Question

Choose the correct answer from the alternatives given.
If ${\epsilon }_0$ and ${\mu }_0$ are respectively the electric permittivity and the magnetic permeability of free space and $\epsilon$ and $\mu$ the corresponding quantities in a medium, the refractive index of the medium is

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

Answer 1

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

So, Refractive index of a medium is given by

$n=\frac{c}{v}$.....................(1)

$c$ is the velocity of light in vacuum.

$v$ is the velocity of light in the medium.

Also, speed is given by $\frac{1}{\sqrt{\mu ϵ}}$

$c$ $=$ $\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$..........(2)

$v$ $=$ $\frac{1}{\sqrt{\mu ϵ}}$.................(3)

From eq (1), (2) and (3):

$n=\sqrt{\frac{\mu ϵ}{{\mu }_0{ϵ}_0}}$