Question

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is $25:1$. The intensities of the sources will be in the ratio

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

Answer 1

The correct option is D $9:4$

Given,

$\frac{I_{max}}{I_{min}}=\frac{25}{1}$

We know that,

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

$\Rightarrow \frac{25}{1}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$

$\Rightarrow \frac{5}{1}=\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)$

$\Rightarrow 5\sqrt{I_1}-5\sqrt{I_2}=\sqrt{I_1}+\sqrt{I_2}$

$\Rightarrow \sqrt{\frac{I_1}{I_2}}=\frac{5+1}{5-1}$

$\therefore \frac{I_1}{I_2}=\frac{9}{4}=9:4$

Hence, option $\left(\text{D}\right)$ is correct.