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Question

In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1m. A parallel beam of light of wavelength 600nm is incident on the slits at angle α as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11.0mm. Which of the following statement (s) is/are correct?


A

For α=0, there will be constructive interference at point P.

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B

For α=0.36π degree, there will be destructive interference at point P.

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C

For α=0.36π degree, there will be destructive interference at point O.

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D

Fringe spacing depends on α.

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Solution

The correct option is B

For α=0.36π degree, there will be destructive interference at point P.


Δx=dsinα+dsinθ
For small angles θ,α ; sinθtanθ=yb, sinα=α.
Δx=dα+dyD

(1)α=0 Δx=dy/D=0.3×111000=33×104mm
Δx in terms of λ33×104600×106λ=11λ2
as Δx=(2n1)λ2
There will be destructive interference.

(2)Δx=0.3mm×0.36π×π180+0.3mm×11mm1000=39×104mm
39×104=(2n1)×600×109×1032
n=7
There will be destructive interference.

(3)Δx=3mm×0.36π×π180+0=600nm
600nm=nλ
n=1
constructive interference.

(4) Fringe width does not depend on α.


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