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)

$\sqrt{\mu_{0}\varepsilon_{0}}$

Answer 2

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 $\mu = \sqrt{\mu _{0}\varepsilon _{0}}$