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Question

In the arrangement shown in figure, slits S1 and S4 are having a variable separation Z. Point O on the screen is at the common perpendicular bisector of S1S2 and S3S4.


The minimum value of Z for which the intensity at O is zero is

A
2λDd
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B
λD2d
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C
λD3d
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D
λDd
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Solution

The correct option is D λDd
For the given condition,
phase difference cosθ=1 orθ=π
kΔx=π , (where, k=2πλ)
so,Δx2πλ=πΔx=λ2
here, Δx= total path difference= ydD
then,ydD=λ2y=Dλ2d
from the digram, Z=2y


so, Z2=Dλ2dZ=λDd

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