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Question

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is d and the screen is at a distance D(>>d) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are :

A
λ=d2D
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B
λ=2d2D
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C
λ=d23D
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D
λ=2d23D
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Solution

The correct option is C λ=d23D
For missing wavelength, destructive interference should take place infront of slits, so minima is formed.
Δx=(y)×dD=(d2)×dD=(n+12)λ
d22D=(2n+1)λ2
for n=0, λ=d2D
n=1 λ=d23D

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