An optical system includes at least one optical element which has an optically effective surface and which is designed for an operating wavelength of less than 30 nm. The optical system also includes a heating arrangement for heating this optical element and comprising a plurality of IR emitters for irradiating the optically effective surface with IR radiation. The IR emitters are activatable and deactivatable independently of each other to variably set different heating profiles in the optical element. The optical system further includes at least one beam shaping unit for shaping the beam of the IR radiation steered onto the optically effective surface by the IR emitters. The optical system also includes a multi-fiber head comprising a multi-fiber connector for connecting optical fibers. IR radiation from a respective one of the IR emitters is suppliable by way of each of these optical fibers.