In a Young's double slit experimental arrange | vedclass

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(B) When a mica sheet of thickness $t$ and refractive index $\mu$ is placed in the path of light from slit $S_1$, the optical path length for the ray

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Increases by $(\mu - 1)t$

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(B) When a mica sheet of thickness $t$ and refractive index $\mu$ is placed in the path of light from slit $S_1$, the optical path length for the ray traveling from $S_1$ to $P$ increases.In vacuum, the path length is $t$, but in the medium, the optical path length becomes $\mu t$.The extra optical path introduced is $\Delta x = \mu t - t = (\mu - 1)t$.Since this extra path is added to the path $S_1P$, the new path difference becomes $(S_1P + (\mu - 1)t) - S_2P$.Therefore, the path difference $(S_1P - S_2P)$ increases by $(\mu - 1)t$.

In a Young's double slit experimental arrangement shown here, if a mica sheet of thickness $t$ and refractive index $\mu$ is placed in front of the slit $S_1$, then the path difference $(S_1P - S_2P)$

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