  The optical properties of a large, detwinned single crystal of BaFe$_2$As$_2$
have been examined over a wide frequency range above and below the structural
and magnetic transition at $T_{\rm N}\simeq 138$ K. Above $T_{\rm N}$ the real
part of the optical conductivity and the two infrared-active lattice modes are
almost completely isotropic; the lattice modes show a weak polarization
dependence just above $T_{\rm N}$. For $T<T_{\rm N}$, the optical conductivity
due to the free-carrier response is anisotropic, being larger along the $a$
axis than the $b$ axis below $\simeq 30$ meV; above this energy the optical
conductivity is dominated by the interband contributions, which appear to be
isotropic. The splitting of the low-energy infrared-active mode below $T_{\rm
N}$ is clearly observed, and the polarization modulation of the new modes may
be used to estimate that the crystal is $\simeq 70$% detwinned. The
high-frequency mode, with a threefold increase in strength of the lower branch
below $T_{\rm N}$ and nearly silent upper branch, remains enigmatic.
