In the laboratory of the Physikalisch-Technische Bundesanstalt (PTB) at the Berlin electron-storage ring BESSY II, a procedure has been developed to investigate the dependence of vacuum-ultraviolet reflection on polarization. It is based on characterizing the elliptically polarized synchrotron radiation at PTB's normal-incidence monochromator beamline for reflectometry by means of polarization-sensitive photodetectors. For this purpose, the polarization dependency in the detector responsivity was determined at a small, low, solid angle of acceptance for the synchrotron radiation, i.e., within the orbital plane of the storage ring where the degree of linear polarization is known to be almost 100%. Our method allows the polarization dependence of reflection samples to be measured with relative standard uncertainties ranging from 2.4% to 11% in the spectral range between 60 and 160 nm. The method has been applied to the optimization of polarizing mirrors at the Lyman-alpha wavelength of 121.6 nm.