We present a detailed theoretical analysis on the quantum efficiency of a resonant cavity enhanced (RCE) GaAs homojunction work function internal photoemission far-infrared (FIR) detector. The quantum efficiency under both resonant and nonresonant conditions has been calculated. All the detector parameters are optimized under the realistically nonresonant condition. The further investigation of the standing wave effect (SWE) shows that the SWE is important and cannot be neglected for the FIR detector. The resulting quantum efficiency is about two times higher than that in the normal GaAs homojunction FIR detector measured by experiment, showing a promising effect. In contrast to the case in the near-infrared region, the wavelength selectivity is not obvious in the FIR region. The theoretical analysis can be applied to other RCE homojunction FIR detectors.