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The gravitational redshift formula is usually derived in the geometric opticsapproximation. In this note we consider an exact formulation of the problem inthe Schwarzschild space-time, with the intention to clarify under whatconditions this redshift law is valid. It is shown that in the case of shocksthe radial component of the Poynting vector can scale according to the redshiftformula, under a suitable condition. If that condition is not satisfied, thenthe effect of the backscattering can lead to significant modifications. Theobtained results imply that the energy flux of the short wavelength radiationobeys the standard gravitational redshift formula while the energy flux of longwaves can scale differently, with redshifts being dependent on the frequency.Comment: Revtex, 5 p. Rewritten Sec. II, minor changes in Secs III - VII. To  appear in the Classical and Quantum Gravit

Schwarzschild horizon and the gravitational redshift formula