Two coherent sources of different intensities | vedclass

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(C) Let the intensities of the two sources be $I_1$ and $I_2$. The maximum and minimum intensities in an interference pattern are given by $I_{\max} =

Vedclass · Accepted Answer

$9:4$

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(C) Let the intensities of the two sources be $I_1$ and $I_2$. The maximum and minimum intensities in an interference pattern are given by $I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$.Given $\frac{I_{\max}}{I_{\min}} = 25$,we have $\left( \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} \right)^2 = 25$.Taking the square root on both sides,$\frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} = 5$.Let $x = \sqrt{\frac{I_1}{I_2}}$. Then $\frac{x+1}{x-1} = 5$.$x + 1 = 5x - 5 \Rightarrow 4x = 6 \Rightarrow x = \frac{3}{2}$.Therefore,$\frac{I_1}{I_2} = x^2 = \left( \frac{3}{2} \right)^2 = \frac{9}{4}$.

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is $25$. The intensities of the sources are in the ratio:

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