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Questions  

In Young's double slit arrangement, let βbe the fringe width and let Io be the intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be 

a
I0cos⁡(x/β)
b
I0cos2⁡(x/β)
c
I0cos2⁡(πx/β)
d
I0/4cos2⁡(πx/β)

detailed solution

Correct option is C

Path difference = x (d /D ) where  d is the separation between two sources and D is the distance of screen from two sources. Phase differenceϕ=2πλ×xdD ⇒φ2=πxβIntensity at a distance x from the central bright fringe is given by I = I0 cos2 φ2=I0 cos2 πxβ

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