Abstract : The techniques of ray-optics, which have provided meaningful results in the study of electromagnetic and acoustic problems, are applied to the integrated dielectric cylinder-cone configuration. The method geometrical optics is presented. The eiconal and transport equations are derived. Asymptotic boundary conditions are dicussed and a generalized reflection coefficient introduced. Before investigating the cylinder-cone non-separable geometry, and understanding of the ray structure in both an infinite dielectric cylinder and, separately, in an infinite dielectric cone is needed. This is accomplished in the report and, consequently, amplitude and phase information is attained. In addition, caustics are discussed. Caustics are envelopes of the ray systems and, thus, are surfaces which separate propagating and non-propagating (or complex evanescent) regions and characterize the modal ray systems in non-uniform regions. The report concludes with a discussion of the transition region between the cylinder and the cone. (Author)