First slide

Young's double slit Experiment

Question

In Young's double slit experiment, the intensity on the screen at a point where path difference is $λ$ is K. What will be the intensity at the point where path difference is $λ / 4 ?$

Moderate

A

$\frac{K}{4}$
B

$\frac{K}{2}$
C

K
D

Zero

Solution

By using phase difference $ϕ = \frac{2 π}{λ} (Δ)$
For path difference $λ,$ phase difference $ϕ_{1} = 2 π and$
for path difference $λ / 4,$ phase difference $ϕ_{2} = π / 2 .$
Also by using $I = 4 I_{0} \cos^{2} \frac{ϕ}{2} \Rightarrow \frac{I_{1}}{I_{2}} = \frac{\cos^{2} (ϕ_{1} / 2)}{\cos^{2} (ϕ_{2} / 2)}$
$\Rightarrow \frac{K}{I_{2}} = \frac{\cos^{2} (2 π / 2)}{\cos^{2} (\frac{π / 2}{2})} = \frac{1}{1 / 2} \Rightarrow I_{2} = \frac{K}{2}$

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