Question

The absolute refractive index values which are not possible

Answer 1

As Anthony Atkielski correctly wrote in an answer collapsed for unknown reason, a refractive index below 1 means a speed above the speed of light in vacuum, which is, according to theory of relativity, the highest possible speed.
This is so because refractive index is DEFINED as “speed of light in vacuum/speed of light in medium“.
Assume a refractive index of 1.5 ( glass), you gather speed of light in glass as 200.000 km/s, i.e. 300.000 km/s divided by 1.5.
Any medium having a refractive index below 1 would violate something which has that often be proven that we can quite savely assume it is a nature of law.

Or


Absolute refractive index being less than one means speed of light in that medium is more then c(3*10^8 m/s).
Which is not observed and not possible.