Question

The interference pattern is obtained with two coherent light sources of intensity ratio $4:1$. And the ratio $\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$ is $\frac{5}{x}$. Then, the value of $x$ will be equal to :

• A. 3
• B. 4
• C. 2
• D. 1

Answer 1

Answer: (B)

$\frac{I_1}{I_2}=4$
$\frac{I_{\max }}{I_{\min }}={\left[\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right]}^2$
$\frac{I_{\max }}{I_{\min }}={\left[\frac{2\sqrt{I_2}+\sqrt{I_2}}{2\sqrt{I_2}-\sqrt{I_2}}\right]}^2$
$\frac{I_{\max }}{I_{\min }}=9$
$\frac{I_{\max }}{I_{\max }-I_{\min }}=\frac{10}{8}$
$\frac{5}{x}=\frac{10}{8}$
$x=4$