  The origin of the Hall effect in many itinerant ferromagnets is still not
resolved, with an anomalous contribution from the sample magnetization that can
exhibit extrinsic or intrinsic behavior. We report the first mid-infared (MIR)
measurements of the complex Hall ($\theta_H$), Faraday ($\theta_F$), and Kerr
($\theta_K$) angles, as well as the Hall conductivity ($\sigma_{xy}$) in a
SrRuO$_3$ film in the 115-1400 meV energy range. The magnetic field,
temperature, and frequency dependence of the Hall effect is explored. The MIR
magneto-optical response shows very strong frequency dependence, including sign
changes. Below 200 meV, the MIR $\theta_H (T)$ changes sign between 120 and 150
K, as is observed in dc Hall measurements. Above 200 meV, the temperature
dependence of $\theta_H$ is similar to that of the dc magnetization and the
measurements are in good agreement with predictions from a band calculation for
the intrinsic anomalous Hall effect (AHE). The temperature and frequency
dependence of the measured Hall effect suggests that whereas the behavior above
200 meV is consistent with an intrinsic AHE, the extrinsic AHE plays an
important role in the lower energy response.
