Two coherent sources of intensity ratio x^2 i | vedclass

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Question

(C) Let the intensities of the two coherent sources be $I_1$ and $I_2$. Given that the ratio of intensities is $I_1/I_2 = x^2$,we can write $I_1 = x^2

Vedclass · Accepted Answer

$\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} = \frac{2x}{1 + x^2}$

Vedclass · Answer

(C) Let the intensities of the two coherent sources be $I_1$ and $I_2$. Given that the ratio of intensities is $I_1/I_2 = x^2$,we can write $I_1 = x^2 I_2$ or $\sqrt{I_1/I_2} = x$.The maximum and minimum intensities in an interference pattern are given by:$I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$$I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$Now,consider the expression $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$:$I_{\max} - I_{\min} = (\sqrt{I_1} + \sqrt{I_2})^2 - (\sqrt{I_1} - \sqrt{I_2})^2 = 4\sqrt{I_1 I_2}$$I_{\max} + I_{\min} = (\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2 = 2(I_1 + I_2)$Therefore,$\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} = \frac{4\sqrt{I_1 I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1/I_2}}{I_1/I_2 + 1}$Substituting $\sqrt{I_1/I_2} = x$ and $I_1/I_2 = x^2$:$\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} = \frac{2x}{1 + x^2}$

Two coherent sources of intensity ratio $x^2$ interfere. In the interference pattern,which of the following relations is correct?

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