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In the adjacent diagram, CP represents wavefront and AO and BP corresponding two rays. One particular condition on θ for destructive interference at P between the ray BP and reflected ray OP is cosθ = λ nd , where n is

Correct answer

2

Step-by-step solution

Path difference = CO + OP + λ 2 = OPcos 2 θ + OP + λ 2 = OP ( 1 + cos 2 θ ) + λ 2 OPcosθ   =   d Path difference = d cosθ ( 1 + cos 2 θ ) + λ 2 = d cosθ ⋅ 2 cos 2 θ + λ 2 = 2 dcosθ + λ 2 ⇒ 2 dcosθ = kλ    ( k ∈ N ) For k = 1 , 2 dcosθ = λ cosθ = λ 2 d

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