An illumination device is specified which comprises an optoelectronic component having a housing body and at least one semiconductor chip provided for generating radiation, and a separate optical element, which is provided for fixing at the optoelectronic component and has an optical axis, the optical element having a radiation exit area and the radiation exit area having a concavely curved partial region and a convexly curved partial region, which at least partly surrounds the concavely curved partial region at a distance from the optical axis, the optical axis running through the concavely carved partial region