Question

Two coherent sources of intensity ratio $\beta$ interfere. Then the value of $\left(\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\right)$ is:

• A. $\frac{1+\beta }{\sqrt{\beta }}$
• B. $\sqrt{\left(\frac{1+\beta }{\beta }\right)}$
• C. $\frac{1+\beta }{2\sqrt{\beta }}$
• D. $\frac{2\sqrt{\beta }}{1+\beta }$

Answer 1

The correct option is D $\frac{2\sqrt{\beta }}{1+\beta }$

$\frac{I_2}{I_1}=\beta$ $\frac{I_{min}}{I_{max}}=\frac{\beta -2\sqrt{\beta }+1}{\beta +2\sqrt{\beta +1}}$
$\frac{A_2}{A_1}=\sqrt{\beta }$
$\frac{A_2-A_1}{A_2+A_1}=\frac{\sqrt{\beta }-1}{\sqrt{\beta }+1}$ $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{\left(2\right)}{\left(2\right)}\left[\frac{2\sqrt{\beta }}{\beta +1}\right]$