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Question

While light is used to illuminate the two slits in Young's double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D (>> d). At a point on the screen directly in front of one of the slits, certain wavelengths are missing. The missing wavelengths are (here m=0, 1, 2, .....is an integer)


A

d2(2m+1)D

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B

(2m+1)d2D

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C

d2(m+1)D

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D

(m+1)d2D

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Solution

The correct option is A

d2(2m+1)D


The distance of the mth minimum from the centre of the screen is given by
y=(m+12)λDd
For a point on the screen directly in front of one of the slits, y=d/2. Hence, for minima (zeros) of intensity, we have
d2=(m+12)λDdor λ=d2(2m+1)D


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