Using the most recent observational data concerning the Extragalactic Background Light and the Radio Background , for a source at an arbitrary redshift in the range 10 ^ { -6 } \leq z _ { s } \leq 3 we compute the energy E _ { 0 } of an observed \gamma -ray photon in the range 10 { GeV } \leq E _ { 0 } \leq 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 } \simeq 0.37 , e ^ { -2 } \simeq 0.14 , e ^ { -3 } \simeq 0.05 and e ^ { -4.6 } \simeq 0.01 , respectively .
Below z _ { s } \simeq 10 ^ { -6 } we find that \tau _ { \gamma } ( E _ { 0 } ,z _ { s } ) < 1 for any value of E _ { 0 } .
In the limiting case of a local Universe ( z _ { s } \simeq 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 .