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. $\frac{\sqrt{n}}{n+1}$
• B. $\frac{2\sqrt{n}}{n+1}$
• C. $\frac{\sqrt{n}}{(n+1{)}^2}$
• D. $\frac{2\sqrt{n}}{(n+1{)}^2}$

Answer 1

Answer: (B)

$I_{\max }={\left(\sqrt{I}+\sqrt{nI}\right)}^2$
$I_{\min }={\left(\sqrt{I}-\sqrt{nI}\right)}^2$
$\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}=\frac{{\left(\sqrt{I}+\sqrt{nI}\right)}^2-{\left(\sqrt{I}-\sqrt{nI}\right)}^2}{{\left(\sqrt{I}+\sqrt{nI}\right)}^2+{\left(\sqrt{I}-\sqrt{nI}\right)}^2}$
$=\frac{1+n+2\sqrt{n}-1-n+2\sqrt{n}}{1+n+2\sqrt{n}+1+n-2\sqrt{n}}=\frac{4\sqrt{n}}{2+2n}=\frac{2\sqrt{n}}{1+n}$