An asymptotic ray analysis of the diffraction of an electromagnetic plane wave by a perfectly conducting half plane that resides on the interface separating half spaces filled with dissimilar media is developed for the case where the plane of incidence is perpendicular to the edge. The diffraction problem is formulated as an integral equation whose unknown is the tangential component of electric field residing on the uncovered half of the interface plane. This integral equation is solved by using the Wiener-Hopf technique. Asymptotic analysis of the resulting diffracted fields is carried out in the angular spectral plane and ray interpretations are assigned to the asymptotic terms. In addition to geometrical optics and edge-diffracted field components, which arise in the Sommerfeld diffraction problem, a lateral wave field is found to contribute to the total (asymptotically evaluated) field. The possibility for a Zenneck wave to be present arises also when the media exhibit magnetic contrast, although this possibility is not explored in the present paper.