First slide

Young's double slit Experiment

Question

In young's double slit experiment path differences at two points A and B between two waves emerging from slits s₁ and s₂ are $\frac{λ}{6} and \frac{λ}{4}$ respectively. Then the ratio of intensities at A and B will be :

Moderate

A

3 : 2
B

3 : 1
C

2 : 1
D

4 : 3

Solution

$ϕ_{A} = \frac{2 π}{λ} . \frac{λ}{6} = \frac{π}{3} and ϕ_{B} = \frac{2 π}{λ} . \frac{λ}{4} = \frac{π}{2} ∴ I_{A} = I + I + 2 \sqrt{I} \sqrt{I} . \cos ϕ_{A} = 2 I + 2 I \cos 60^{o} = 3 I I_{B} = I + I + 2 \sqrt{I} \sqrt{I} . \cos ϕ_{B} = 2 I + 2 I \cos 90^{o} = 2 I ∴ I_{A} : I_{B} = 3 : 2$

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