Question

The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be

• A. $\frac{2\sqrt{n}}{(n+1{)}^2}$
• B. $\frac{\sqrt{n}}{n+1}$
• C. $\frac{2\sqrt{n}}{n+1}$
• D. $\frac{\sqrt{n}}{(n+1{)}^2}$

Answer 1

The correct option is C $\frac{2\sqrt{n}}{n+1}$

Given : $I_2=n{I}_1$

Maximum intensity of interference $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$

$\therefore$ $I_{max}=(\sqrt{I_1}+\sqrt{n{I}_1}{)}^2=(1+\sqrt{n}{)}^2{I}_1=(1+n+2\sqrt{n})I_1$

Minimum intensity of interference $I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$

$\therefore$ $I_{min}=(\sqrt{I_1}-\sqrt{n{I}_1}{)}^2=(1-\sqrt{n}{)}^2{I}_1=(1+n-2\sqrt{n})I_1$

$\therefore$ $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{2\sqrt{n}-(-2\sqrt{n})}{2(1+n)}=\frac{2\sqrt{n}}{1+n}$