Question

If ${\mu }_0$ be the permeability and ${\epsilon }_0$ be the permittivity of a medium, then its refractive index is given by

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

Answer 1

Answer: (C)

Refractive index of medium is
$=\frac{c}{v}$
where $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$ and $v=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0{\mu }_r{\epsilon }_r}}$
$\therefore \mu =\frac{1/\sqrt{{\mu }_0{\epsilon }_0}}{1/\sqrt{{\mu }_0{\epsilon }_0{\mu }_r{\epsilon }_r}}=\sqrt{{\mu }_r{\epsilon }_r}$
Given ${\mu }_r={\mu }_0$ and ${\epsilon }_r={\epsilon }_0$ then
$\mu =\sqrt{{\mu }_0{\epsilon }_0}$