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Interference of Light Waves and Young’s Experiment

In Young's double slit experiment, one of the slit is wider th

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Solving time: 4 mins

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity I when they interfere at phase difference $ϕ$ is given by

\frac{I _{m}}{9} (4 + 5 cos ϕ)

\frac{I _{m}}{3} (1 + 2 cos^{2} \frac{ϕ}{2})

\frac{I _{m}}{5} (1 + 4 cos^{2} \frac{ϕ}{2})

\frac{I _{m}}{9} (1 + 8 cos^{2} \frac{ϕ}{2})

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Updated on: Apr 8, 2023

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Benjamin Discussed

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If

I_{m}

be the maximum intensity, the resultant intensity I when they interfere at phase difference

ϕ

is given by

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Let

A_{1} = A_{0}

, Then

A_{2} = 2 A_{0}

Intensity

I \propto A^{2}

Hence

I_{1} = I_{0}, I_{2} = 4 I_{0}

We have

I = I_{0} + 4 I_{0} + 2 I_{0} \times 4 I_{0} cos ϕ

For

I_{m a x}, cos ϕ = 1

Hence

I_{m} = 9 I_{0}

I_{0} = \frac{I _{m}}{9}

When phase difference is

ϕ

then

I = I_{0} + 4 I_{0} + 2 4 I_{0}^{2} cos ϕ = I_{0} + 4 I_{0} (1 + cos ϕ) = I_{0} (1 + 8 cos^{2} \frac{ϕ}{2}) [∵ 1 + cos ϕ = 2 cos^{2} \frac{ϕ}{2}] = \frac{I _{m}}{9} (1 + 8 cos^{2} ϕ /2)

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Question Text	In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity I when they interfere at phase difference $ϕ$ is given by
Updated On	Apr 8, 2023
Topic	Wave Optics
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	520
Avg. Video Duration	8 min

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity I when they interfere at phase difference $ϕ$ is given by

Text solutionVerified

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In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity I when they interfere at phase difference $ϕ$ is given by