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

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Source S

Beam splitter A

Compensating plate B

Mirror C

Detector E

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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

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21/03/99 18:39

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d Mirror D

Source S

Beam splitter A

Compensating plate B

Mirror C

Detector E

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21/03/99 18:52

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? E % ¥ªH@'a)+*P,!68,5BPY ,W)3*PH@IJAp'P,C.3.5c &ÁE/68, UP.3,$69*PHM)3,v>@HMY=*L)`69HT)+*x)3*P,v4 H@G1G3?=GW:D)`)+*P,$.+: 4 ,vB-H@.1)+: 'PIC, QPU-)t.3>@HMY=*L)+>T0 : '-Y=>@,CBgu/Fringes 6 , Y=,j)aI5? >@?=UPMichelson G1,5B EOG1H@'PY=,CInterferometer .5u/EF: BPHM'PYx)3?æ69*PHM)3, : .v)3*P, BPHM[\,5G1,5'L)aIC?=>@?=U-G3,5B EODoublet G1H@'PY=,C./.102.1)3,54 .%in?l< the ,5G3>@: Sgc 2 .π .d . I ( θ , λ , d ) sin ð ¯ûOóp÷ õClð ýoï=ó λ cos ( θ ) 2

Two waves differing in frequency by 5%

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5

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£ HMY=UPG1, ¤¯¥D¦-c^ -¨ ©/*P, <D: G1Hr:D)3H@?='y? E`EOG1H@'PY , H@'L)+,C'P.3HT)(0 69HM)3* BPHM.1)+: 'PI5, EO?=G « )+?=S;¬Z: 6 : <=,5>M,5'PYD)+* % ug«FIC,5'L)+G1,l¬/:`6 :l< ,5>M,5'PY )3*X?DE §}QsI} % : '-B «FQw? )3)3?=4 ¬ :ªBP?=U-QP>@,j)/.3?=U-G3I5, IC?='L)J: HM'PH@'PY Qw? )3*Z6 : <=,C>@,5'-Y )+*P.Cc &ÁEP)3*P, >MH@Y=*L) IC?=4$,C.bEOG1?=4 :%.1?=UPG1I5,869HT)+*W)(6 ? .1S\,CIC)3G+: >2>@HM'P,5. I5>M?=.3,7)+?=Y ,C)+*-,5G «F.3?2BPHMUP4 HM.R)3*P,t)(02SPH@I5: >b,j^-: 4 SP>@, ¬9,5: IJ* >@HM'P,W69HM>@>è*;: < ,K:$.3HM4$HM>r: G/Q-U-) 'P?D) H@B-,5'L)+HMI : >èEOG3HM'PY=, .N0_.N)+,C4XcK&ÁE9E¥ 8I5? .l « ¬VH@.W: ' H@'L)3,5Y=,CGW'pUP4tQ\,CGW?DE86 : <=,5>M,5'PYD)+*P.mEO?= G ? q v>@HM'P,5.Cug)+*P, EOG1H@'PY=,C.k69H@>M>gI5?=HM'PI5HMBP,m: 'PBZ)+*-,m<2HM.3H@Q-H@>@HT)(0K69H@>@>\Q\,mY=?2?2Bgc"°V.9)+*P,m4 H@G1G3?=GkHM./4$?l< ,5Bgu )3*P,!EOG3H@'-Y=,V<2H@.1H@QPHM>@HM)(0K69HM>@>{<D: GN0=u;: .9.1*P?l69'eH@'a];Y UPG3,W¤b¥ ¦- c Pc *P,C'X)+*-,m<2HM.3H@Q-H@>@HT)(0K? E )3*P,!EOG3HM'PY=,5./HM./Y=?2?_Bgu-: 'PBsI5?=.l « = ¬ §=u ¥ $# i % i $# % ?=G # i 2 # ¥ M § 2 § O Q ±VE8I5?=UPG1.3,Du¯)+*-H@. 69H@>M> *;: S-S\,C' EO?= G ¡n¢ £ ¤¦¥%< :D>@% UPi ,C.W?D%E # HME7)+*P, )(68?X6 : <=,5>M,5'PYD)+*P.t: G3, IC>@?=.1, )+?=Y=,j)+*P,CG5c &Á0E HM.WIJ*P: 'PY=,CBx)+§? ©¨ e)+?eG1, : IJ*ú)+*P, 'P,j^2)tS\,5: A H@' <_HM.3HMQPH@>MHM)(0=u\6 ,$4ªUP.1) *;: < ,`IJ*;:D'PY=,5B # i 2 # QL0 §v«O.3,C,W)3*P,mI5>@? .3,jqÁUPSZH@'a];Y=U-G3,W¤b¥ ¦-sc =¬juP.1? # i 2 # ¨´§ ¥P«" ¨ 2¬ M § 2 § O Q %i % ¤b¥ ¦­qª

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£ HMY=UPG1,t¤b¥ ¦-cs _¨R² >M?=.3, q(UPS ? E")3*P,t<D: G1Hr:D)3H@?='Z? E"EOG1H@'PY=,`H@'L)+,C'P.3HT)(0Z69HM)+*eBPH@.N)J: 'PIC,tEO?=G « )+?=S®¬":!6k: < ,5>@,C'PY )3* u\«OI5,5'L)3G3,l¬7:m6 : <=,C>@,5'-Y )+* ?DE §}Q^I % :D'PB «OQ\? )1)+?=4v¬ :mBP?=UPQP>M,C) .1?=UPG3IC,mI5?='L)J:DH@'PHM'PYKQ\% ? )3*a6k: <=,C>@,C'PY )+*-.5c « U-Q-)+G3: IC)3H@'PY : 'PBsG3,5: G3G3: 'PY=HM'PY % % 2 % i % ¥ i % ¥ % Q ©/*2U-. QL0XIC?=UP'L)+HM'PYv)3*P,t'pUP4ªQw,5GR? E <D: G1Hr:D)3H@?='-.R?DE <2H@.3HMQPH@>MHM)(0v? E )+*-,`EOG3HM'PY=,C.%HM's)3*P, dXH@IJ*P,C>@.1?=' H@'L)3,5G1EO,CG3?=4 ,C)3,5G%: .%)3*P,ª4 H@G1G3?=G9H@.R4 ?­< ,5Bguw)+? Y ,C)V: ' : <=,CG+: Y=,`< :D>@UP,W? E ;uP68,mI : 's4$,5: .3U-G3,!)+*P,m.1SP>@HT)3)+HM'PYª? E :KBP?=UPQP>M,C)9.1S\,CIC)+G3: >è>@HM'P, c d

1001

0.1 0.08 0.06 0.04 0.02

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0.1 0.08 0.06 0.04 0.02

0

0.02 0.04 0.06 0.08 0.1

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1001.1

0.1 0.08 0.06 0.04 0.02

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ยคbยฅ ยฆยญqยชยฌ

Interference - Michelson's Stellar Inteferometer

P

Focal plane

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1

21/03/99 18:55

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