Given below are two statements: one is labell | vedclass

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(C) The optical path length of a wave traveling through a medium of thickness $t$ and refractive index $\mu$ is given by $\Delta = \mu t$.When two wav

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Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$.

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(C) The optical path length of a wave traveling through a medium of thickness $t$ and refractive index $\mu$ is given by $\Delta = \mu t$.When two waves travel through media with different refractive indices $\mu_1$ and $\mu_2$ but the same thickness $t$,their optical paths are $\mu_1 t$ and $\mu_2 t$ respectively.The phase difference $\Delta \phi$ is related to the path difference $\Delta x$ by the relation $\Delta \phi = \frac{2 \pi}{\lambda_0} \Delta x$,where $\lambda_0$ is the wavelength in vacuum.Since the refractive index $\mu = \frac{\lambda_0}{\lambda_m}$ (where $\lambda_m$ is the wavelength in the medium),the wavelength in the medium is $\lambda_m = \frac{\lambda_0}{\mu}$.Because the wavelengths in the media are different due to different refractive indices,the optical paths differ,leading to a change in phase difference.Thus,both Assertion $A$ and Reason $R$ are correct,and $R$ is the correct explanation of $A$.

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