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.
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