  We study theoretically the concept of homogenization in optics using an
ensemble of randomly distributed resonant stationary atoms with density $\rho$.
The ensemble is dense enough for the usual condition for homogenization, viz.
$\rho\lambda^3 \gg 1$, to be reached. Introducing the coherent and incoherent
scattered powers, we define two criteria to define the homogenization regime.
We find that when the excitation field is tuned in a broad frequency range
around the resonance, none of the criteria for homogenization is fulfilled,
meaning that the condition $\rho\lambda^3\gg 1$ is not sufficient to
characterize the homogenized regime around the atomic resonance. We interpret
these results as a consequence of the light-induced dipole-dipole interactions
between the atoms, which implies a description of scattering in terms of
collective modes rather than as a sequence of individual scattering events.
Finally, we show that, although homogenization can never be reached for a dense
ensemble of randomly positioned laser-cooled atoms around resonance, it becomes
possible if one introduces spatial correlations in the positions of the atoms
or non-radiative losses, such as would be the case for organic molecules or
quantum dots coupled to a phonon bath.
