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While conduction the Young's double slit...

While conduction the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources `(S_(1),S_(2))` emitting light of wavelength 600nm. The student mistakenly placed the screen parallel to the x-z plane `(for zgt0)` at a distance D=3 m from the mid-point of `S_(1)`,`S_(2)`, as shown schematically in the figure. The distance between the sources `d=0.6003 mm`. The origin O is at the intersection of the screen and the line joining `S_(1)S_(2)`. Which of the following is (are) true of the intensity pattern of the screen?

A

Straight bright and dark bands parallel to the X-axis

B

The region very close to point O will be dark

C

Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction

D

Semi-circular bright and dark bands centred at point O.

Text Solution

Verified by Experts

The correct Answer is:
B, D
Sources are point, hence option (a) and (c ) are not possible.
Path difference between the waves arriving at point O from the sources `S_1 and S_2` is equal to distance d between the sources. Let `d = n lambda`, then we can write the following :
`n = d/lambda = (0.6003 xx 10^(-3))/(600 xx 10^(-9)) = 1000.5`
Hence we can write as follows:
`d = (1000 + 1/2) lambda`
Above condition is for destructive interference, hence there will be a dark at point O. Option (b) is correct. If we draw semicircle on x-z plane with its centre at the origin as sohwn in the figure, then we can see that path difference between waves arriving from sources `S_1 and S_2` for all points on this circle remains same. Hence semi-circular dark and bright bands are obtained with centre at O
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