Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28

Transcription

1 Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton

2 Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of multpl bam ntfnc

3 Dffacton Lght dos not always tavl n a staght ln. It tnds to bnd aound objcts. Ths tndncy s calld dffacton. Shadow of a hand llumnatd by a Hlum- Non las Any wav wll do ths, ncludng matt wavs and acoustc wavs. Shadow of a znc oxd cystal llumnatd by lctons

4 Dffacton by an dg vn wthout a small slt, dffacton can b stong. Tansmsson Lght passng by dg x Smpl popagaton past an dg ylds an unntutv adanc pattn. lctons passng by an dg (MgO cystal)

5 Rado wavs dffact aound mountans. Whn th wavlngth s km long, a mountan pak s a vy shap dg! Anoth ffct that occus s scattng, so dffacton s ol s not obvous.

6 Dffacton of ocan wat wavs Ocan wavs passng though slts n Tl Avv, Isal Dffacton occus fo all wavs, whatv th phnomnon.

7 Dffacton of a wav by a slt Whth wavs n wat o lctomagntc adaton n a, passag though a slt ylds a dffacton pattn that wll appa mo damatc as th sz of th slt appoachs th wavlngth of th wav. slt sz slt sz slt sz

8 Why t s had to s dffacton Dffacton tnds to caus ppls at dgs. But poo souc tmpoal o spatal cohnc masks thm. xampl: a lag spatally ncohnt souc (lk th sun) casts bluy shadows, maskng th dffacton ppls. Scn wth hol Untltd ays yld a pfct shadow of th hol, but off-axs ays blu th shadow. A pont souc s qud.

9 Sngl slt dffacton? xpctaton: Ralty: No dffacton Wth dffacton

10 Huygns-Fsnl pncpl vy pont of a wavfont svs as a souc of a sconday sphcal wav that has th sam phas as th ognal wav at ths pont. Chstaan Huygns Augustn Fsnl Th ampltud of th optcal fld at any pont byond s th supposton of all sconday wavs.

11 Sngl slt: dffacton mnmum a a a sn whn a sn ays 1 and 1 ntf dstuctvly. Rays and also stat a apat and hav th sam path lngth dffnc. Und ths condton, vy ay ognatng n top half of th slt ntfs dstuctvly wth th cospondng ay ognatng n th bottom half. 1 st mnmum at sn = a

12 Sngl slt: dffacton mnmum a a 4 a sn( ) 4 a Whn sn( ) ays 1 and 1 4 wll ntf dstuctvly. Rays and also stat a4 apat and hav th sam path lngth dffnc. Und ths condton, vy ay ognatng n top quat of slt ntfs dstuctvly wth th cospondng ay ognatng n scond quat. nd mnmum at sn = a

13 Sngl slt: dffacton mnmum Sngl slt dffacton mnma: a sn = m (m=±1,±,...) o sn = ma a sn Naow slts - boad maxma Not: mnma only occu whn a >

14 Fsnl and Faunhof dffacton Fsnl dffacton: na-fld a Faunhof: fa-fld R >> a R - smallst of th dstancs fom th aptu to th souc o to th scn (plan wavs)

15 Faunhof vs. Fsnl Dffacton Clos to th slt z Fa fom th slt Slt S Incdnt wav P Fsnl: na-fld Faunhof: fa-fld

16 Faunhof dffacton Faunhof (fa-fld) dffacton: Both th ncomng and outgong wavs appoach bng plana. R >> a. R s th small of th two dstancs fom th souc to th aptu (wth sz a) and fom th aptu to th obsvaton pont. Mathmatcal cta: Path dffnc s a lna functon of th aptu vaabls. S S a R R 1 P a P a sn

17 Faunhof dffacton: sngl slt

18 Faunhof dffacton: sval cohnt oscllatos N oscllatos, d apat N ays mt fa away and ntf Ampltuds a all about th sam t k t k t k k k t k sn 1 kd k sn 1 3 kd k N t k gomtc ss 1 1 N N N N sn sn 1 N N

19 Faunhof dffacton: sval cohnt oscllatos 1 kd sn 0 dstanc to th pont P fom cnt of th slt: R k sn 1t N 1 N sn 1 N 1d sn 1 0 Intnsty: I I 0 krt snn sn sn N I I0 sn sn sn N kd sn kd sn apd slow

20 Faunhof dffacton: sval cohnt oscllatos 1 sn N kd I I0 sn kd sn sn maxma: ( kd )sn m m d m m sn I I 0 N Nd to know I 0 du to a sngl souc and I n a lmt N

21 Faunhof dffacton: ln souc k t sn 0 Sngl oscllatng souc: souc stngth Souc stngth p unt lngth L L k t y sn N L k t y 0 sn sn sn D D L D D L dy k t dy k t

22 Sngl slt: Faunhof dffacton Intnsty du to lmnt dy: L d snt kdy R y sn R Path dffnc s a lna functon of th aptu vaabls. L b b sn t k R kb Lb sn sn t kr R y sn dy sn +b y -b R P I sn I0 I 0 snc R >> b

23 Sngl slt: Faunhof dffacton Mnma: =m, wh m=±1, ± kb sn m k bsn m I I0 snc kb sn Maxma: s gaph

24 Sngl slt: Faunhof dffacton Addng dmnson: long naow slt Symmty: cylndcal

25 What f w shft th lns? Cntal maxmum