  The effect of a tunable, externally coupled Fabry-P\'{e}rot cavity to
resonantly enhance the optical Hall effect signatures at terahertz frequencies
produced by a traditional Drude-like two-dimensional electron gas is shown and
discussed in this communication. As a result, the detection of optical Hall
effect signatures at conveniently obtainable magnetic fields, for example by
neodymium permanent magnets, is demonstrated. An AlInN/GaN-based high electron
mobility transistor structure grown on a sapphire substrate is used for the
experiment. The optical Hall effect signatures and their dispersions, which are
governed by the frequency and the reflectance minima and maxima of the
externally coupled Fabry-P\'{e}rot cavity, are presented and discussed. Tuning
the externally coupled Fabry-P\'{e}rot cavity strongly modifies the optical
Hall effect signatures, which provides a new degree of freedom for optical Hall
effect experiments in addition to frequency, angle of incidence and magnetic
field direction and strength.
