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In fig PQ represents a plane wavefront and AO and BP the corresponding extreme rays of monochromatic light of wavelength $λ$ . The value of angle $θ$ for which the ray BP and the reflected ray OP interfere constructively is given by

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$\cos θ = \frac{λ}{2 d}$

$\cos θ = \frac{λ}{4 d}$

$\sec θ = \frac{λ}{3 d}$

$\sec θ = \frac{2 λ}{3 d}$

answer is B.

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Detailed Solution

$Δ l = \frac{d}{\cos θ} (1 + \cos 2 θ) = 2 d \cos θ$

$Since there is a sudden path change of \frac{λ}{2}$

$due to reflection, the condition of constructive interference at P is$

$Δ l = \frac{λ}{2} o r \frac{3 λ}{2} o r \frac{5 λ}{2}$

$Or 2 dcos θ = \frac{λ}{2}, \frac{3 λ}{2}, \dots etc$

$Or \cos θ = \frac{λ}{4 d}, \frac{3 λ}{4 d}, \dots etc$

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