Question

If ${\epsilon }_0\text{and}{\mu }_0$ are respectively the permittivity and magnetic permeability of free space, $\epsilon$ and $\mu$ are the corresponding quantities in a medium. The refractive index of the medium is-

• A. $\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}$
• B. $\sqrt{\frac{{\mu }_0{\epsilon }_0}{\mu \epsilon }}$
• C. $\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}$
• D. ${\left(\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}\right)}^2$

Answer 1

The correct option is A $\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}$

The refractive index of the medium $\left(n\right)$ is given by,

$\text{Refractive index}=\frac{\text{velocity of light in vacuum}\left(c\right)}{\text{velocity of light in medium}\left(v\right)}$

$\because c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

$n=\frac{\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}}{\frac{1}{\sqrt{\mu \epsilon }}}=\sqrt{\frac{\mu \epsilon }{{\mu }_0{\epsilon }_0}}=\sqrt{{\mu }_r{\epsilon }_r}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.