Question

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

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

Answer 1

Answer: (B)

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