We report measurements of the optical response of polycrystalline DyN thin films. The frequency-dependent complex refractive index in the near IR-visible-near UV was determined by fitting reflection/transmission spectra. In conjunction with resistivity measurements these identify DyN as a semiconductor with 1.2 eV optical gap. When doped by nitrogen vacancies it shows free carrier absorption and a blue-shifted gap associated with the Moss-Burstein effect. The refractive index of 2.0+/-0.1 depends only weakly on energy. Far infrared reflectivity data show a polar phonon of frequency 280 cm-1 and dielectric strength delta epsilon= 20.