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(C) The ratio of intensities of two coherent sources is given as $\frac{I_1}{I_2} = \frac{64}{1}$.Let $I_1 = 64k$ and $I_2 = k$,where $k$ is a constan

Vedclass · Accepted Answer

$81: 49$

Vedclass · Answer

(C) The ratio of intensities of two coherent sources is given as $\frac{I_1}{I_2} = \frac{64}{1}$.Let $I_1 = 64k$ and $I_2 = k$,where $k$ is a constant.The ratio of maximum intensity to minimum intensity in an interference pattern is given by the formula:$\frac{I_{\max}}{I_{\min}} = \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2}$.Substituting the values:$\frac{I_{\max}}{I_{\min}} = \frac{(\sqrt{64k} + \sqrt{k})^2}{(\sqrt{64k} - \sqrt{k})^2} = \frac{(8\sqrt{k} + \sqrt{k})^2}{(8\sqrt{k} - \sqrt{k})^2}$.$\frac{I_{\max}}{I_{\min}} = \frac{(9\sqrt{k})^2}{(7\sqrt{k})^2} = \frac{81k}{49k} = \frac{81}{49}$.

Two coherent sources whose intensity ratio is $64: 1$ produce interference fringes. The ratio of intensities of maxima and minima is

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