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The reflection problem for a TE mode traveling toward the end of a semi-infinite parellel-plane waveguide is solved by ray methods. Unlike a previous solution due to Yee et al., the present ray-optical solution is a rigorous asymptotic result, i.e., it is identical with the asymptotic expansion (width of waveguide large compared to wavelength) of the exact solution. Numerical results for the modal reflection coefficients are presented and are compared with calculations based on the exact solution. It is found that the agreement between ray-optical and exact values is excellent and even better than in the approach of Yee et al., especially in the vicinity of cutoff frequencies of higher order modes.