Question

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

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

Answer 1

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

Given, $\frac{I_1}{I_2}=\beta =\frac{a^2}{b^2}$
$\Rightarrow \frac{a}{b}=\sqrt{\beta }$
$I_{max}=(a+b{)}^2$
and $I_{min}=(a-b{)}^2$
$\therefore \frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{(a+b{)}^2-(a-b{)}^2}{(a+b{)}^2+(a-b{)}^2}$
$=\frac{4ab}{2(a^2+b^2)}=\frac{2ab}{(a^2+b^2)}$
$=\frac{2b\cdot b\sqrt{\beta }}{b^2+\beta b^2}=\frac{2\sqrt{\beta }}{1+\beta }$.