Q48 / 107 · NTA Abhyas (JEE Main) 2020 · Physics · Wave Optics

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=λnd, where n is

Figure

Correct answer: 2

Solution

Path difference =CO+OP+λ2

=OPcos2θ+OP+λ2

=OP(1+cos2θ)+λ2

OPcosθ = d


Path difference =dcosθ(1+cos2θ)+λ2

=dcosθ⋅2cos2θ+λ2=2dcosθ+λ2

⇒2dcosθ=kλ  (k∈N)


For k=1, 2dcosθ=λ

cosθ=λ2d

Hence, the correct answer is 2.

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