Question

If ${\mu }_r$ is the relative permeability and ${\epsilon }_r$ is the relative permittivity of a medium, the refractive index of the medium is given by

• A. $\frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}$
• B. $\sqrt{\frac{2{\mu }_r}{{\epsilon }_r}}$
• C. $\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}$
• D. $\sqrt{{\mu }_r{\epsilon }_r}$

Answer 1

Answer: (D)

$\sqrt{{\mu }_r{\epsilon }_r}$

Given: ${\mu }_r=relativepermeability,{\epsilon }_r=relativepermittivity$

Solution: Refractive index$=\frac{speedinvacuum\left(c\right)}{speedinmedium\left(v\right)}$

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

Where,${\mu }_0=$permeability in vacuum and

${\epsilon }_0=$pemittivity in vacuum

$v=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}{\mu }_r{\epsilon }_r}$ (${\mu }_r{\mu }_0=\mu$) (${\epsilon }_0{\epsilon }_r=\epsilon$)

Now putting together in refractive index equation

We get, refractive index$=\sqrt{{\mu }_r{\epsilon }_r}$

Hence, the correct option is D