The History of Rays & Normal Planes in Optics.

  Hamilton was not the first to study the use of rays and normal planes in optics but he put the subject on a sound mathematical ground. Newton's books on optics dwelt primarily with physical optics which was concerned with optical phenomena. When Huygens was developing his wave theory of light in the 1600's he postulated that as light propagated the surface of each wave front acted as a new source of waves which combined to form a new wave front. In the 1760 Lambert published Photometria which dealt with the variation of the intensity of light with distance.  Malus in his 1808 paper, Optique, wrote about the rectilinear propagation of light with surfaces and systems of rays. So when Hamilton's works on optics were published in the late 1820's and 1830's much of its content was already known. His characteristic function and the associated differential equations were arrived at using the Calculus of Variations which Lagrange had used in Mechanics.

  Hamilton was a contemporary of Faraday who developed a field theory to help understand electromagnetism. In it he used the idea of tubes of flux. Hamilton's study of systems of rays and surfaces would have put flux tubes on solid mathematical ground. This and his discovery of quaternions were later used by Maxwell to develop a mathematical theory of Electricity and Magnetism.