Question

Refractive index of materials is approximately equal to square root of

Answer 1

Ans : Dielectric constant

Hope it will help you

Answer 2

Given that,

Refractive index = n

We know that,

Refractive index is equal to the ratio of speed of light in medium and speed of light in vacuum.

In mathematically,

$n=\dfrac{v}{c}$

We know that,

From maxwell's equation,

Speed of light in medium $v=\dfrac{1}{\sqrt{\mu\epsilon}}$

Speed of light in vacuum $c=\dfrac{1}{\sqrt{\mu_{0}\epsilon_{0}}}$

We need to calculate the refractive index of materials

Using formula of refractive index

$n=\dfrac{v}{c}$

Put the value of v and c from maxwell's equation

$n=\dfrac{\dfrac{1}{\sqrt{\mu\epsilon}}}{\dfrac{1}{\sqrt{\mu_{0}\epsilon_{0}}}}$

$n=\dfrac{\sqrt{\mu_{0}\epsilon_{0}}}{\sqrt{\mu\epsilon}}$

$n=\sqrt{\dfrac{\mu_{0}\epsilon_{0}}{\mu\epsilon}}$

Hence, The refractive index of materials is  equal to square root of $\dfrac{\mu_{0}\epsilon_{0}}{\mu\epsilon}$