  We determine the Compton effect from the Volkov solution of the Dirac
equation for a process in a medium with the index of refraction n. Volkov
solution involves the mass shift, or, the mass renormalization of an electron
mass. We determine the modified Compton formula for the considered physical
situation. The index of refraction causes that the wave lenghths of the
scattered photons are shorter for some angles than the wave lengths of the
original photons. This is anomalous Compton effect. Since the wave length shift
for the visible light is only 0,01 percent, it means that the Compton effect
for the visible light in the dielectric medium needs experimental virtuosity.
