Question

Two coherent sources of intensity ratio $9:4$ produce interference. The intensity ratio of maxima and minima of the interference pattern is:

• A. $13:5$
• B. $5:1$
• C. $25:1$
• D. $3:2$

Answer 1

The correct option is C $25:1$

Given : $\frac{I_2}{I_1}=\frac{9}{4}$
Maximum intensity $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$
Minimum intensity $I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$
Thus ratio of maximum to minimum intensities $\frac{I_{max}}{I_{min}}=\frac{(1+\frac{\sqrt{I_2}}{\sqrt{I_1}}{)}^2}{(1-\frac{\sqrt{I_2}}{\sqrt{I_1}}{)}^2}$
$\therefore$ $\frac{I_{max}}{I_{min}}=\frac{(1+\frac{3}{2}{)}^2}{(1-\frac{3}{2}{)}^2}$
Or $\frac{I_{max}}{I_{min}}=\frac{(2+3{)}^2}{(2-3{)}^2}=\frac{25}{1}$