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31_Chapter 24 HomeworkCH24 Wave Optics

# 31_Chapter 24 HomeworkCH24 Wave Optics - Wave Optics 333...

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Wave Optics 333 Apply the given identity, realizing that ( ) ( sin sin ) θ β θ + = − + ( ) β and ( ) cos cos θ β + = ( ) θ + β , to obtain ( ) ( ) ( ) ( 2 cos 180 sin sin n ) 1 2 sin sin 180 cos n n θ θ β + θ β θ β ° + = = ° ( ) + Apply the identity once again to get ( ) 2 sin n 1 2 sin cos sin n n cos θ β θ = + ( ) ( 1 2 2 cos sin sin n n n β θ ) , or cos β θ β = θ Since sin cos tan θ θ θ = , this simplifies to 2 1 2 sin tan cos n n n β θ β = (b) If 1 2 , and 90 , 1 n n n β = ° , the above result reduces to = = tan n θ = , which is Brewster’s law. 24.67 In the single slit diffraction pattern, destructive interference (or minima) occur where ( ) sin m a θ λ = for . The screen locations, measured from the center of
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