A novel prototype of two-stage non-imaging solar concentrator (2S-NISC) for active daylighting in a building has been constructed and presented in our previous paper. In this work, the optical characteristics of the 2S-NISC have been explored to analyze the overall performance embracing maximum solar concentration ratio, percentage of energy in uniform illumination area, spillage loss, tolerance angle towards tracking error etc. using analytical formulas assisted by ray-tracing software based on designed parameters including the focal distance, f/D ratio and size of the receiver. In our simulation, we consider the case of 2S-NISC consisted of eighty primary facet mirrors of 5 cm x 5cm each, twenty secondary facet mirrors of 8 cm x 8 cm each, and plastic optical fibers as a daylight transmitter. When focal distance is changed from 50 to 100 cm, the maximum solar concentration ratio increases from 65.1 to 70.1 suns; whilst the percentage of energy in the uniformly illuminated area shows the overall trend of decreasing when focal distance is changed from 50 to 100 cm except at focal distances 60 cm and 100 cm due to the slope error. Finally, the total tolerance angle of the 2S-NISC that allows at least 95% of energy to be collected with respect to perfect tracking is determined as 0.54 degrees.