Based on the principle of general relativity,geometrization of interaction,the interaction of the inhomogeneous isotropic medium to light can be equated to a non-Euclidean geometry field just like the situation of gravity,i.e.,light travels in the null geodesic in the non-Euclidean curved space-time,which is equivalent to the Fermat principle for the inhomogeneous media.In this paper,the propagation of light in an inhomogeneous media is studied by means of the effective metric theory.The modification to the classical ray equation of photons is derived from the geodesic equation of photon by considering the spin effect of photons,which is induced via the spin-orbit coupling of photons,and the corresponding Hamiltonian of photonis proposed.Based on the spin-orbit coupling of photon,a light splitting phenomenon emerges in the inhomogeneous media,which is the spin hall effect of photon.
