In a method and an arrangement for transmitting data from a rotary part to a stationary part of a system, a light-transmitting channel is formed by an optically reflecting half channel in the stationary part and an optically reflecting half channel in the rotary part, facing each other, with each half channel having a parabolic cross-section and with the half channels being oriented so that the respective focal points and the respective vertices of the two half channels are co-linear. A light emitter is supplied with data to be transmitted and is disposed in the wall of the half channel in the rotary part, and emits modulated light representing the data into the light channel in two opposite directions. At least one of these light beams is detected by a light detector disposed in the wall of the half channel in the stationary part, and the data in the detected beam is then made available for transmission from the stationary part. A light barrier is disposed in the light channel to, generally, block one of the light beams so that, generally, only one beam at a time is detected by the light detectors.