Two light rays having the same wavelength lam | vedclass

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(C) The optical path length in a medium of refractive index $\mu$ for a physical path length $L$ is defined as $\Delta = \mu L$.For the first ray,the

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$\frac{2 \pi}{\lambda}[\mu_1 L_1-\mu_2 L_2]$

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(C) The optical path length in a medium of refractive index $\mu$ for a physical path length $L$ is defined as $\Delta = \mu L$.For the first ray,the optical path is $\Delta_1 = \mu_1 L_1$.For the second ray,the optical path is $\Delta_2 = \mu_2 L_2$.The path difference between the two rays is $\Delta x = |\Delta_1 - \Delta_2| = |\mu_1 L_1 - \mu_2 L_2|$.The phase difference $\phi$ is related to the path difference $\Delta x$ by the formula $\phi = \frac{2 \pi}{\lambda} \Delta x$.Therefore,the phase difference is $\frac{2 \pi}{\lambda} |\mu_1 L_1 - \mu_2 L_2|$.Comparing this with the given options,the correct expression is $\frac{2 \pi}{\lambda} [\mu_1 L_1 - \mu_2 L_2]$.

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