Abstract: In an isotropic non-absorbing medium， light propagates without the amplitude attenuation and refracts at the interface of two media obeying Snell’s law with real numbers. However， light travels in a homogeneous absorption medium with not only the attenuation of amplitude along the direction of propagation，but also the separation between equi-amplitude and equi-phase surfaces. Considering these phenomena， this work reviews the concept of the complex refractive index and Snell’s law with complex indexes. Then two typical cases are discussed，namely， light incident from an absorbing medium to an absorbing medium，and light incident from a non-absorbing medium to an absorbing medium，by which the necessity and convenience of Snell’s law with complex indexes are demonstrated. The relationship between Snell’s law with real form and Snell’s law with complex form is also clarified.