The light propagation within an absorbing medium and the reflection and refraction at the interface of two absorbing media are studied. By using the unit vectors denoting the planes of constant field amplitude and constant phase respectively, the light propagation and attenuation are described by the effective refractive indices which depend on both the complex refractive index of the medium and the angle between the unit vectors. With the expression for the light propagation, the corresponding Snell's law and the expression of Fresnel coefficients are obtained, which can be applied to describe the re°ection-refraction event at the interface between an arbitrary combination of transparent and absorbing media.