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

$9:4$

Step 1: Given

The ratio of maximum intensity $I_{max}$ to minimum intensity $I_{min}$ is $25$.

Step 2: Formula used

We know that,

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

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

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

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

Taking under root both sides,

$$\begin{gathered} \Rightarrow 5=\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}} \\ \Rightarrow 5(\sqrt{I_1}-\sqrt{I_2})=\sqrt{I_1}+\sqrt{I_2} \\ \Rightarrow 5\sqrt{I_1}-5\sqrt{I_2}=\sqrt{I_1}+\sqrt{I_2} \\ \Rightarrow \sqrt{I_1}(5-1)=\sqrt{I_2}(1+5) \\ \Rightarrow \frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{6}{4}=\frac{3}{2} \end{gathered}$$

Squaring on both sides,

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

Thus, option (C) is the correct answer.