  Using the most recent observational data concerning the Extragalactic
Background Light and the Radio Background, for a source at a redshift z_s < 3
we compute the energy E_0 of an observed gamma-ray photon in the range 10 GeV <
E_0 < 10^13 GeV such that the resulting optical depth tau_gamma(E_0,z_s) takes
the values 1, 2, 3 and 4.6, corresponding to an observed flux dimming of e^-1 =
0.37, e^-2 = 0.14, e^-3 = 0.05 and e^-4.6 = 0.01, respectively. Below a source
distance D = 8 kpc we find that tau_gamma(E_0,DH_0/c) < 1 for any value of E_0.
In the limiting case of a local Universe (z_s = 0) we compare our result with
the one derived in 1997 by Coppi and Aharonian. The present achievement is of
paramount relevance for the planned ground-based detectors like CTA, HAWC and
HiSCORE.
