For a medium with permittivity \( (\varepsilon) \) and permeability \( (\mu) \), the speed of light \( (v) \) is given by:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( v = \sqrt{\displaystyle\frac{1}{\mu\varepsilon}} \)
Maxwell's equations give the speed of an electromagnetic wave in vacuum in terms of \( \mu_0 \) and \( \varepsilon_0 \). In a material medium the same result holds with the permeability and permittivity of the medium.
\( \displaystyle c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \quad\Rightarrow\quad v = \frac{1}{\sqrt{\mu\varepsilon}} = \sqrt{\frac{1}{\mu\varepsilon}} \)
Shortcut: Check the units: \( \mu_0\varepsilon_0 = 1/c^{2} \) has the unit \( \mathrm{s^{2}\,m^{-2}} \), so only \( 1/\sqrt{\mu\varepsilon} \) comes out in \( \mathrm{m\,s^{-1}} \). Option (2) has the unit \( \mathrm{s\,m^{-1}} \), and options (1) and (4) are not speeds at all.
Note: A similar question was also asked in CUET (UG) 2026 on 19-05-2026 (Slot 1).
NCERT (2026-27):
Summary – “… The speed of light, or of electromagnetic waves in a material medium is given by
\( \displaystyle v = \frac{1}{\sqrt{\mu\,\epsilon}} \)
where μ is the permeability of the medium and ε its permittivity.”