  Heavily-boron-doped diamond films become superconducting with critical
temperatures $T_c$ well above 4 K. Here we first measure the reflectivity of
such a film down to 5 cm$^{-1}$, by also using Coherent Synchrotron Radiation.
We thus determine the optical gap, the field penetration depth, the range of
action of the Ferrell-Glover-Tinkham sum rule, and the electron-phonon spectral
function. We conclude that diamond behaves as a dirty BCS superconductor.
