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Q.

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)
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