ABSTRACT
This chapter introduces the Lagrange invariant H as part of the structure of Gaussian optics but, as indicated at that point, it has a much wider significance; for example, H2 represents in Gaussian approximation the total light flux through a given transverse section of an optical system and its invariance through a system is therefore a consequence of the conservation of energy. Other invariants in an optical system can be found, involving finite rays, and, as with the Lagrange invariant, they have physical implications beyond the immediate geometrical optics. It also turns out that they provide neat and simple proofs of certain geometrical optics theorems which are otherwise not so directly proven. This chapter shows the configuration of an intermediate image, paraxial principal ray, paraxial ray from the centre of the object, and so on in an intermediate space of an optical system.
