29 - Concentric systems

Summary

Basic properties

A concentric system is constructed of spherical surfaces, refracting or reflecting, that all have a common center. A solid sphere is a simple example; two other examples are shown in fig. 29.1. A concentric lens is insensitive to rotations around its center; this high degree of symmetry determines the special properties of concentric systems.

For any incident ray the plane containing the ray and the center of the system divides the lens into two symmetric halves. There is no reason for the ray to prefer one of these halves over the other; so the ray will remain in the symmetry plane as it traverses the lens. It follows that every ray travels in a plane containing the center.

As long as the lens is not afocal the angle eikonal W(L, M, L′, M′) can be used. We choose any straight line through the center as the axis, and locate both the (x, y) reference plane in the object space and the (x′, y′) reference plane in the image space right in the center of the system. Then the angle eikonal is the optical distance from the projection P of the center onto the ray in the object space to the projection P′ of the center onto the ray in the image space. On account of the spherical symmetry of the lens a rotation of the entire ray around the center has no effect on the value of the eikonal function.