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 intensity of source :

• A. $25:1$
• B. $5:1$
• C. $9:4$
• D. $25:16$

Answer 1

The correct option is C $9:4$

$\frac{I_{max}}{I_{min}}={\left[\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right]}^2$

Where and are intensities of two waves

given

$\frac{I_{max}}{I_{min}}=\frac{25}{1}\therefore \frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}=\frac{5}{1}$

use componendo and dividendo

we get

$\frac{\sqrt{I_1}+\sqrt{I_2}+\sqrt{I_1}-\sqrt{I_2}}{\sqrt{I_1}+\sqrt{I_2}-\sqrt{I_1}+\sqrt{I_2}}=\frac{5+1}{5-1}or,\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{3}{2}or,\frac{I_1}{I_2}=\frac{9}{4}$