Nodal points and the eye

Abstract

Nodal points are defined using parallel object and image rays at very small angles to the optical axis, and Johann Listing described them when characterizing the eye in 1845. They are only distinct from principal points when there is a refractive index difference, but Reginald Clay used the term “nodal slide” in 1904 for equipment that uses lens rotation when measuring a lens focal length in air. Over time, sketches of nodal rays at large angles have become common, and these perhaps appear to support observations that input angles to the eye match image angles measured to the nodal point. Raytrace calculations confirm that this is correct for very large angles, but the relationship comes from the cornea curving around, towards incoming light, angles being rescaled at the exit pupil by a constant factor, and then the retina curving around to meet the image rays. The eye has high linearity, with 1:1 angular scaling occurring at approximately the nodal point, but ray bundles passing through the pupil center, rather than paraxial nodal rays, define the optical properties.