Magnification equations for a two-lens system.

There are some useful expressions for the magnification of a two-lens system which the author has been unable to find in the literature. The trick is in specifying distances relative to the focal points of the lenses. In the optical system shown in Fig. 1 the first lens has a front focal length ƒ1 and a rear focal length ƒ′1; the second lens has focal lengths ƒ2 and ƒ′2. The distance from the rear focal point of the first lens to the front focal point of the second is q, the distance from the front focal point of the first lens to the axial object point is s, and the distance from the near focal point of the second lens to the axial image point is s'. All distances are directed, with the sign convention that those from left to right are positive and conversely. Using Newton's relations, the system magnification is easily found to be