Exact solution of the generalized Shockley – Queisser model provides simple and effective tool for modeling of photovoltaic (PV) and thermophotovoltaic (TPV) devices with advanced photonic management. This formalism takes into account spectral characteristics of absorption/emission and a variety of recombination processes in semiconductor cell. In the current work we generalize this formalism to devices with non-ideal light reflectors used for light recycling and trapping. As an example, we investigate effects of the light management in InGaAsSb TPV converters (0.53 eV bandgap) with back surface reflector and with an additional front surface scattering layer, which provides Lambertian trapping of photons. We calculate the output power (efficiency) and investigate tradeoff between photon absorption and Auger recombination processes as a function of the device thickness. Finally, we compare performance of these TPV devices with the performance of traditional devices.