Question

If ${ϵ}_0$ and ${\mu }_0$ are, respectively, the electric permittivity and magnetic permeability of free space, $ϵ$ and $\mu$ are the corresponding quantities in a medium, the index of refraction of the medium in terms of the above parameters is _________.

• A. $\sqrt{\frac{\mu ϵ}{{\mu }_0{ϵ}_0}}$.
• B. $\sqrt{\frac{ϵ}{{\mu }_0{ϵ}_0}}$.
• C. $\sqrt{\frac{2}{{\mu }_0{ϵ}_0}}$.
• D. $\sqrt{\frac{1}{{\mu }_0{ϵ}_0}}$.

Answer 1

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

$\mu =\frac{c}{\upsilon }$ and $\upsilon =\sqrt{\frac{1}{{\mu }_o\epsilon }}$

Combining both

$\mu =\sqrt{\frac{1}{{\mu }_o\epsilon }}\times \sqrt{\frac{\mu \epsilon }{1}}=\sqrt{\frac{\mu \epsilon }{{\mu }_o{\epsilon }_o}}$