First slide

Coherent sources and their importance in interference

Question

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 $\frac{I_{0}}{4}$

Moderate

A

$\frac{λ D}{3 d}$
B

$\frac{λ D}{d}$
C

$\frac{λ D}{2 d}$
D

$\frac{λ D}{8 d}$

Solution

$I = I_{0} \cos^{2} \frac{θ}{2} \Rightarrow \frac{I_{0}}{4} = I_{0} \cos^{2} \frac{θ}{2} \Rightarrow \cos \frac{θ}{2} = \frac{1}{2} ∴ \frac{θ}{2} = \frac{π}{3} o r θ = \frac{2 π}{3} N o w, ∆ x = \frac{λ}{2 π} θ \Rightarrow ∆ x = \frac{λ}{2 π} \times \frac{2 π}{3} = \frac{λ}{3} \Rightarrow y \frac{d}{D} = \frac{λ}{3} ∴ y = \frac{D λ}{3 d} a l t e r n a t e s o l u t i o n : I = 4 I_{0} \cos^{2} (\frac{π x}{λ}) w h e r e x i s t h e p a t h d i f f e r e n c e . n o w t h e d i s \tan c e o f t h e r e q u i r e d p o i n t i s Y = \frac{x D}{d}$

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