refraction - How phase velocity is related to deflection angle?

Refractive index is a function of velocity in the medium.How is this related to deviation angle inside the medium?

Answer

Provided that the electron & the atomic beams also exhibit refraction,it seems that this is a particle's property.Deflection angle is proportional to particle's mass/size for specific medium.Photon behaves as particle in this effect.Mass is given by de Broglie equation:m=hv/c^2 , v=frequency