Abstract
This chapter presents the rationale behind and the refinement of the laws of geometrical optics. Ray fields are considered, i.e. the solutions of the wave equation, that possess a special form of asymptotic expansions called ray expansions. The leading term of a ray expansion is the geometrical optics solution, and the following terms are corrections to this solution. The ray expansions for the general case were analysed and then their form for particular and some recurrent types of waves, namely, plane, cylindrical, spherical, and toroidal, the analogue of cylindrical waves for axially symmetric problems were examined. These results are used to refine the second group of geometrical optics laws and to solve simple boundary-value problems which do not evolve diffraction fields in the form of edge waves or creeping waves.
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