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(C) Let the intensities of the two sources be $I_1$ and $I_2$. The ratio of maximum to minimum intensity in an interference pattern is given by the fo

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$9:4$

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(C) Let the intensities of the two sources be $I_1$ and $I_2$. The ratio of maximum to minimum intensity in an interference pattern is given by the formula:$\frac{I_{max}}{I_{min}} = \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2} = 25$Taking the square root on both sides:$\frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} = \sqrt{25} = 5$By applying componendo and dividendo:$\frac{(\sqrt{I_1} + \sqrt{I_2}) + (\sqrt{I_1} - \sqrt{I_2})}{(\sqrt{I_1} + \sqrt{I_2}) - (\sqrt{I_1} - \sqrt{I_2})} = \frac{5 + 1}{5 - 1}$$\frac{2\sqrt{I_1}}{2\sqrt{I_2}} = \frac{6}{4} = \frac{3}{2}$$\frac{\sqrt{I_1}}{\sqrt{I_2}} = \frac{3}{2}$Squaring both sides,we get:$\frac{I_1}{I_2} = \frac{9}{4}$

Two coherent sources have different intensities. They produce an interference pattern. If the ratio of maximum to minimum intensities is $25:1$,find the ratio of the intensities of the sources.

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