Purely algebraic algorithms are presented for solving the zoom curves of a three-component zoom lens of which the second component is fixed on zooming. Two separated algorithms for infinite and finite conjugate imaging conditions are provided. For the infinite-conjugate condition, the transverse magnifications of the second and third components are solved to match the required system focal length, resulting in solving a quadratic equation. For the finite-conjugate condition, three nonlinear simultaneous equations regarding the system magnification, the object-to-image thickness, and the position of the second component are combined into a fourth-order polynomial equation. The roots can all be directly obtained by simple algebraic calculations. As a result, the proposed algebraic algorithms provide a more efficient and complete method than do earlier algorithms adopting scanning procedures.
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