Question

How is the refractive index of a medium related to the speed of light? Obtain an expression for refractive index of a medium with respect to another in terms of speed of light in these two media?

Answer 1

The refractive index of the medium n_m is given by 
n_m=  (Speed of light in air) / (Speed of light in medium)=c/v 
Let v₁ be the speed of light in medium 1 and v₂ be the speed of light in medium 2. The refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. This is usually represented by the symbol n₂₁. 
n₂₁ =(Speed of light in medium 1)/ (Speed of light in medium 2)=v₁/v₂