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(B) The fringe visibility $V$ is defined as $V = \frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$.Given the intensities of the two sources are $I_1$ a

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

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(B) The fringe visibility $V$ is defined as $V = \frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$.Given the intensities of the two sources are $I_1$ and $I_2$,such that $\frac{I_1}{I_2} = p$.The maximum intensity is $I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and the minimum intensity is $I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$.Substituting these into the visibility formula:$V = \frac{(\sqrt{I_1} + \sqrt{I_2})^2 - (\sqrt{I_1} - \sqrt{I_2})^2}{(\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2} = \frac{4\sqrt{I_1 I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1 I_2}}{I_1 + I_2}$.Dividing the numerator and denominator by $I_2$:$V = \frac{2\sqrt{I_1/I_2}}{I_1/I_2 + 1} = \frac{2\sqrt{p}}{p + 1}$.Thus,the correct option is $B$.

The intensity ratio of two coherent sources of light is $p$. They are interfering in some region and produce an interference pattern. Then the fringe visibility is

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