Prismatic structures having at least certain conventionally linear surfaces thereof configured in a non-linear fashion to control the direction of light exiting said structures, the invention functions to reduce light losses in a luminaire or the like while facilitating the emanation of light from the luminaire at an acceptable viewing angle and with a reduction in glare. Prisms, particularly splitter prisms, configured according to the invention are formed with at least portions of conventionally linear surfaces as arcuate, curvilinear or generally curving segmented surfaces so as to direct light out of the luminaire for useful illumination rather than in a wasteful direction back into the luminaire. Prisms configured according to several embodiments of the invention function to increase light efficiencies either upwardly or downwardly depending on illumination requirements.