  The basic cosmological distances are linked by the Etherington cosmic
distance duality relation, $\eta (z) = D_{L}(z)(1+z)^{-2}/D_{A}(z) \equiv 1$,
where $D_{L}$ and $D_{A}$ are, respectively, the luminosity and angular
diameter distances. In order to test its validity, some authors have proposed
phenomenological expressions for $\eta(z)$ thereby deforming the original
Etherington's relation and comparing the resulting expressions with the
available and future cosmological data. The relevance of such studies is
unquestionable since any violation of the cosmic distance duality relation
could be the signal of new physics or non-negligible astrophysical effects in
the usually assumed perfectly transparent Universe. In this letter, we show
that under certain conditions such expressions can be derived from a more
fundamental approach with the parameters appearing in the $\eta(z)$ expression
defining the cosmic absorption parameter as recently discussed by Chen and
Kantowski. Explicit examples involving four different parametrizations of the
deformation function are given. Based on such an approach, it is also found
that the latest Supernova data can also be explained in the framework of a pure
cold dark matter model (Einstein-de Sitter). Two different scenarios with
cosmic absorption are discussed. Only if the cosmic opacity is fully
negligible, the description of an accelerating Universe powered by dark energy
or some alternative gravity theory must be invoked.
