Two coherent point sources A and B are at separation $d = \frac{3 λ}{2},$ where $λ$ is wavelength of light emitted by these sources. The oscillations of source B lag in phase behind the oscillations of source A by $π .$ The point P is at angular position $θ$ as indicated in figure. Then

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At $θ = \cos^{- 1} (\frac{1}{3}),$ P is point of maximum

At $θ = \sin^{- 1} (\frac{2}{3}),$ P is point of minimum

At $θ = 0^{0},$ P is point of minimum

At $θ = π,$ P is point of maximum

answer is A, D.

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Detailed Solution

$\frac{3 λ}{2} \cos θ = \frac{λ}{2}$ for maxima
$\Rightarrow θ = \cos^{- 1} (\frac{1}{3})$
$\frac{3 λ}{2} \cos θ = λ$
For minima,
$\Rightarrow θ = \cos^{- 1} (\frac{2}{3}) a n d, a t θ = π,$ maximum occurs.

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