ABSTRACT
This chapter intends to convey the basic formulas as well as the flavor of geometrical optics and optical design in a concise and compact form. The basic elements of geometrical optics are rays and wavefronts: neither exist, except as mathematical abstractions. A ray can be thought of as a beam of light with an infinitesimal diameter. A normal congruency of rays incident on either a refracting or a reflecting surface gives rise to an aggregate of refracted or reflected rays, which also constitutes a normal congruence. Usually the formulas of Gaussian optics are derived from paraxial optics, a system based on approximations to the equations for ray tracing. Aberration theory and optical design are so profoundly intertwined as to be almost indistinguishable. The most obvious difference is that mathematicians do one and optical engineers do the other with some physicists playing an intermediate role.
