Winkelvergrößerung

Winkelvergrößerung, or angular magnification, is a measure of how much larger an object appears through an optical instrument compared to the naked eye. It is defined as the ratio of the angle subtended by the apparent image to the angle subtended by the object at the eye. If θ is the angle of the object and θ' the angle of the image, the magnification M equals θ'/θ. This quantity is dimensionless and indicates the perceived enlargement of the object, independent of distance.

In practice, angular magnification is used to describe devices such as magnifying glasses, binoculars, and telescopes. An eyepiece that produces an apparent image of the same size as the object but at a closer distance gives a larger angular size, thus a higher M. The design of the instrument determines this value; for example, a simple magnifying glass with focal length f effectively provides a magnification of (25 cm)/f, where 25 cm is the near point distance for a normal eye.

Unlike linear magnification, which depends on the actual size of the image, angular magnification depends solely on the relative angles and therefore remains constant over a range of viewing distances. It is particularly useful in vision science and the design of optical instruments, where perception of detail is of primary concern.