An optical system for transmitting data between stationary part and a rotating part, such as for transmitting data from the rotating live ring in a computer tomography apparatus, has a number of light transmitter arranged on a circle on one of the parts, with the radiation output of the light transmitters being modulated according to the data to be transmitted, and a light receiver disposed on the other part. The light transmitters emit thin, fan-shaped light beams, each of the light beams being in a plane which is defined by the circle, or parallel thereto. Each fan-shaped light beam has a central ray disposed at an angle relative to a radius of the circle, and the light receiver is disposed relative to the circle and the light transmitters so that the light receiver is within the light beam of at least one light transmitter at every position of the rotating part, and thus supplies a constant output signal, given a constant transmitted signal, during rotation.