On Compton scattering in dielectric medium

The Compton scattering in a dielectric medium is adopted. We have found that the momentum and energy of the photon inside the medium are related by the formula E′ = ncp′, where n is the refractive index of the medium. This formula is shown to stem from the invariance of the Einstein relativity relation, p=v(E/c2) inside and outside the medium. The Minkowski and Abraham models of refractive index p′ = nE/c and p′ = E/(nc), respectively, require that E′ = E and E′ = n2E, respectively. The former model treated the photon as a wave (massless) and the latter treated the photon as a particle (matter) with an effective mass. The Snell's law is obtained by further imposing that the horizontal component of the light momentum remains the same.