Final review Interference and diffraction

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1 Phys 3 Lectue 37 Fnl evew nteeence n cton ene: Plese coplete the onlne couse evluton

2 Fnl ex Fnl Ex Stuy Decebe 4 :00-3:00 p n PHYS 3. Mtel covee: Hecht Chptes -0 except Plese bng two oul sheets lette-sze ppe scentc clculto D etc. otes:. The nl ex s copehensve but the ephss wll be on the lst pt o the tel Ch Two cb sheets 8 ½" x " e pette. 3. Thee wll be 4-5 pobles one wth qulttve questons n the est quntttve pobles.

3 evew poble n ouble slt nteeence expeent the stnce D o the slts to sceen s the slt septon s n the wvelength o the ncent plne wve s 500 n. Fn the eence n the postons o two consecutve x ne the cente o the nteeence ptten. y D Fn the septon between the 6th n 8th x locte on ech se o the centl nge the 6th s on the postve se n the 8th nge s on the negtve se.

4 nteeoetes 9.3 Wveont-splttng nteeoetes 9.3. Young s expeent 80 Young s ognlty: Obtnng sptlly coheent lght o pnhole n splttng the wveont o the sptlly coheent lght wth two pnholes. Optcl pth length eence: = θ = ys s>> s>> y Poston o bght nges: s = 0 ± ± s the oe nube. s Spce between nges: y ntensty stbuton o the nges: y s k 40 cos 40 cos 40 cos y s ys

5 n ouble slt nteeence expeent the stnce D o the slts to sceen s the slt septon s n the wvelength o the ncent plne wve s 500 n. Fn the eence n the postons o two consecutve x ne the cente o the nteeence ptten. y D = s = D y sll ngle ppoxton.0 9 y Fn the septon between the 6th n 8th x locte on ech se o the centl nge the 6th s on the postve se n the 8th nge s on the negtve se. D D y ~ ~7

6 evew poble A sop l suoune by hs n nex o ecton o.34. egon o the l ppes bght e 0 = 633 n n nolly electe lght wht s the nu thckness o the l thee?

7 9.4 Apltue-splttng nteeoetes 9.4. Delectc ls ouble-be nteeence Applcton: Optcl cotng euces o enhnces electon o optcl evces though thnl nteeence eects. Fnges o equl nclnton Conse the st two electons othes e wek. Optcl pth length eence: n AB BC n AD n n cos t t AC n n t n cos cos t n n cos t cos tn t t Phse eence: Assue n >n n >n. Thee s phse sht o between extenl n ntenl electons when the ncent ngle s not lge. 4n k cost Bght spot: cost Dk spot: cost 4 4 S A D t B C P n n n

8 A sop l suoune by hs n nex o ecton o.34. egon o the l ppes bght e 0 = 633 n n nolly electe lght wht s the nu thckness o the l thee? cos t eqn n 633n 0 8n 4n 4.34

9 evew poble 3 A ouble-slt cton ptten s oe ug Hee lse lght t 63 n. Ech slt hs wth o The ptten evels tht the th-oe nteeence x e sg o the ptten. Wht s the slt septon? b Wht s the nce o the st two nteeence nges eltve to the zeo th -oe xu?

10 Coheent lne souce: E x y D L D exp k y L s the souce stength pe unt length. Ths equton chnges cton poble nto n ntegton nteeence poble. y y D -D P xy x 0. Funhoe cton 0.. The gle slt D exp k E x y L y D D exp[ k y ] L y D LD [ kd ] exp k kd LD exp k n phse s ppoxte by -y Funhoe conton n pltue s ppoxte by kd y y D -D P xy x 0 The phse s the se s pont souce t the cente o the slt

11 0 cos tn n x The ouble slt F z exp[ k z ] E x z C b b F z z C b b F z z bc exp k exp[ k ] 40 cos k kb b z - P xz x The esult s ply vyng ouble-slt nteeence ptten cos oulte by slowly vyng gle-slt cton ptten.

12 40 cos b 0 cos b two-slt nteeence Fnges k kb gle-slt cton Envelope Queston: Whch nteeence xu conces wth the st cton nu? b b Hl nge splt nge y occu thee. WU OptoLb

evew poble 3 A ouble-slt cton ptten s oe ug Hee lse lght t 63 n. Ech slt hs wth o 0.080.

13 evew poble 3 A ouble-slt cton ptten s oe ug Hee lse lght t 63 n. Ech slt hs wth o The ptten evels tht the th-oe nteeence x e sg o the ptten. Wht s the slt septon? b Wht s the nce o the st two nteeence nges eltve to the zeo th -oe xu? Fo =

14 evew poble 4 Wht s the eltve nce o the subsy x n thee slt Funhoe cton ptten?

15 0..3 Dcton by ny slts exp exp exp ] exp[... 4 exp exp exp... ] exp[ k bc k bc z z F C z z F C z z F C z z F C z x E z k z F b b b b b b b b z x P xz - b - 0 Pncple x: Mn -: Subsy x -: b

16 Wht s the eltve nce o the subsy x n thee slt Funhoe cton ptten? 0 3 o sll ~ ~ 0 9

17 evew poble 5 You wnt to stngush between =500. n n lght wth gtng t nol ncence to the lght n wth xu ngle o th-oe cton o 5. Wht s the nu wth o the gtng?

18 Gtngs Dctve gtng: An optcl evce wth egully spce y o ctng eleents. Tnssson gtngs n electon gtngs. Gtng equton: Blze gtng: Enhncng the enegy o cetn oe o cton. Blze ngle: Specul electon: specul Gtng spectoscopy: -slt nteeence: 0 k Angul speson: cos Angul wth ue to nstuentl boenng cos 0 0th

19 Lt o esoluton: Angul wth Angul speson n cos cos yleghs cteon n n cos n cos esolvng powe n Fee spectl nge: s n =3 s = = n Queston: Why oes the esolvng powe ncese wth nceg oe nube n wth nceg nube o llunte slts?

20 evew poble 5 You wnt to stngush between =500. n n lght wth gtng t nol ncence to the lght n wth xu ngle o th-oe cton o 5. Wht s the nu wth o the gtng?

21 Sple qulttve questons. T o F: Zone pltes e use to chnge the polzton o n electognetc wve.. T o F: The blze on electon gtng cn pove the ount o enegy n ese oe o cton. 3. T o F: The esolvng powe o gtng spectoete use n ptcul cton oe epens only on the nube o lnes llunte not wvelength o gtng peo. 4. T o F: The centl pek o the Funhoe cton o two now slts septe by spcng h hs the se wth s the centl cton pek o gle slt wth wth x = h. 5. T o F: The Funhoe cton ptten ppeng t the ocus o lens ves n ngul wth epenng on the ocl length o the lens use. 6. T o F: Funhoe cton cn be vewe s sptl Foue tnso o nvese tnso you pee on the el t the petue. 7. T o F: t s lwys possble to copletely elnte electons wth gle-lye ntelecton cotng s long s the ght thckness s chosen o gven el nex. 8. T o F: A hl-wve plte ottes lght ntlly lnely polze t n ngle wth espect to the st xs though totl ngle. 9. T o F: A Mchelson nteeoete cn be use to esue the spectl ntensty o lght. 0. T o F: A Mchelson nteeoete cn be use to esue the wvelength o lght.

22 Moe qulttve questons T o F: Vetclly polze lght lluntes Young s ouble-slt setup n nges e seen on stnt sceen wth goo vsblty. A hl wve plte s plce n ont o one o the slts so tht the polzton o tht slt becoes hozontlly polze. Hee s the stteent: The nges t the sceen wll sht poston but ntn the goo vsblty.

23 Eects o nte coheent length: Lght o ech slt hs coheent length l c. Fo sunlght l c s bout 3. The wves o two slts cn only nteee <l c. The contst o the nges eges when the ount o the ovelp between uncoelte wvegoups nceses. l c A A B B P Othe Wveont-splttng nteeoetes Fesnel s ouble o: Slts S n S ct s vtul coheent souces. They e ges o slt S n two os. = y = s S M S Shel s P y S M

24 Fesnel ouble ps: nteeence between lght ecte o the uppe n the lowe pss. Two vtul coheent souce S n S e pouce by the pss. S S Queston: Whee e S n S? S Lloy s o: nteeence between lght o souce S n ts ge S n the o. Glncng ncence cuses phse sht o. The nges e copleenty to Young s. S y 4 0 y s S s

25 Extene souce: All ys nclne t the se ngle ve t the se pont. Fnges o equl nclnton: Acs centee on the pepencul o the eye to the l. Hnge nges: The nges o equl nclnton vewe t nely nol ncence. Concentc ccul bns. n cost Fnges o equl thckness Fzeu nges: Contous o non-uno l when vewe t nely nol ncence. Thckness: = x nteeence xu: n = + ½ 4 Fnge spce: x = x 4 x n n n

26 ewton s ngs: nteeence ptten o l between glss suces. x Thckness: Bght ngs: n = + ½ Dk ngs: x x x 4 x x n

27 Multple be nteeence 9.4. Moe nteeoetes Mchelson nteeoete Copenston plte: egtes speson o the be spltte Collte souce: Fnges o equl thckness 3 Pont souce: nteeence o sphecl wves 4 Extene souce: Fnges o equl nclnton P S S S Movble o Be spltte M M Optcl pth length eence: cos Phse eence: Dk nges: cos 4 cos WU OptoLb

28 9.6 Multple be nteeence nteeence between ultple electon n ultple ectons: t S n E 0 E 0 0 t t E 3 0 t t E 5 0 t t E E 0 tt 0 tt E 4 0 tt E F Coecent o nesse: Ay uncton: cos... cos 4 cos e e E e tt E e e e tt E E tt n k n t t t t t F F F t F A

29 t F t F F = 0. = F = = 0.7 F = 00 = The Fby-Peot nteeoete Hgh esolvng powe Pototype o lse cvty A F F Hl-wth o tnssson: Fnesse: F F 4 F S P

30 Funhoe cton Chpte 0 Dcton 0. Pelny consetons Dcton: The evton o lght o ectlne popgton. Thee s no sgncnt physcl stncton between nteeence n cton. Huygens-Fesnel Pncple: Evey unobstucte pont o wve ont seves s souce o sphecl wvelets. The pltue o the optcl el t ny pont beyon s the supeposton o ll these wvelets conseng the pltues n phses. Fesnel ne el cton: Funhoe el cton: Both the ncong n outgong wves ppoch beng pln. >. s the slle o the two stnces o the souce to the petue wth sze n o the petue the to obsevton pont. Mthetcl cte: Pth eence s lne uncton o the petue vbles. S S P P

31 0..4 The ectngul petue Coheent petue: Apetue exp S k E A Zz Yy Zz Yy Zz Yy z y z Z y Y X Z Y X S=yz PYZ x y z Y Z b Apetue exp exp S Zz Yy k k Z Y E A exp exp exp k b yz Zz Yy k k Z Y E A b b A ectngul petue: kby kz 0 Z Y

32 0 Z Y kb Y kby... Y nu: k Z kz... Z nu:

33 0..5 The ccul petue potnce n optcl nstuentton: The ge o stnt pont souce s not pont but cton ptten Apetue 4 exp exp cos exp exp cos exp exp exp exp cos cos cos kq kq J A E kq J kq k q k J k q k k q k k S Zz Yy k k Z Y E q q q Zz Yy A A A A A A l ] [ ] cos exp[ cos exp u u J u J u u J u u v v u v u J v v u u J u Bessel unctons:. 0 0 k k J kq kq J PYZ x y z Y Z q Ccul petue

34 J k 0 k J 0 u J u u q 0 us o Ay sk: J kq 0 kq k q.. D D P

35 0..6 esoluton o gng systes Ovelp o two ncoheent pont souces: ylegh s cteon o be esoluton: The cente o one Ay sk lls on the st nu o the othe Ay sk. S S D P q. D Angul lt o esoluton: 550 n Ou eyes: n P n. Wvelength epenence: CD DVD Queston: Copng the ccul n the sque petue why oes the sque petue pouce slle cton ptten? D vs.. D D

PHYS 2421 Fields and Waves

PHYS 2421 Fields and Waves PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4