Question

Two coherent sources of different intensities send waves that interfere. The ratio of maximum to minimum intensity is $25$. The intensity ratio of the sources is

• A. $25:1$
• B. $5:1$
• C. $9:4$
• D. $625:1$

Answer 1

The correct option is C $9:4$

$\frac{I_{max}}{I_{min}}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$
or
$\frac{25}{1}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$
or
$\frac{5}{1}=\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}$
or
$\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{5+1}{5-1}$
or
$\frac{I_1}{I_2}=\frac{9}{4}$