K2SO4:Cu2+ (3%) crystal has been synthesized and its crystal structure is characterized by means of the X-ray diffraction method and discussed within the second coordination environment description. Experimental dispersions of the refractive indices and birefringence have been studied. The introduction of impurity leads to a decrease in refractive indices values for all principal directions and significantly change the absolute birefringence values, without altering the character of the dispersions. Electronic structure and optical spectra of K2SO4: Cu2+ (3%) crystal are calculated using the density functional theory. To verify data of the present band-structure calculations, X-ray photoelectron spectroscopy and X-ray emission spectroscopy were used. These allowed to measure binding energy values of the core-level electrons of the constituting atoms, energy distribution of electronic states within the valence-band region and partial distribution of O(2)p states. The experimental data is found to be in good agreement with theoretical band-structure calculations.