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(B) The ratio of maximum intensity to minimum intensity is given by: $\frac{I_{max}}{I_{min}} = \left( \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sq

Vedclass · Accepted Answer

$25 : 9$

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(B) The ratio of maximum intensity to minimum intensity is given by: $\frac{I_{max}}{I_{min}} = \left( \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} \right)^2 = 16$. Taking the square root on both sides: $\frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} = 4$. Cross-multiplying gives: $\sqrt{I_1} + \sqrt{I_2} = 4\sqrt{I_1} - 4\sqrt{I_2}$. Rearranging the terms: $5\sqrt{I_2} = 3\sqrt{I_1}$. Squaring both sides: $25I_2 = 9I_1$. Therefore,the ratio of intensities is $\frac{I_1}{I_2} = \frac{25}{9}$.

Two coherent sources produce waves of different intensities which interfere. After interference,the ratio of the maximum intensity to the minimum intensity is $16$. The ratio of the intensities of the waves is:

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