I know taking the refractive index of the vacuum as unity, the refractive index of all the objects is calculated. So my question is that is it possible that a medium can have refractive index less than the reference refractive index (that is less than 1)? If yes, then what is its physical significance?
[Physics] Can a medium can have refractive index less than the reference refractive index (that is less than 1)
opticsrefractionspeed-of-light
Best Answer
Yes, you can have refractive indices less than one.
This is because the theory of relativity limits the group velocity to be less than $c$. Group velocity is the spèed at which information travels, and can be computed as:
$$v_g = \frac{d\omega}{dk}$$
where $\omega$ is the frequency and $k$ the wave number. In a non-dispersive medium, $\omega = k v_p$ and then $v_g = v_p$.
$v_p$ is the phase velocity, at which the perturbation of the wave travels. The index of refraction is defined using this speed: $$n=\frac{c}{v_p}$$
Since most times the relation $\omega = k v_p$ holds, both velocities (phase and group) are the same, so we cannot have $v_p$ greater than $c$ and the index of refraction is usually larger than 1.
However, the thing is that in some cases, we can have $v_p > c$ (always with $v_g < c$). This leads to rare cases where we can have a refractive index which less than 1, without violating special relativity.
It is also in the Wiki: https://en.wikipedia.org/wiki/Refractive_index#Refractive_index_below_unity