The invention provides a method and apparatus for adjusting the direction of a beam of radiation 13 in which a mirror 19 is mounted on a shaft 1 so that the normal to the mirror is inclined relative to the longitudinal axis 11 of the shaft, the shaft being mounted in a bearing 2,3 for rotational adjustment relative to a supporting structure 20, 21. The invention may, for example be applied to monochromators or interferometers in which radiation beams must be adjusted in direction to very close tolerances, typically seconds of arc, and maintained in direction with a corresponding stability. In accordance with the invention the shaft is rigidly secured in the bearing after adjustment by means of an adhesive. A stress-free structure is realised in which hysteresis effects due to temperature cycling are minimised.