  We report an infrared spectroscopy study of a 200 nm thick
FeSe$_{0.5}$Te$_{0.5}$ film grown on LaAlO$_3$ with T$_c$=13.7 K. We analyze
the 20 K normal state absolute reflectance R$_N$ measured over a broad infrared
range and the reflectance ratio R$_S$/R$_N$, R$_S$ being the superconducting
state reflectance, measured at 6 K in the terahertz range down to 12 cm$^{-1}$.
We show that the normal state model conductivity is given by two Drude
components, one of which much broader and intense than the other. In the
superconducting state, we find that a gap $\Delta$=37$\pm$3 cm$^{-1}$ opens up
in the narrow Drude band only, while the broad Drude band results to be
ungapped, at least in the explored spectral range. Our results show that only a
two-band model can coherently describe both normal and superconducting state
data.
