A method and apparatus for the quantitative determination of optically active substances includes two light-emitting diodes, each with a respective collimator lens and polarization filter, a cell filled with dialysate, an analyzer, a detector and measurement and evaluation electronics. The clocked light of the light-emitting diodes is linearly polarized by the polarization filters. The polarization directions differ by a few degrees. The polarization direction of the analyzer is aligned essentially perpendicularly relative to the polarization filters, such that the radiation of the two light-emitting diodes passing through an optically non-rotating dialysate generates the same photosignal in the detector. The polarization of the radiation passing through an optically rotating dialysate, by contrast, is rotated farther in the same direction, so that the detector receives two different photosignals from the light-emitting diodes from which the concentration of optically active substances can be deduced on the basis of comparison. The cell has a chamber filled with a reference fluid, through which the radiation of the two light-emitting diodes passes. The passing through the reference fluid radiation is registered with a further photodiode and is compared for an automatic signal balancing.