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 or medium is, $= \frac{c}{v}$

where $c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$

and $V = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}\mu_{r}\varepsilon_{r}}}$

$\therefore\mu = \frac{1/\sqrt{\mu_{0}\varepsilon_{0}}}{1/\sqrt{\mu_{0}\varepsilon_{0}\mu_{r}\varepsilon_{r}}} = \sqrt{\mu_{r}\varepsilon_{r}}$

Given $\mu_{r} = \mu_{0}$ and $\varepsilon_{r} = \varepsilon_{0}$ then $\mu\sqrt{\mu_{0}\varepsilon_{0}}$