Double refraction , Birefringence

There exists some type of crystal in which when light pass through them they are refracted in 2 way (calcites and quartz crystals) . I.e it has different refractive index for different  polarized light results some ray behave Ordinarily we call Ordinary Ray (O-ray) some Ray behave Extra Ordinarily we call it's Extraordinary Ray(E-ray) both E-ray and O-ray are plane polarized and E-vector(or B) of those two wave are perpendicular to each other i.e the plane of polarization perpendicular to each other . 

Why some type of crystal has this property ?

The secret lies on the structure of solid . Atomic dipole that exist in the  solid allows wave pass(absorbing vibrating & re-radiating) certain E vector absorbed by atomic dipole  more efficiently in one direction and less efficiently in other direction that results E-ray and O-ray have different velocity in same medium because refractive index depends upon velocity it has two different refractive index for different polarized light .

Let Ve is the velocity of E-ray

Vo is the velocity of O-ray 

If 

Ve<Vo the crystal is positive (eg . quartz)

If Vo<Ve the crystal is negative (calcites)

 But when unpolarized light i.e both mixed of with E-ray and O-ray get through the glass E-ray and O-ray both behave differently or accordingly to refractive index resulting double refraction this is why we call this bi-fringness bi mean 2 fringness - ray lines