Results of optical spectroscopy studies of the face-centered icosahedral (fci) single-grain Zn-Mg-Y, Zn-Mg-Ho, and Zn-Mg-Er quasicrystals (QCs) are presented. The dielectric function of the QCs was measured in the 0.01–6 eV spectral range by IR-UV spectroscopic ellipsometry and far infrared reflection spectroscopy techniques. A theoretical scheme of optical conductivity calculations is extended to account for the Fermi level positions within and below a pseudogap. The model of the QC electron energy spectrum, based on a band structure hypothesis, is suggested, which treats the electronic subsystem as a nearly free electron gas affected by intersections of the Fermi surface with several families of Bragg planes. The experimental optical spectra are reproduced in detail by theoretical calculations carried out within the framework of the model. The parameters of the electron energy spectrum deduced from an analysis of optical data are close to those previously determined in an analysis of fci Zn-Mg-R valence band photoemission spectra.