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(D) Given that the ratio of intensities of two coherent sources is $\frac{I_1}{I_2} = 2x$.We know that $I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I

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$\frac{2 \sqrt{2x}}{2x + 1}$

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(D) Given that the ratio of intensities of two coherent sources is $\frac{I_1}{I_2} = 2x$.We know that $I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$.Substituting these into the expression $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$:Numerator: $I_{\max} - I_{\min} = (I_1 + I_2 + 2\sqrt{I_1I_2}) - (I_1 + I_2 - 2\sqrt{I_1I_2}) = 4\sqrt{I_1I_2}$.Denominator: $I_{\max} + I_{\min} = (I_1 + I_2 + 2\sqrt{I_1I_2}) + (I_1 + I_2 - 2\sqrt{I_1I_2}) = 2(I_1 + I_2)$.Thus,the ratio is $\frac{4\sqrt{I_1I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1I_2}}{I_1 + I_2}$.Dividing the numerator and denominator by $I_2$,we get $\frac{2\sqrt{I_1/I_2}}{I_1/I_2 + 1}$.Substituting $\frac{I_1}{I_2} = 2x$,we get $\frac{2\sqrt{2x}}{2x + 1}$.

Two coherent light sources having intensity in the ratio $2x$ produce an interference pattern. The ratio $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$ will be

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