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44       LENSES AND GEOMETRICAL OPTICS

















                                Figure 4-1
                                Geometrical optics of a positive lens. (From Hecht, 1998.)



                                    For any given lens there are two principal planes: one each for the front and back
                                surface of the lens. For the special case of a thin biconvex lens, the two principal planes
                                are coincident in the middle of the lens. Microscope objectives contain multiple lens ele-
                                ments, some of which may be united with transparent sealing compound to make a com-
                                plex thick lens. The principal planes of thick lenses are physically separated, but their
                                locations can be determined by ray tracing. Most lens elements used in microscope
                                optics are ground and polished with spherical curvatures.













                                                    Double      Plano      Convex
                                                    convex      convex    meniscus
                                                           Positive lenses












                                                    Double      Plano     Concave
                                                   concave     concave    meniscus
                                                           Negative lenses

                                Figure 4-2
                                Examples of positive and negative lenses.
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