Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 56.1

The Propagation of Light

Physics — Landau & Lifshitz · narrow-bundles-of-rays-focal-distance

Problem

Find the focal distance for image formation with the aid of two axially-symmetric optical systems whose optical axes coincide. Let

f_1

and

f_2

be the focal lengths of the two systems. For each system separately, we have

X_1 X_1' = -f_1^2, \quad X_2 X_2' = -f_2^2.

Since the image produced by the first system acts as the object for the second, denoting by

l

the distance between the rear principal focus of the first system and the front focus of the second, find the focal length

f

of the composite system. Also consider the special case

l = 0