Monochromatic light waves of wavelength λ from two coherent sources fall on a large plane screen. One of the waves is emanated from a point source S located at distance L from the screen and other one is a broad plane wave as shown in the figure. Mark the correct options
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a
Central point of screen is dark spot
b
The shape of fringe on screen is elliptical
c
The distance between nth and (n – 1)th bright fringe is 2λL(n−n−1)
d
None of the above
answer is C.
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Detailed Solution
Let say nth bright fringe is forming at point P Path difference, Δx = SP- RP = nλ ⇒Δx=L2+r2− L=nλ ⇒L2+r2=nλ+L ⇒L2+r2=n2λ2+L2+2nλL ⇒r=2nλL [∵n2λ2 may be neglected] ∴rn = 2nλL and rn−1=2(n−1)λL Spacing between them = rn - rn−1 = 2nλL - 2(n−1)λL =2λL(n−n−1)