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} $