  The experimental data on the $^{16}$O$+^{12}$C and $^{18}$O$+^{12}$C elastic
scatterings and their optical model analysis are presented. Detailed and
complete elastic angular distributions have been measured at the Strasbourg
Vivitron accelerator at several energies covering the energy range between 5
and 10 MeV per nucleon. The elastic scattering angular distributions show the
usual diffraction pattern and also, at larger angles, refractive effects in the
form of nuclear rainbow and associated Airy structures. The optical model
analysis unambiguously shows the evolution of the refractive scattering
pattern. The observed structure, namely the Airy minima, can be consistently
described by a nucleus-nucleus potential with a deep real part and a weakly
absorptive imaginary part. The difference in absorption in the two systems is
explained by an increased imaginary (mostly surface) part of the potential in
the $^{18}$O$+^{12}$C system. The relation between the obtained potentials and
those reported for the symmetrical $^{16}$O$+^{16}$O and $^{12}$C$+^{12}$C
systems is drawn.
