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chp42_2 - = N N a a a S with sin y ik i e e a ∆ ∆ = =...

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PHY2061 R. D. Field Department of Physics chp42_2.doc University of Florida Single-Slit Diffraction Intensity Pattern (1) Consider N point sources a distance y = W/(N-1) apart across the width of the slit such that W = (N-1) y (we will let N become large). In the limit L >> W , θ θ θ θ θ sin sin ) 1 ( sin ) 1 ( sin sin 1 1 1 1 1 2 W r y N r r y n r y r r y r r N n n + = + = + = + = + = Thus, the phase difference between the source n and source n-1 is given by θ λ π φ φ φ sin 2 ) ( 1 1 y r r k n n n n = = = and the phase difference between source 1 and source N is φ θ λ π φ φ = = = = ∆Φ ) 1 ( sin 2 ) ( 1 1 N W r r k N N The overall wave function at the point P on the screen is the sun of all the individual wavelets as follows: ( ) ( ) N ikr t i r r ik r r ik ikr t i ikr ikr ikr t i N n n N S e Ae e e e Ae e e e Ae N N 1 1 1 2 1 2 1 ) ( ) ( 1 ... 1 ... ω ω ω = = + + + = +
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Unformatted text preview: + + + = N N a a a S with sin y ik i e e a ∆ ∆ = = . Note that aS N & S N = a N &1 and hence ( ) ( ) ( ) ( ) ( ) ( ) ∆ ∆ = ∆ ∆ = − − = − − = − − = ∆ − ∆ ∆ ∆ − ∆ ∆ ∆ − ∆ ∆ ∆ ∆ 2 1 2 1 2 / ) 1 ( 2 1 2 / 2 1 2 / 2 / 2 / 2 / 2 / 2 / 2 / sin sin sin sin 1 1 1 1 N e e N e e e e e e e e e a a S N i i iN i i i iN iN iN i iN N N W =(N-1) ∆ y W sin θ ∆ y 1 2 n n-1 N-1 N θ ∆ y sin θ r 1 r 2 r n r n-1 center axis Maximum Phase Shift Overall Wave Function at P...
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