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For a real lens with a known aperture and working for an object at a given position, calculates the position of the principal planes, the object position referred to the primary principal plane, the image position referred to the apex of the second surface, the image position referred to the secondary principal plane, the magnification, the numerical aperture in the object space and the numerical aperture in the image space as functions of the refraction index, the surfaces radii, the center thickness, the object position referred to the apex of the first surface and the diameter of the aperture in the object space.

Note that the aperture is the plane perpendicular to the optical axis which intersection with the first surface is a circle of diameter D. Therefore, it is in general not tangent to the vertex of the first surface.