The ratio of speed of light in vacuum to the speed of light in a medium is :
Where \( \mu_{r} = \) relative permeability of the medium
\( \epsilon_{r} = \) relative permittivity of the medium
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sqrt{\mu_{r} \epsilon_{r}} \)
Maxwell's equations give the speed of an electromagnetic wave in terms of the permeability and permittivity of the medium:
\( \displaystyle c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}, \qquad v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{1}{\sqrt{\mu_r \mu_0\,\epsilon_r \epsilon_0}} \)
Dividing,
\( \displaystyle \frac{c}{v} = \sqrt{\frac{\mu_r \mu_0\,\epsilon_r \epsilon_0}{\mu_0 \epsilon_0}} = \sqrt{\mu_r \epsilon_r} \)
This ratio is the refractive index of the medium.