Question

Two coherent light sources having intensity $I_1$ and $I_2$. If the ratio of $I_{max}:I_{min}$ is $25:9$. Find $\frac{I_1}{I_2}$​​?

• A. $\frac{4}{1}$
• B. $\frac{16}{1}$
• C. $\frac{16}{9}$
• D. $\frac{25}{9}$

Answer 1

The correct option is B

$\frac{16}{1}$

Step 1: Given data

Given the ratio $\frac{I_{max}}{I_{min}}=\frac{25}{9}$

Step 2: To find

$\frac{I_1}{I_2}$

Step 3: Calculation

We know, for two coherent waves, the relation between maximum and minimum intensity is given as

$\frac{I_{max}}{I_{min}}=\frac{{\left(a_1+a_2\right)}^2}{{\left(a_1-a_2\right)}^2}$

Where $a_1=\sqrt{I_1}$ and $a_2=\sqrt{I_2}$

Substituting the given value,

$$\begin{gathered} \frac{25}{9}=\frac{{\left(a_1+a_2\right)}^2}{{\left(a_1-a_2\right)}^2} \\ \Rightarrow \frac{\sqrt{25}}{\sqrt{9}}=\frac{a_1+a_2}{a_1-a_2} \\ \Rightarrow 5a_1-5a_2=3a_1+3a_2 \\ \Rightarrow \left(5-3\right)a_1=\left(5+3\right)a_2 \\ \Rightarrow \frac{a_1}{a_2}=\frac{\left(5+3\right)}{\left(5-3\right)} \\ \Rightarrow \frac{a_1}{a_2}=\frac{8}{2} \\ \Rightarrow \frac{a_1}{a_2}=4 \\ \Rightarrow \frac{I_1}{I_2}={\left(\frac{a_1}{a_2}\right)}^2 \\ \Rightarrow \frac{I_1}{I_2}=16 \end{gathered}$$

The ratio $\frac{I_1}{I_2}$ equals to $\frac{16}{1}$

Hence, Option(C) is correct.