Polarization in Nicol prism My book reads
"When unpolarized light is incident on nicol prism (made of 2 crystals joined by Canada balsam a type of glue) it divides into 2 rays, both rays are plane polarized and electric field vectors of one of the rays are perpendicular to plane. These ray is Ordinary Ray. And electric field vector of another ray have oscillatios parallel  to the plane. These ray is Extra ordinary ray. For these refractive index are 1.658 &1.486 respectively.The refractive index of Canada Balsam is 1.55. so, ordinary ray experiencs TIR at the surface of the glue Canada Balsam and comes out from one side of the prism while extra ordinary ray comes out as plane polarized light"
My question is
"Is it possible for a medium (here calcite) to have two refractive indices?"
 A: "Is it possible for a medium (here calcite) to have two refractive indices?"
Yes. Birefringence refers to the property that the refractive index of a material depends upon the polarization or direction of light through the material.   
A: Yes, an object standing responsible for polarization can  have two refractive indices.
For example, calcite is a bireferingent material which splits up a plane polarised light into an e ray (one which doesnt obey Snell's law) and an o ray (one which obeys Snell's law) once incident on its surface. Since the velocity of both the rays will be different, there arises the concept of two refractive indices. The velocity of the o ray remains the same at every point, but that of e ray will be maximum in the direction perpendicular to the optic axis in the case of calcite. $v=c/n$, where $v$ is velocity, $c$ is the speed of light, and $n$ is the refractive index. Hence, let the velocity of the e ray be $V$ and velocity of the o ray be $v$, and hence $N=c/V$ and $n=c/v$, hence two refractive indices
