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 CI0cos2(πxβ) At point P, Δϕ=2πλΔx
and, Δx=xdD
⇒Δϕ=2πλ×xdD=2πxβ
Where, β=λDd is the fringe width.
The resultant intensity at point P is, Ip=I1+I2+2√I1I2cosΔϕ∵I1=I2=I Ip=4Icos2(Δϕ2)
Now, Imax=I0=4I