ABSTRACT
Geometrical optics is used as the basic tool in designing almost any optical system, image-forming or not. Geometrical optics is used as the basic tool in designing almost any optical system, image-forming or not. A major part of the design and analysis of concentrators involves ray-tracing—that is, following the paths of rays through a system of reflecting and refracting surfaces. To formulate a ray-tracing procedure suitable for all cases, it is convenient to put the laws of reflection and refraction into vector form. In principle, the use of ray-tracing tells the reader all there is to know about the geometrical optics of a given optical system, image-forming or not. Questions regarding the extent to which it is theoretically possible to eliminate aberrations from an image-forming system have not yet been fully answered. However, it is not very difficult to show that the generalized etendue or Lagrange invariant as calculated in one medium is independent of coordinate translations and rotations.
