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Q.

Two coherent point sources S₁ and S₂ vibrating in phase emit light of wavelength $λ$ . The separation between the sources is $2 λ$ . The smallest distance from S₂ on a line passing through S₂ and perpendicular to S₁ S₂, where a minimum of intensity occurs is

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a

$X = \frac{5 λ}{9}$

b

$X = \frac{7 λ}{12}$

c

$X = \frac{3 λ}{5}$

d

None

answer is B.

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Detailed Solution

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Path difference at S₂ is $2 λ$ . Therefore for minimum intensity at P let x be the minimum distance from S₂. Then
Question Image
$_{s_{1}} P - s_{2} P = \frac{3 λ}{2} \neq \frac{λ}{2} \dots \dots (1)$
or $\sqrt{4 λ^{2} + X^{2}} - X = \frac{3 λ}{2}$ solving this equation we get $X = \frac{7 λ}{12}$

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