An optical unit, in particular a facet mirror unit, includes an optical element and a supporting device. The optical element has an optical surface, in particular an elongate optical surface, which defines a plane of main extension and a direction of main extension in the plane of main extension. The supporting device includes a supporting unit and an actuator unit. The actuator unit is configured for tilting the optical surface, in that a tilting moment is exerted on the optical element by way of the actuator unit. The tilting moment runs in an inclined manner in relation to the plane of main extension. The supporting unit is configured to predefine a tilting axis for the optical surface that lies substantially in the plane of main extension of the optical surface when there is tilting of the optical surface by the tilting moment of the actuator unit.