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As shown in the figure, two coherent sources separated by distance d and are radiating in phase having λ wavelength. In the plane of the two sources, a detector. moves in a big circle around the two sources. Find the angular position of n = 4 interference maxima.

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$\sin^{- 1} \frac{n λ}{d}$

$\cos^{- 1} \frac{4 λ}{d}$

$\tan^{- 1} \frac{d}{4 λ}$

$\cos^{- 1} \frac{λ}{4 d}$

answer is B.

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Detailed Solution

Consider a point P on circle. Line OP makes angle $θ$ with line S₁S₂.

Here path difference at P can be given by

$Δ x = d \cos θ \dots (i)$

For maxima at

P, $Δ x = n λ \dots (i i)$

From equations (i) and (ii)

$\begin{array}{l} d \cos θ = n λ \\ \Rightarrow θ = \cos^{- 1} (\frac{n λ}{d}) \end{array}$

For $n = 4, θ = \cos^{- 1} (\frac{4 λ}{d})$

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