Refractive index of the medium having absolute permeability \( \mu \) and absolute permittivity \( \epsilon \) is
\( \mu_0 \) – Permeability of free space
\( \epsilon_0 \) – Permittivity of free space
\( \mu_r \) – Relative Permeability
\( \epsilon_r \) – Relative Permittivity
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \sqrt{\mu_r \epsilon_r} \)
The refractive index is the ratio of the speed of light in vacuum to its speed in the medium, and the speed of an electromagnetic wave depends on the permeability and permittivity of the medium.
\( \displaystyle c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \qquad v = \frac{1}{\sqrt{\mu \epsilon}} \)
\( \displaystyle n = \frac{c}{v} = \sqrt{\frac{\mu \epsilon}{\mu_0 \epsilon_0}} \)
With \( \mu = \mu_r \mu_0 \) and \( \epsilon = \epsilon_r \epsilon_0 \):
\( \displaystyle n = \sqrt{\mu_r \epsilon_r} \)