lecture29 - Lecture 29 Lecture 29 Physics 2102 Jonathan...

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Unformatted text preview: Lecture 29 Lecture 29 Physics 2102 Jonathan Dowling Ch. 36: Diffraction Ch. 36: Diffraction Things You Should Learn from This Lecture 1. Whe n lig ht pas s e s thro ug h a s m a ll s lit, is s pre a ds o ut a nd pro duc e s a diffra c tio n patte rn, s ho wing a princ ipa l pe ak with s ub s idiary m axim a and m inim a o f de c re a s ing inte ns ity. The prim ary diffrac tio n m a xim um is twic e as wide as the s e c o nda ry m a xim a . 2. We c a n us e Huyg e ns ’ Princ iple to find the po s itio ns o f the diffrac tio n m inim a by s ub dividing the ape rture , g iving θ min = ±p λ /a, p = 1, 2, 3, ... . 3. Calculating the complete diffraction pattern takes more algebra, and gives I θ =I [sin( α )/ α ] 2 , where α = π a sin( θ )/ λ . 4. To predict the interference pattern of a multi-slit system, we must combine inte rfe re nc e and diffrac tio n e ffe c ts . Single Slit Diffraction Whe n lig ht g o e s thro ug h a na rro w s lit, it s pre a ds o ut to fo rm a diffraction pattern . Analyzing Single Slit Diffraction Fo r an o pe n s lit o f width a , s ub divide the o pe ning into s e g m e nts and im ag ine a Hyug e n wave le t o rig inating fro m the c e nte r o f e ac h s e g m e nt. The wa ve le ts g o ing fo rwa rd ( θ =0) a ll tra ve l the s a m e dis tanc e to the s c re e n and inte rfe re c o ns truc tive ly to pro duc e the c e ntra l m a xim um . No w c o ns ide r the wa ve le ts g o ing at a n a ng le s uc h tha t λ = a s in θ 2245 a θ . The wa ve le t pair (1, 2) has a path le ng th diffe re nc e ∆ r 12 = λ/2 , and therefore will cancel. The same is true of wavelet pairs (3,4), (5,6), etc. Moreover, if the aperture is divided into p sub-parts, this procedure can be applied to each sub-part. This procedure locates all of the dark fringes....
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

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lecture29 - Lecture 29 Lecture 29 Physics 2102 Jonathan...

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