  Here we report an optical investigation in the terahertz region of a 40 nm
ultrathin BaFe$_{1.84}$Co$_{0.16}$As$_2$ superconducting film with
superconducting transition temperature T$_c$ = 17.5 K. A detailed analysis of
the combined reflectance and transmittance measurements showed that the optical
properties of the superconducting system can be described in terms of a
two-band, two-gap model. The zero temperature value of the large gap
$\Delta_B$, which seems to follow a BCS-like behavior, results to be
$\Delta_B$(0) = 17 cm$^{-1}$. For the small gap, for which $\Delta_A$(0) = 8
cm$^{-1}$, the temperature dependence cannot be clearly established. These gap
values and those reported in the literature for the BaFe$_{2-x}$Co$_{x}$As$_2$
system by using infrared spectroscopy, when put together as a function of
T$_c$, show a tendency to cluster along two main curves, providing a unified
perspective of the measured optical gaps. Below a temperature around 20 K, the
gap-sizes as a function of T$_c$ seem to have a BCS-like linear behavior, but
with different slopes. Above this temperature, both gaps show different
supra-linear behaviors.
