An apparatus (5) for measuring the dimensions of an object (1) where a measuring carriage (6) moves the object at a distance thereabove. A polygonal mirror unit (32) receives laser light (16) and reflects it in a fan-shaped form toward a stationary angled mirror unit (37, 38) which directs the light towards a double-curved stationary mirror unit (39) which reflects the beam onto the object. Mirrors (40) of the polygonal unit are adjustable.