Question

How is the refractive index of a medium related to the speed of light in it and in vacuum or air??

Answer 1

For going to the actual answer first, let us know about the basics. It can help you for precise overview of every concepts.

For oblique incidence of light ray, and for a particular (definite) colour of light, the ratio of the sine of the angle of incidence in the first medium to the sine of the angle of refraction in second medium is always constant according to Snell's law. This constant, however, is actually called as the ${REFRACTIVE\:INDEX}$ of the second medium with respect to the first medium.

Now, the refractive index of the second medium with respect to the first medium is also defined as the the ratio of the velocity of light in the first medium to the velocity of light in second medium. This is actually RELATIVE refractive index.

Coming to your question, you are asking about ABSOLUTE refractive index.

Now, Absolute refractive index is equal to $\frac{Velocity \: of \: light \: in \: vacuum}{Velocity \: of \: light \: in \: that \: \: medium}$.

Now, speed of light in vacuum is almost equal to speed kf light in air. Hence, it is taken into consideration that velocity of light in VACUUM is equal to velocity of light in AIR.

Also, remember the $\bold{FACTORS}$ affecting the refractive index of a medium.

[1] Nature of the medium (rarer/denser)

[2] Physical condition like temperature of the medium.

[3] Colour of light used.