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Among the simple optical imaging systems, a thin lens consisting of two spherical surfaces is the most common as well as practical. By applying the results of Section 1.8 and the procedure of Section 1.9, we give the imaging equations and expressions for the primary aberrations of a thin lens with aperture stop located at the lens. Its aberrations for other locations of the aperture stop may be obtained by applying the results of Section 1.7 to those given here. It is shown that when both an object and its image are real, the spherical aberration of a thin lens cannot be zero (unless its surfaces are made nonspherical). We illustrate by a numerical example, however, that it is possible to design a two-lens combination such that its spherical aberration and coma are both zero. In such a combination, these aberrations associated with one lens cancel the corresponding aberrations of the other. This cancellation is illustrated with a numerical example.


Consider a thin lens of refractive index n and focal length f′ consisting of two spherical surfaces of radii of curvature R1 and R2 as illustrated in Figure 2-1. A lens is considered thin if its thickness is negligible compared to f′, R1, and R2. Its optical axis OA is the line joining the centers of curvature C1 and C2 of its surfaces. Since the lens is thin, we neglect the spacing between its surfaces. We assume that its aperture stop AS is located at the lens, so that its entrance and exit pupils EnP and ExP, respectively, are also located there. The lens is located in air; therefore, the refractive index of the surrounding medium is 1.

Consider a point object P located at a distance S from the lens and at a height h from its axis. The first surface forms the image of P at P′ and the second surface forms the image of P′ at P″. Applying the results of Section 1.8 to imaging by the two surfaces of the lens, where n = 1 and n′ = n for the first surface and n = n and n′ = 1 for the second surface, we can show that the image distance S′ and its height h′ are given by the relations





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