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Question

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is 18th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:

A
0.74
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B
0.85
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C
0.94
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D
0.80
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Solution

The correct option is B 0.85
Given that,
path difference, Δx=λ8

Phase difference (Δϕ) is given by
Δϕ=2πλ(Δx)

Δϕ=(2π)λλ8=π4

For two sources with same intensity, in different phases,

I=Imaxcos2(Δϕ2)

I=Imaxcos2(π8)

The intensity at the centre of the bright fringe is given by,

I0=Imax

II0=cos2(π8)

II0=1+cosπ42=1+122

II0=0.85

Hence, option (B) is correct.

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