not necessarily pass through the centre of the lens, and in general may not lie inside the lens at all. Nodal points The front and rear nodal points have the property that a ray aimed at one of them will be refracted by the lens such that it appears to have come from the other, and with the same angle with respect to the optical axis. (Angular magnification between nodal points is +1.) The nodal points therefore do for angles what the principal planes do for transverse distance. If the medium on both sides of the optical system is the same (e.g., air), then the front and rear nodal points coincide with the front and rear principal points, respectively. The nodal points were first described by Johann Listing in 1845 to evaluate the eye, where the image is formed in fluid. Over time it was found that if a line was drawn through the posterior apex of the crystalline lens at the visual angle of a distant object, then it would point to the image location on the retina, even for very large angles. This line passes approximately through the 2nd nodal point, but rather than being an actual paraxial ray, it identifies the image formed by ray bundles that pass through the center of the pupil. This can be used to find the magnification, or to scale retinal locations. This extends the use of the nodal point for the eye, but the imaging properties come from the cornea and retina being highly curved, rather than paraxial properties, and this is rarely clear in publications. The nodal points are widely misunderstood in photography, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the iris diaphragm of the lens is located there, and that this is the correct pivot point for panoramic photography, so as to avoid parallax error. These claims generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. (A better choice of the point about which to pivot a camera for panoramic photography can be shown to be the centre of the system's entrance pupil. On the other hand, swing-lens cameras with fixed film position rotate the lens about the rear nodal point to stabilize the image on the film.) Surface vertices In optics, the surface