First slide

Young's double slit Experiment

Question

In Young's double slit experiment intensity of light emerging from each slit is I₀. Wavelength of light used is $λ$ , separation between the slits is d and separation between the slits and screen is D. P is a point on the screen where the resultant intensity is 3I₀. Then the minimum path difference between rays emerging from the slits at point P is

Moderate

A

$\frac{λ}{4}$
B

$\frac{λ}{2}$
C

$\frac{λ}{3}$
D

$\frac{λ}{6}$

Solution

At any point on the screen whose position is defined by the angle $θ$ is
$I = I_{m} \cos^{2} \frac{ϕ}{2} = 4 I_{0} \cos^{2} \frac{ϕ}{2}$
At point P, $3 I_{0} = 4 I_{0} \cos^{2} \frac{ϕ}{2} \Rightarrow \cos \frac{ϕ}{2} = \frac{\sqrt{3}}{2} \Rightarrow ϕ = 60^{o}$
$∴ ϕ = \frac{2 π}{λ} \times (path difference) = \frac{π}{3} \Rightarrow dsinθ = \frac{λ}{6}$

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