The ratio of intensities of two coherent sour | vedclass

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(A) The visibility $V$ of interference fringes is defined as $V = \frac{I_{max} - I_{min}}{I_{max} + I_{min}}$.Given the intensities of two coherent s

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$2\sqrt{p} / (1 + p)$

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(A) The visibility $V$ of interference fringes is defined as $V = \frac{I_{max} - I_{min}}{I_{max} + I_{min}}$.Given the intensities of two coherent sources are $I_1$ and $I_2$,we have $I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$ and $I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2$.Substituting these into the formula for $V$:$V = \frac{(\sqrt{I_1} + \sqrt{I_2})^2 - (\sqrt{I_1} - \sqrt{I_2})^2}{(\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2} = \frac{4\sqrt{I_1 I_2}}{2(I_1 + I_2)} = \frac{2\sqrt{I_1 I_2}}{I_1 + I_2}$.Dividing the numerator and denominator by $I_2$:$V = \frac{2\sqrt{I_1/I_2}}{I_1/I_2 + 1}$.Given the ratio $p = I_1/I_2$,we substitute $p$ into the equation:$V = \frac{2\sqrt{p}}{1 + p}$.

The ratio of intensities of two coherent sources is $p$. The visibility of the fringes in the interference pattern is given by:

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