First slide

Coherent sources and their importance in interference

Question

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

Moderate

A

$\frac{I_{m}}{9} (4 + 5 \cos ϕ)$
B

$\frac{I_{m}}{3} (1 + 2 \cos^{2} \frac{ϕ}{2})$
C

$\frac{I_{m}}{5} (1 + 4 \cos^{2} \frac{ϕ}{2})$
D

$\frac{I_{m}}{9} (1 + 8 \cos^{2} \frac{ϕ}{2})$

Solution

$W e k n o w t h a t, I n t e n s i t y \propto A m p l i t u d e^{2} G i v e n : A_{1} = 2 A_{2} ∴ I_{1} = 4 I_{2} I_{\max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = {(3 \sqrt{I_{2}})}^{2} = 9 I_{2} = I_{m} I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ = 4 I_{2} + I_{2} + 2 \sqrt{4 I_{2} . I_{2}} \cos ϕ = 5 I_{2} + 4 I_{2} \cos ϕ = \frac{I_{m}}{9} (5 + 4 \cos ϕ) [∵ I_{0} = \frac{I_{m}}{9}] = \frac{I_{m}}{9} [1 + 4 (1 + \cos ϕ)] = \frac{I_{m}}{9} (1 + 8 \cos^{2} \frac{ϕ}{2}) [∵ \cos ϕ = 2 \cos^{2} \frac{ϕ}{2} - 1]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App