We present a mathematical model for a phytoplankton-zooplankton system, based on a predator-prey scheme. The model considers the effects of sinking in the phytoplankton, vertical mixing and attenuation of photosynthetically active radiation (PAR) and ultraviolet radiation (UVR) in the water column. In a first approach, the model was studied under conditions of average PAR irradiance and shows fluctuations and stable equilibrium points. Secondly, we introduced the effects of photoperiod and photoinhibition by UVR and vertical mixing. Under these conditions, the phytoplankton biomass oscillates depending on the combined effects of UVR and mixing. Higher inhibition by UVR and longer mixing periods can induce strong fluctuations in the system but can also produce higher plankton peaks.