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Question

(C) The refractive index $n$ of a medium is related to its relative permittivity $\varepsilon_{r}$ and relative permeability $\mu_{r}$ by the formula:

Vedclass · Accepted Answer

$v=\frac{c}{\sqrt{\varepsilon_{r}\mu_{r}}}$

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(C) The refractive index $n$ of a medium is related to its relative permittivity $\varepsilon_{r}$ and relative permeability $\mu_{r}$ by the formula: $n = \sqrt{\varepsilon_{r}\mu_{r}}$.Since the refractive index is defined as the ratio of the speed of light in vacuum $c$ to the speed of light in the medium $v$,we have $n = \frac{c}{v}$.Rearranging this for $v$,we get $v = \frac{c}{n}$.Substituting the expression for $n$,we obtain the velocity of light in the medium as $v = \frac{c}{\sqrt{\varepsilon_{r}\mu_{r}}}$.

When light propagates through a material medium of relative permittivity $\varepsilon_{r}$ and relative permeability $\mu_{r}$,the velocity of light,$v$,is given by: ($c$ = velocity of light in vacuum)

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