Question

Two coherent sources of intensity ratio $\beta$ interfere. Find the ratio $\frac{[I_{max}-I_{min}]}{[I_{max}+I_{min}]}$ in the interference pattern.

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

Answer 1

The correct option is A $\frac{2\sqrt{\beta }}{[1+\beta ]}$

$\frac{a_1}{a_2}=\sqrt{\frac{I_1}{I_2}}=\sqrt{\beta }$
$I_{max}={(\sqrt{I_1}+\sqrt{I_2})}^2;I_{min}={(\sqrt{I_1}-\sqrt{I_2})}^2$
$\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{4\sqrt{I_1}\sqrt{I_2}}{2I_1+2I_2}=\frac{2\sqrt{\beta }}{1+\beta }$