The angular magnification, M, (also sometimes called magnifying power) produced by an optical instrument is defined as

An expression for the angular magnification produced by a telescope can easily be found by looking at ray diagrams.

An astronomical telescope consists of a long focal length (low power) convex lens (the object lens or objective) and a short focal length (high power) convex lens, the eye lens.

Consider three rays from the "top" point of a very distant object. (The "bottom" point of the object is assumed to be on the principal axis.) See diagram below. a is the angle subtended by the distant object at the objective. The angle which would be subtended by the distant object at the unaided eye of an observer is also a.

The objective forms a real, inverted image of the distant object in its focal plane, as shown below.

This image is then observed using a simple microscope (the eye lens) usually adjusted so as to give a virtual image at infinity, as shown in the next diagram.

Putting these two ray diagrams together shows us the complete telescope "in normal adjustment" (with final image at infinity).

The diagram is not to scale: the angles a and b are in practice very small.

Therefore a (in rad) = h/f_o and b (in rad) = h/f_e and the angular magnification is given by

• Optics Homepage
• Return to top of page