According to Maxwell's equations, the velocity of light in any medium…

The correct answer is Option (2) → \( \displaystyle\frac{1}{\sqrt{\mu\varepsilon}} \)

Maxwell’s equations lead to a wave equation for the fields, and the speed of the electromagnetic wave depends on the permeability \( \mu \) and permittivity \( \varepsilon \) of the medium:

    \( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} \)

With \( \mu = \mu_r\mu_0 \) and \( \varepsilon = \varepsilon_r\varepsilon_0 \):

    \( \displaystyle v = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\cdot\frac{1}{\sqrt{\mu_r\varepsilon_r}} = \frac{c}{\sqrt{\mu_r\varepsilon_r}} \)

Why the other options are incorrect

• Option (1) \( \displaystyle\frac{1}{\sqrt{\mu_0\varepsilon_0}} \) — Incorrect. \( 1/\sqrt{\mu_0\varepsilon_0} = c \) is the speed in vacuum only, not in any medium.

• Option (3) \( \displaystyle\frac{1}{\sqrt{\mu/\varepsilon}} \) — Incorrect. \( 1/\sqrt{\mu/\varepsilon} \) does not have the dimensions of speed; \( \sqrt{\mu/\varepsilon} \) has the dimensions of resistance.

• Option (4) \( \sqrt{\displaystyle\frac{\mu_o}{\varepsilon}} \) — Incorrect. This expression also has the dimensions of resistance, not of speed.

NCERT (2026-27):
Summary – “… The speed \( c \) of electromagnetic wave in vacuum is related to \( \mu_0 \) and \( \varepsilon_0 \) (the free space permeability and permittivity constants) as follows:

    \( \displaystyle c = 1/\sqrt{\mu_0\varepsilon_0} \)

The value of \( c \) equals the speed of light obtained from optical measurements.

Light is an electromagnetic wave; \( c \) is, therefore, also the speed of light. Electromagnetic waves other than light also have the same velocity \( c \) in free space.

The speed of light, or of electromagnetic waves in a material medium is given by

    \( \displaystyle v = 1/\sqrt{\mu\varepsilon} \)

where \( \mu \) is the permeability of the medium and \( \varepsilon \) its permittivity.”