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Question

In Young's double slit experiment, having slits of equal width, β is the fringe width and I0 is the maximum intensity. At a distance x from the central bright fringe, the intensity will be,

A
I0cos(xβ)
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B
I0cos2(2πxβ)
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C
I0cos2(πxβ)
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D
I04cos2(πxβ)
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Solution

The correct option is C I0cos2(πxβ)
At point P,
Δϕ=2πλ Δx
and, Δx=x dD



Δϕ=2πλ×x dD=2πxβ
Where, β=λDd is the fringe width.

The resultant intensity at point P is,
Ip=I1+I2+2I1I2cosΔϕI1=I2=I
Ip=4Icos2(Δϕ2)
Now, Imax=I0=4I

Ip=I0cos2(Δϕ2)=I0cos2(πxβ)

Hence, (C) is the correct answer.

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