We report conventional and time-resolved infrared spectroscopy on LaFeAsO$_{1-x}$F$_x$ superconducting thin films. The far-infrared transmission can be quantitatively explained by a two-component model including a conventional s-wave superconducting term and a Drude term, suggesting at least one carrier system has a full superconducting gap. Photo-induced studies of excess quasiparticle dynamics reveal a nanosecond effective recombination time and temperature dependence that agree with a recombination bottleneck in the presence of a full gap. The two experiments provide consistent evidence of a full, nodeless though not necessarily isotropic, gap for at least one carrier system in LaFeAsO$_{1-x}$F$_x$.
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