)3G3?=>g?l< ,5G9)+*P,mY=,C?=4$,j)+GN0=c n%?D)+,!)+*;:o)9H@'ZH@'L)+,CG1EO,CG3,5'-I5,WQp0ZB-HM<2H@.1H@?='a? E : 4 SP>@HT)+UPB-,V6 ,mBP? 'P? )R'P,C,5BX: .1S;:oq )3Hr: >M>M0sI5?=*-,5G3,C'L)t6 :l< , u : .`HT)mH@. )3*P,v:D4$SP>MHM)3UPBP, :D)W?='-, Sw?=HM'p)!69*-H@IJ*xHM.m.3SP>MHM)m: '-B .1,5'L)aQL0yB-HM[\,5G3,C'L) S;:D)3*P.v)3?xH@'L)3,5G1EO,CG3,DuR'-? )v)3*;:D)vEOG1?=4zBPHT[{,CG3,5'L)aSw?=HM'p)3.$? 'y)+*P, EOG1?='L) c | } ~9 N€  Â‚Nƒw„ Â…b†ˆ‡-‰8Š‹‚NŠ ÂŒPÂ… Â?;ÂŽÂ?Â… Â?;‰ Â?‘…gÂŒPÂ… Â?“’•”—–e˜/™9š9›kÂœ`Â?ž’ZÂ&#x;W›"Â&#x;mÂœW ¥ÂšR¢ Â&#x; Interference - Michelson's Inteferometer Mirror D

Source S

Beam splitter A

Compensating plate B

Mirror C

Detector E

ÂŁ HMY=UPG1,t¤bÂĽ ÂŚ-cT§=¨9Š/*P, dXHMIJ*P,5>M.3?=' HM'L)+,5GNEO,5G1?=4$,j)+,CG5¨9.3,C,t)+*P,`)+,j^2)!EO?=GV:vBP,j)J: HM>@,5BeBP,jq .1I5G3HMS-)+HM?='gc Š/*P,ÂŞ: G3G3: 'PY=,C4$,C'p)VH@.R<=,5GN0 .1H@4 SP>@,vÂŤF.1,5,t];Y UPG3, ¤bÂĽ ÂŚ_cM§­Â?¨R:v.3?=U-G3I5,aÂŤO69*PHMIJ* 4v: 0sQ\, ,Â?^_)3,5'PB-,5BÂŽÂŹ HM.ÂŻBPHT<2H@BP,CBÂŞQL0ÂŞ:VSP: G1)3>M0Lq(.1H@>M< ,5G1,5Bt4 H@G1G3?=GCuo)3G+: <=,C>@.b)+?V)(68?!4$HMG3G1?=G3.Cu : '-BÂŞH@. G1,5I5? 4ÂŞQPH@'-,5B$: YL: HM'$QL0 )+*-,%Qw, : 4 q(.1SP>@HT)3)3,5G5cb°V'L0 S;:D)3*$>M,5'PYD)+* BPHM[\,5G1,5'PIC,VY=HT<=,5.7G3HM.3, )3? HM'L)+,5GNEO,5G1,5'PIC, c Âą!'-,`4 H@G1G3?=G ³²´HM'a)+*P,mBPH@: Y=G+:D4 ÂŹ8I5: 'sQ\,m4 ?­< ,5BsS\,CG3Sw,5'PB-H@I5U->r: G )3? HT)+./?l69'sSP>r: '-, ¨"HM)9I5: 'X: >@.1? Q\,!)+HM>M)3,5Bgc ÂľÂˆÂś ¡š¸DÂş1ÂťFÂź ½!žš¿à Ă€oÂşN¡ĂƒĂ‚FĂ„CĂ…VÆgÇjĂ‚ ¸DĂ„CÂťĂˆĂ…!žšĂ…WÉ5ÂźĂˆ³ĂŠNÂş1¡Ă‹Ă…oĂ„oĂŒDĂ?PĂ„C¡šĂ‡jĂ…oĂŽLĂŒDĂ„jĂ…!Ă?bÂş3ÂżÂˆÂş1Ă?7¸ ÂşNÂť7Ă‘3Ă’JŸ³Ă€ Ă‘1Ă“CĂ”CĂ•lĂ–{Ă—gĂ€­º Ă˜TÇjĂ? žš¡šĂ™ ¡Ă‹ÂşNĂ˜ĂšÂź Ă?PĂ„C¡šĂ‡jĂ…oĂŽ`ÂźĂˆĂ„mÂş3Ă‚ĂˆÂż1ÇÂ?Ă› ÂşRÇÂ?Ă…5ÂźĂˆžĂ‹ĂœOÉ ÂşNĂ?kžĂ‹ÂźĂˆžĂƒĂ‚FĂ? ĂŒPÆ\Ă„CÂťĂˆĂ?CÂş1뻂jÂżNÂťĂˆĂ„5Ă‚ĂˆĂ‚"ĂžwĂ&#x;­³Ă„jĂ› ÂşjĂŒPĂ‚OŸ³º1ÇÂ?Ă?kÂş3ĂŽÂŞÂźĂˆĂ„WĂ bÂşNÆxĂĄÂŽĂ„j³Ă?=ĂŒ;ÇÂ?Ă…oĂŽ â Ă?/Ă„jžšĂ‡Â?Ă…­¡ĂƒĂ‡Â?Âş1ĂŽZ³žšĂ‡ ÂźĂˆĂ€­Ă‡Â?ÂştĂ…oĂŽ ĂŁjĂ„CĂ‚ĂˆĂ?/¡šĂŽZÇÂ?¡šĂˆ¡hĂ&#x;oĂœrĂ›DĂ‚ĂˆĂ€aĂ„+ĂŠ%Ÿ³Ă„aÂťĂˆžĂƒĂŽ­ä{ĂŽlÇjÂş1¡Ă‹Ă…VžĂ‹Ă˜ĂĽĂ„jÂżNžh³ŸOĂ…­Ă™%žĂƒĂ‡­Ă„Â?Ă–ĂŚĂ˜;Ă?PĂ—2Ă„jà ĂˆĂ‡+ÂźĂˆçjĂ„kÂş1¡Ă‹ĂŞ\¡šžĂ‹Âş1Ă…o¡Ă‹ĂŁK¡šĂ„kç ¸ žšĂ™%Ç$ÂżNĂ?;ÇjÇÂ?Ă…­Ă…oĂ„ ÇjÂş Ă?kÂźĂˆĂ€­Ă‡o³ĂŒgĂ„jÂźĂˆĂ&#x;­Ă€­ãCÂş1Ă€RĂ™aŸ³º1Ă€­Ă‚³º7ÂżNÇjĂ‚ĂˆĂ†{Ă›DÂş3ÇjĂŽaĂ?kĂ›oÂźĂˆĂ€oĂ‚èº`ÇÂ?Ă…o¡ĂƒĂ‡+ĂŽ%Æè¡Ăƒ¡Ă‹Ă‡JÂş3ÂźĂˆĂ‚ĂˆÂş1Ă‚1Âť ĂŒ ¸ Ă™"Ă?7Ă&#x;­¡šºjĂ–PĂŤ-žĂ‹Ă…oÇj¡Ă‹¡šĂ™ ÂźĂˆĂ€oÂşNĂ™ ³º1ÇC¿à Ă€­º1ĂŽ7ɭÇÂ?Ă…8ĂŤo³Ă‡jĂ…oÂżÂˆžĂƒĂ‚³¿ÂˆĂ„oĂŒÂ?ÇjĂ…oĂŽ7Âśb¡Ă‹¸ ÂşNÂťĂˆÂź1ĂŹ Ă‚-Ă˜TÇJŸ³Ă€­ºNÂť;Ă‚ĂˆÂşÂˆÂź;Ă&#x;­Ă› ǯÂFÂźĂˆĂ„CÂťĂˆÂş{žĂ‹Ă…kǯĂ? žšĂ…­žšĂ…­ã ÂźĂˆĂ„JÆèĂ…pĂ– Âśb¡Ă‹¸ ÂşNÂťĂˆÂźbĂ€­žšĂ?/Ă‚FÂş1¡hĂ˜ÂŽÂş1çjÂş1Ă…CŸ³Ă&#x;oÇÂ?¡š¡šĂ™%Æ{ÂşNĂ…5Âź Ÿ³Ă„RĂ bÇ+çJÇÂ?¡;ä\Ă„j¡š¡Ă‹Âş1ĂŁjÂşCĂŒoÆèĂ€­º1ÂťĂˆÂş"Ă€­º ÂżNÇjĂ? Âş ÂźĂˆĂ„jĂ›!žšĂ…mĂ„CĂ›lÂźĂˆžĂƒÂżN¯ÇÂ?Ă…oĂŽ Ă•jĂ”JÂźĂˆĂ€VžĂ‹Ă…!Ă‚ĂˆÂş1ÇÂ?Ă?/ÇjĂ…oĂ‚FĂ€ožĂ‹Ă›pĂ–;Ă—gĂ€­º"à ¯Ç+ç5Ă™9ÂźĂˆĂ€­º1Ă… Ă‚ĂˆÂşNĂ…5Âź Ă€­žšĂ?ퟳĂ„/Ă‚FÂş3Ç7Ă˜ĂĽĂ„CÂťgÂźOÆ\Ă„kĂ™CÂş1ÇÂ?à Ă‚1ĂŽ ¤bÂĽ Œ­qJ§

Mirrors C and D are silvered on their front faces, and the beam splitter A consists of a glass plate part-silvered on its rear surface.

Circular fringes will be observed at the detector if the reflection of D in the beam splitter is parallel to C.

The glass in the beam splitter will be dispersive, but it is traversed three times by (SADAE) but only once by (SACAE). This results in a wave-length dependent optical path difference. If the compensator plate is identical (apart from any silvering) to the beam splitter, and is aligned parallel to it, it will introduce an extra path length into the second path which is exactly equivalent to the two extra traverses of the beam splitter in the first path. Michel1.mcd

1

21/03/99 18:39


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.