The figure below indicates approximately where the principal points fall in
relation to the lens surfaces for various standard lens shapes. The exact
positions depend on the index of refraction of the lens material, and on the
lens radii, and can be found by formula. In extreme meniscus lens shapes
(short radii or steep curves), it is possible that both principal points will
fall outside the lens boundaries. For symmetric lenses, the principal points
divide that part of the optical axis between the vertices into three approximately
equal segments. For plano lenses, one principal point is at the curved vertex, and
the other is approximately one-third of the way to the plane vertex.
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