Question

The interference pattern is obtained with two coherent light sources 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 $\frac{2\sqrt{n}}{n+1}$

$I_2=n{I}_1$
Maximum intensity of interference, $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$
$\therefore I_{max}=(\sqrt{I_1}+\sqrt{n{I}_1}{)}^2$
$I_{max}=(1+\sqrt{n}{)}^2{I}_1=(1+n+2\sqrt{n})I_1$

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

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

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