Question

If ${\mu }_0,{\epsilon }_0$ are the absolute permeability and permitivity respectively, of space, ${\mu }_r,{\epsilon }_r$ are the relative permeability and permittivity respectively of mediums and $\mu ,\epsilon$ are the absolute permeability and permittivity of medium respectively, then the refractive index of the medium is

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

Answer 1

Answer: (A), (C)

As, $\mu =\frac{c}{v}=\frac{1/\sqrt{{\mu }_0{\epsilon }_0}}{\sqrt{\mu \epsilon }}$
$=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}=\sqrt{\frac{{\mu }_r{\mu }_0{\epsilon }_0{\epsilon }_r}{{\mu }_0{\epsilon }_0}}$
$=\sqrt{{\mu }_r{\epsilon }_r}$