Position detector for determining the rotation angle position of a rotatably mounted object, having a light source for producing a light beam, a diffraction grating, a mirror, which is connected to the object corotationally in such a way that the light beam is reflected by said mirror onto the diffraction grating and, in the event of a rotation of the mirror, passes over the diffraction grating so as to produce diffraction light, an interference apparatus, which is designed in such a way that different orders of diffraction of the diffraction light can be brought to interference by said interference apparatus so as to produce an interference pattern, a light detector, by means of which a brightness profile of the interference pattern which is brought about by the reflected light beam passing over the diffraction grating can be detected, and an evaluation unit, by means of which the rotation angle position of the object can be determined on the basis of the brightness profile.