In an operation microscope, an illumination beam or ray is projected from a lateral position toward the main optical axis or observation axis, to intersect the observation axis at a point below the main objective of the microscope. At this point of intersection, a beam splitter element (plate or cube) reflects the illumination beam downwardly along the observation axis, toward the object or specimen being examined, while allowing the observation rays to pass along the observation axis. This allows the object to be examined under truly coaxial illumination, which is especially useful for certain types of examination or operation upon the eye. The beam splitter and other parts may be mounted in a housing which may be swung aside when coaxial illumination is not wanted. In a disclosed variation, provision is made for combined coaxial and oblique illumination of the object.