Two coherent point sources S₁ and S₂ vibrating in phase emit light of wavelength $λ$ . The separation between them is 2 $λ$ as shown in figure. The first bright fringe is formed at ‘P’ due to interference on a screen placed at a distance ‘D’ from $S_{1}$ (D >> $λ$ ), then OP is

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$\sqrt{2} D$

1.5 D

$\sqrt{3} D$

answer is C.

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Detailed Solution

$\begin{array}{l} Δx = dcos θ = nλ \Rightarrow 2 λcos θ = (1) λ \\ \Rightarrow 2 \frac{D}{\sqrt{D^{2} + x^{2}}} = 1 \Rightarrow 4 D^{2} = D^{2} + x^{2}; x^{2} = 3 D^{2} \\ x = \sqrt{3} D \end{array}$

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