  We measured the THz reflectance properties of a high quality epitaxial thin
film of the Fe-based superconductor BaFe$_{1.84}$Co$_{0.16}$As$_2$ with
T$_c$=22.5 K. The film was grown by pulsed laser deposition on a DyScO$_3$
substrate with an epitaxial SrTiO$_3$ intermediate layer. The measured
$R_S/R_N$ spectrum, i.e. the reflectivity ratio between the superconducting and
normal state reflectance, provides clear evidence of a superconducting gap
$\Delta_A$ close to 15 cm$^{-1}$. A detailed data analysis shows that a
two-band, two-gap model is absolutely necessary to obtain a good description of
the measured $R_S/R_N$ spectrum. The low-energy $\Delta_A$ gap results to be
well determined ($\Delta_A$=15.5$\pm$0.5 cm$^{-1}$), while the value of the
high-energy gap $\Delta_B$ is more uncertain ($\Delta_B$=55$\pm$7 cm$^{-1}$).
Our results provide evidence of a nodeless isotropic double-gap scenario, with
the presence of two optical gaps corresponding to 2$\Delta/kT_c$ values close
to 2 and 7.
