Heavily boron-doped, diamond films can become superconducting with critical temperatures Tc 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 2Delta, the field penetration depth lambda, the range of action of the Ferrell-Glover-Tinkham sum rule, and the electron-phonon spectral function alpha2F(omega). We conclude that diamond behaves as a dirty BCS superconductor.