If \( \varepsilon_0 \) and \( \mu_0 \) represent the permittivity and permeability of vacuum, and \( \varepsilon \) and \( \mu \) represent the permittivity and permeability of a medium, then the refractive index of the medium is given by
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \sqrt{\frac{\mu\varepsilon}{\mu_0\varepsilon_0}} \)
The refractive index of a medium is the ratio of the speed of light in vacuum to its speed in the medium, \( n=c/v \). In vacuum the speed is \( c=1/\sqrt{\mu_0\varepsilon_0} \). In a material medium of permittivity \( \varepsilon \) and permeability \( \mu \) it becomes \( v=1/\sqrt{\mu\varepsilon} \).
Taking the ratio of the two speeds:
\( \begin{aligned} n &= \frac{c}{v} \\ &= \frac{1/\sqrt{\mu_0\varepsilon_0}}{1/\sqrt{\mu\varepsilon}} \\ &= \sqrt{\frac{\mu\varepsilon}{\mu_0\varepsilon_0}} \end{aligned} \)
NCERT (2026-27):
Nature of Electromagnetic Waves – “… one finds that ω = ck, where,
\( \displaystyle c=1/\sqrt{\mu_0\varepsilon_0} \qquad [8.9(a)] \)”
Nature of Electromagnetic Waves – “… in a material medium of permittivity ε and magnetic permeability μ, the velocity of light becomes,
\( \displaystyle v=\frac{1}{\sqrt{\mu\varepsilon}} \)\( \qquad (8.11) \)
Thus, the velocity of light depends on electric and magnetic properties of the medium. We shall see in the next chapter that the refractive index of one medium with respect to the other is equal to the ratio of velocities of light in the two media.”