Question

If ${\varepsilon}_0$ and ${\mu}_0$ are the electric permittivity and magnetic permeability in a free space, $\varepsilon$ and $\mu$ are the corresponding quantities in medium, the index and refraction of the medium is

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

Answer 1

Answer: (B)

$\sqrt{ \frac{\varepsilon \mu}{{\varepsilon}_0 {\mu}_0}}$

Answer 2

$c= \frac{ 1}{ \sqrt{{\mu}_0 { \varepsilon}_0 }}$(free space)
$v= \frac{1}{ \sqrt{\mu \varepsilon}}$ (medium)
$\therefore \, \, \, \, \, \mu = \frac{c}{v} = \sqrt{ \frac{ \mu \varepsilon }{ { \mu}_0 {\varepsilon}_0 }}$