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Question

Two plane mirrors, a source S of light, emitting monochromatic rays of wavelength λ and a screen are arranged as shown in figure. If angle θ is very small, find the fringe width of the interference pattern formed by reflected rays.


A
λ(b+2a)4aθ
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B
λ(b+a)2aθ
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C
λ(b+2a)2bθ
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D
λ(b+a)4bθ
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Solution

The correct option is A λ(b+2a)4aθ
Distance between two virtual sources S1 and S2 is

d=2×2acosθ sinθ=2a sin2θ


Screen distance D=b+2acos2 θ

Fringe width,

β=λDd=λ(b+2acos2θ)2asin2θ

If θ is much small cosθ1 and sinθθ

β=λ(b+2a)4aθ

Hence, (A) is the correct answer.

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