  We present magneto-optical reflectivity results in the basal-plane of the
hexagonal $MgB_2$. The data were collected on a mosaic of $MgB_2$ single
crystals with $T_{c}=38 ~K$ from the ultraviolet down to the far infrared as a
function of temperature and magnetic field oriented along the c-axis. In the
far infrared there is a clear signature of the superconducting gap with a
gap-ratio $2\Delta/k_{B}T_{c}\sim 1.2$, well below the weak-coupling value. The
gap is suppressed in an external magnetic field, which is a function of
temperature. We extract the upper critical field $H_{c2}$ along the c-axis. The
temperature dependence of $H_{c2}$ is compatible with the Helfand-Werthamer
behaviour.

Superconductivity