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Question

A double-slit arrangement produces interference fringes that are 0.250 apart using wavelength00nm.if angular separation is increased to 0.30 by changing the length of the light used, then the new wavelength must be :

A
480mm
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B
540mm
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C
720mm
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D
840mm
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Solution

The correct option is B 720mm
The optical path difference is given by
dsinθ=nλ
For small values of θ, sinθθ
Therefore, dθ=λ, since n=1
d=λθ
If we consider, two angles then we have
d=λ1θ1=λ2θ2
Given λ1=600nm, θ1=0.25o and θ2=0.3o
600×1090.25=λ20.3
λ2=600×109×0.30.25
λ2=720nm

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