Question

If ${\epsilon }_0$ and ${\mu }_0$ are the electric permittivity and magnetic permeability in a free space, $\epsilon$ and $\mu$ are the corresponding quantities in a medium, the index of refraction of the medium is,

• A. $\sqrt{\frac{{\epsilon }_0{\mu }_0}{\epsilon \mu }}$
  
• B. $\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}$
• C. $\sqrt{\frac{{\epsilon }_0\mu }{\epsilon {\mu }_0}}$
• D. $\sqrt{\frac{\epsilon }{{\epsilon }_0}}$

Answer 1

The correct option is B $\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}$

We know that refractive index of a medium is given by
$n=\frac{c}{v}$

Where, $c$ is the speed of light in vacuum and $v$ is the speed of light in the given medium.

We know that
$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

and $v=\frac{1}{\sqrt{\mu \epsilon }}$

$\Rightarrow n=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\times \sqrt{\mu \epsilon }$

or, $n=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}$

Hence, option $\left(B\right)$ is correct.