Another argument in favor of the Minkowski form of the momentum of light in matter

Abstract

Magnitudes of the momentum of light are compared in a two situations where identical ideal reflectors are moving at identical speeds towards the light waves of identical energy density fluxes propagating in free space and in an optical medium. First, increases of frequencies the reflected waves are compared. Based on the Doppler law, it is shown that an increase of the frequency of the reflected wave in the second case is greater by n times as compared with that in the first case where n is the reflective index of the optical medium. Second, it is shown that an increase of the energies of the reflected wave in the second case is also by n times greater than that in the first one. As a result, the pressure on the reflector is greater by n times in second case than that in the first one. Third, it is shown that the pressure on the reflector is produced due to a change of the momentum density flux of the wave reflected from the reflector. Since the pressure on the reflector in the second case is greater by n times than that in the first case, a conclusion is made that the momentum flux density of the wave propagating in an optical medium is greater by n times than that of the wave propagating in free space provided that the energy density fluxes of these waves are identical.