Strong magnetic fields are often needed to produce observable Zeeman splittings in the optical absorption spectra of semiconductors and other crystals because of the large natural line-widths. An apparatus is described for studying Zeeman spectra of crystals at temperatures down to 1.3° K and magnetic fields up to 130 kG in the region 5000-30 000 cm^-1 with a resolution of 1 cm^-1.