If \( \varepsilon_{0} \) and \( \mu_{0} \) are dielectric permittivity and magnetic permeability of free space, respectively, \( \varepsilon \) and \( \mu \) are the corresponding quantities pertaining to a medium, then the refractive index of the medium is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \sqrt{\displaystyle\frac{\varepsilon\mu}{\varepsilon_{0}\mu_{0}}} \)
The speed of electromagnetic waves in a medium is \( v = 1/\sqrt{\mu\varepsilon} \), and in free space \( c = 1/\sqrt{\mu_0\varepsilon_0} \). The refractive index is the ratio \( n = c/v \).
\( \displaystyle n = \frac{c}{v} = \frac{1/\sqrt{\mu_0\varepsilon_0}}{1/\sqrt{\mu\varepsilon}} = \sqrt{\frac{\varepsilon\mu}{\varepsilon_0\mu_0}} \)