Consider a thick lens (Figure 1-21). Gaussian reduction can be used to show that there is a pair of conjugate points on the optic axis for which an object ray directed at one of these points, N1, making an arbitrary small angle, θ, with the optic axis will, on exiting the lens, appear to emerge from the other point, N2, at the same angle θ with the optic axis.
The points N1 and N2 are referred to as the front (or first) and back (or second) nodal points, respectively. They serve, for ray tracing in a general optical system, as an analogue for the central point in a thin lens, and have a role similar to that of the front and back principal planes for determining object and image vergence. When the refractive indices n1 and n2 are equal, the nodal points coincide with the principal points. Nodal points are particularly useful for determining image size (Example 9-1).
Figure 1-21 Nodal points of a thick convex lens in air. The inclination of an incident ray through the first nodal point equals the inclination of the exiting ray as it apparently emerges from the second nodal point.
(Redrawn from Creative Commons illustration by Bob Mellish.)
It is tempting to draw an analogy between the role of the nodal points in ray tracing and the “fulcrum-like” action of a pinhole aperture, as described in Part 1 of the Quick-Start Guide. In both cases, the angles between the incident and emergent rays and the optic axis for rays passing through the pinhole or nodal points are equal. But this analogy is potentially misleading for optical systems with finite apertures. For these systems (unlike simple pinholes), it is not true that all the light passes through the nodal points, only that the unique rays that do pass through the nodal points preserve the same simple geometry as the rays passing through a pinhole aperture. In particular, a small posterior subcapsular lens opacity does not cause a disproportionate reduction in visual acuity by virtue of its proximity to the posterior nodal point of the eye. (Such an opacity may, however, be an effective scatterer of light, greatly reducing a patient’s contrast sensitivity.)
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.