I'm reading the text "General theory of rectilinear ray systems" By E. E. Kummer. (http://neo-classical-physics.info/uploads/3/0/6/5/3065888/kummer_-_rectilinear_ray_systems.pdf). I'm new in this topic about the optic and system of straigh lines, and I find the following affirmation in the first paragraph of the introduction.
''[...] Here, one of the most beautiful theorems of optics has hindered the development of the general theory to a remarkable degree, namely, the theorem that was discovered by Malus and generalized by Dupin that after the light rays that emanate from a point have experienced an arbitrary number of reflections from arbitrarily-shaped mirrors and refractions from passing through arbitrarily-bounded media with various refracting powers, they will always preserve the property that they are the normals to a surface"[...]
I understand that in the introduction of the text the author try to introduce the notion of system of straight lines that fill up the space part of this in such way that the for every point in the space pass one or a discrete number of them and he also said that his theory only has been studied only a little generality only examining the system which are normal to a surface. (If I wrong please let me know)
But:
I don't understand how the Theorem of Malus contributed of this lack of study.
I haven't find many examples that I imagined - the set the straight lines that go through the origin and put the surface the sphere and perhaps the ellipse.
