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In Young’s double slit experiment, intensity at the centre of screen is $I_{0}$ . Find the minimum distance from centre of screen, when intensity is $\frac{I_{0}}{4}$

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a

$\frac{λ D}{3 d}$

b

$\frac{λ D}{d}$

c

$\frac{λ D}{2 d}$

d

$\frac{λ D}{8 d}$

answer is A.

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Detailed Solution

$I = I_{0} \cos^{2} \frac{θ}{2} \Rightarrow \frac{I_{0}}{4} = I_{0} \cos^{2} \frac{θ}{2} \Rightarrow \cos \frac{θ}{2} = \frac{1}{2} ∴ \frac{θ}{2} = \frac{π}{3} o r θ = \frac{2 π}{3} N o w, ∆ x = \frac{λ}{2 π} θ \Rightarrow ∆ x = \frac{λ}{2 π} \times \frac{2 π}{3} = \frac{λ}{3} \Rightarrow y \frac{d}{D} = \frac{λ}{3} ∴ y = \frac{D λ}{3 d}$

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