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(D) Given the ratio of intensities of two coherent sources is $\frac{I_1}{I_2} = n$.The maximum and minimum intensities in an interference pattern are

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

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(D) Given the ratio of intensities of two coherent sources is $\frac{I_1}{I_2} = n$.The maximum and minimum intensities in an interference pattern are given by $I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2$.We need to find the value of $R = \frac{I_{max} - I_{min}}{I_{max} + I_{min}}$.Substituting the expressions for $I_{max}$ and $I_{min}$:$R = \frac{(\sqrt{I_1} + \sqrt{I_2})^2 - (\sqrt{I_1} - \sqrt{I_2})^2}{(\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2}$Using the algebraic identities $(a+b)^2 - (a-b)^2 = 4ab$ and $(a+b)^2 + (a-b)^2 = 2(a^2 + b^2)$:$R = \frac{4\sqrt{I_1}\sqrt{I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1}\sqrt{I_2}}{I_1 + I_2}$Divide the numerator and denominator by $I_2$:$R = \frac{2\sqrt{I_1/I_2}}{I_1/I_2 + 1}$Since $\frac{I_1}{I_2} = n$,we get:$R = \frac{2\sqrt{n}}{n + 1}$

The interference pattern is obtained with two coherent light sources of intensity ratio $n$. In the interference pattern,the ratio $\frac{I_{max} - I_{min}}{I_{max} + I_{min}}$ will be

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