Question

If $ \mu_{0}$ be the permeability and $\varepsilon_{0} $ be the permittivity of a medium, then its refractive index is given by

• A. $ \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}} $
• B. $\frac{1}{ \mu_{0}\varepsilon_{0} }$
• C. $ \sqrt{\mu_{0}\varepsilon_{0}} $
• D. $ \mu_{0}\varepsilon_{0} $

Answer 1

Answer: (C)

Refractive index of medium is
$= \frac{c}{v}$
where $c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$ and $v = \frac{1}{\sqrt{\mu _{0}\varepsilon _{0}\mu_{r}\varepsilon_{r}}}$
$\therefore \quad\mu = \frac{1 /\sqrt{\mu _{0}\varepsilon _{0}}}{1 / \sqrt{\mu _{0}\varepsilon _{0}\mu _{r}\varepsilon _{r}}} = \sqrt{\mu _{r}\varepsilon _{r}}$
Given $\mu_{r} = \mu_{0}$ and $\varepsilon_{r} = \varepsilon_{0}$ then
$\mu = \sqrt{\mu _{0}\varepsilon _{0}}$