The speed of light in a material medium is given by:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( (\mu\varepsilon)^{-1/2} \)
Maxwell’s theory shows that an electromagnetic wave travels with speed \( \frac{1}{\sqrt{\mu\varepsilon}} \), where \( \mu \) and \( \varepsilon \) are the permeability and permittivity of the medium in which it travels.
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = (\mu\varepsilon)^{-1/2} \)
Why the other options are incorrect
Option (2) \( (\mu_0\varepsilon_0)^{1/2} \) — Incorrect. This is \( 1/c \), the reciprocal of the speed of light in vacuum.
Option (3) \( (\mu_0\varepsilon_0)^{-1/2} \) — Incorrect. This is the speed of light in vacuum, \( c \), since it uses the constants of free space and not those of the medium.
Option (4) \( (\mu\varepsilon)^{1/2} \) — Incorrect. This is \( 1/v \), the reciprocal of the speed in the medium.
Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 2), and in CUET (UG) 2025 on 20-05-2025 (Slot 2).
NCERT (2026-27):
Nature of Electromagnetic Waves – “… These replace ε0 and μ0 in the description to electric and magnetic fields in Maxwell’s equations with the result that in a material medium of permittivity ε and magnetic permeability μ, the velocity of light becomes,
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} \qquad (8.11) \)”