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In Young's double slit experiment, the separation between two coherent sources $S_{1} and S_{2}$ is d and the distance between the source and screen is D. In the interference pattern, it is found that exactly in front of one slit, there occurs a minimum. Then the possible wavelengths used
in experiment are

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$λ = \frac{d^{2}}{D}, \frac{d^{2}}{2 D}, \frac{d^{2}}{3 D}$

$λ = \frac{d^{2}}{D}, \frac{d^{2}}{3 D}, \frac{d^{2}}{5 D}$

$λ = \frac{d^{2}}{D}, \frac{d^{2}}{5 D}, \frac{d^{2}}{9 D}$

$λ = \frac{d^{2}}{3 D}, \frac{d^{2}}{7 D}, \frac{d^{2}}{11 D}$

answer is A.

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Detailed Solution

$y = \frac{d}{2} = \frac{2 (n - 1) Dλ}{2 d}$

$\Rightarrow λ = \frac{d^{2}}{D (2 n - 1)}; n = 1, 2, 3$

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