Question

If ${ϵ}_{o}and{\mu }_o$ are the electric permeability and magnetic permeability in free space $ϵand\mu$ are the corresponding quantities in a medium , then of refraction of the medium is

• A. $\sqrt{\frac{{ϵ}_o{\mu }_o}{ϵ{\mu }_o}}$
• B. $\sqrt{\frac{ϵ}{{ϵ}_o}}$
• C. $\sqrt{\frac{{ϵ}_o{\mu }_o}{ϵ\mu }}$
• D. $\sqrt{\frac{ϵ\mu }{{ϵ}_o{\mu }_o}}$

Answer 1

Answer: (D)

$\sqrt{\frac{ϵ\mu }{{ϵ}_o{\mu }_o}}$

The velocity of the electromagnetic waves in free space is given by
$\frac{1}{\sqrt{{\mu }_o{ϵ}_o}}$
and the velocity of the electromagnetic waves in the medium is given by
$V=\frac{1}{\sqrt{\mu ϵ}}$
Now, refractive index of the medium
$n=\frac{C}{V}$
$=\frac{1}{{\mu }_o{ϵ}_o}\times \frac{\sqrt{\mu ϵ}}{1}=\sqrt{\frac{\mu ϵ}{{\mu }_o{ϵ}_o}}$
$\therefore$ the correct option is (D)