Investigation of the thin lens theory of zoom lenses results in a general statement concerning conjugate points, a simple proof of the maximum number of crossing points, and an algorithm for computing component focal lengths of a five-component symmetrical zoom lens. The three-component optically compensated zoom lens is discussed in detail. Results of applying the algorithm are given. A prototype of the five-component zoom lens has been built and is briefly discussed.
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Wooters et al. (1965) studied this question.