  The gravitational redshift formula is usually derived in the geometric optics
approximation. In this note we consider an exact formulation of the problem in
the Schwarzschild space-time, with the intention to clarify under what
conditions this redshift law is valid. It is shown that in the case of shocks
the radial component of the Poynting vector can scale according to the redshift
formula, under a suitable condition. If that condition is not satisfied, then
the effect of the backscattering can lead to significant modifications. The
obtained results imply that the energy flux of the short wavelength radiation
obeys the standard gravitational redshift formula while the energy flux of long
waves can scale differently, with redshifts being dependent on the frequency.
