First slide

Interference

Question

Two coherent sources of different intensities send waves which interfere. If the ratio of maximum and minimum intensity in the interference pattern is 25 then find ratio of intensities of sources:

Moderate

A

25 : 1
B

5 : 1
C

9 : 4
D

25 : 16

Solution

$\frac{I_{max}}{I_{min}} = {(\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}})}^{2} \Rightarrow \frac{25}{1}$
$= {(\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}})}^{2}$
$\frac{5}{1} = \frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}}$
$\frac{\sqrt{I_{1}}}{\sqrt{I_{2}}} = \frac{3}{2} or \frac{I_{1}}{I_{2}} = \frac{9}{4}$

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