If $v_{1}, v_{2}$ and $c$ represent the speed of light in medium $1$ , medium $2$ , and vacuum respectively, write the expression for
a)absolute refractive index of medium $1$
b)absolute refractive index of medium $2$
Hence show that, $η_{2} = \frac{v_{1}}{v_{2}}$

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Solution

Given,
$v_{1} =$ speed of light in medium $1$
$v_{2} =$ speed of light in medium $2$
$c =$ Speed of light in vacuum.

(a) Absolute refractive index of medium $1$ ,
$η_{1} = \frac{c}{v_{1}}$

(b) Absolute refractive index of medium $2$ ,
$η_{2} = \frac{c}{v_{2}}$

$η_{21} = \frac{η_{2}}{η_{1}}$

$= \frac{c / v_{2}}{c / v_{1}}$

$η_{21} = \frac{v_{1}}{v_{2}}$

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