Waves01 - Chapter 9 Interference and Diffraction 9.1 9 I nt roduction 453 454 verage tr n cling W3"e a,16 1 Photon flux ~62 Two-slit interfer ence

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Chapt er 9 I nt erf erence an d D iff ra ct ion 9.1 Introduction 453 9:) Interference between Two Cohe rent Point Sources 454 Coherent sources -t54 Construct ive and destructi ve in terference ..55 In terference pat tern 455 Xea r field :m d far field -156 " Bou ndary" bet ween near and far 457 Use of a cOll\'erging lens 10 ob taiu Iar-Geld interference p3ttem 458 Far-field interference pattern 459 Priucipal maximum 460 Relative phase due to path difference 461 •·. .average. . trn cling W3\"e ,161 Photon flux ~62 Two-slit interference paU:em -'62 Sources oscillati ng in phase ...63 Sou rces oscillati ng out of phase 463 In terference patt ern near 9 = 0 3 '1&1 Energ)" conserva tion 465 On e plus one equa ls Iour 'l65 On e plus one equa ls zero ·166 9.3 Interference between Two Independent Sources 466 I.n depeudent sources and cohe rence time 466 " Incoherence" and interference 467 Brown and Twiss exper iment 468 9.4 How Large Can a " Point" Ligh t Source Be? 470 Classica l point source 470 Simple exten ded source 471 Coherence condition -'72 9.5 Ang ular \Vidth of a "Beam" of Tra veling w aves Angula r width of a beam is di ffractio n limited 4i 3 A beam is an interfere nce maximum 4i5 9.6 Diffr action and Huygens' Principle 478 Difference between interfer en ce and diffn dion ·H8 How an opaque screen works 4i S Shinj- and black opa que screens 4i9 Effect of a hole in an opaq ue screen 480 Huygeus' pri nciple 48 1 Cnlcujaticn of single·!olil rliffracliOIl pattern using ll uygens' construc tion 482 Sing le-slit diffracti on patt ern 485 Angular width of a diffraction ·limited beam 487 Angular resolution of the human eye ·l87 Rayleigh 's criterion 488 Nomencla ture: Fraun hofer and Fresne l diffracti on 488 4 7 ~ Angular width or bea m 4i6 Applir.ntinn: Laser beam IJeTSUS finsMight beam 477 Fourier an alysis of the transverse space dependen ce of a co he ren t sour ce 489 Jmportant results of Four ier ana lysis .490 Diffracti on patt ern for two wide slits 491 Diffraction pattern for many identi cal par allel wide slits 492 Multip le-slit int erference pattem 493 Principal maxi ma, ce ntral maxim um , white ligh t source 493 Angu lar wid th of a princi pal maximum 495 Transmission-type diff ract ion grating 496 Diffraction by an opaq ue obstacle 496 How far downstream does a shadow extend? 497
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9,1 Introd uction Most of our studies so far have been esse ntially one-dime nsional. in the sense that there was only one pa th by which a wave emitte d at one place couJd go to anothe r place. Now we shall consider situ ations where there are differ ent possible path s from an emi tte r to a detector. Th ese lead to what are called interference or diffraction phenomena. resulting from con- struc tive and destructiv e superposition of waves that have different phase shifts, depending on the path taken . In Sec. 9.2 we conside r the supe rpos itio n at a detect or of the waves emitte d by two poin t sources having the same frequ ency and a constan t ph ase relation . Examples are water waves emitted by two screwheads jiggling the surface of a pan of water or ligh t emitted by the currents in the edges of two
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This note was uploaded on 08/06/2008 for the course PHYS 25 taught by Professor Nelson during the Spring '08 term at UCSB.

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Waves01 - Chapter 9 Interference and Diffraction 9.1 9 I nt roduction 453 454 verage tr n cling W3"e a,16 1 Photon flux ~62 Two-slit interfer ence

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