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 DλDd For the given condition,
phase difference cosθ=−1orθ=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