The complex ray method is employed to analyze a Gaussian beam reflected at

a plane interface from a denser medium into a thinner one. Besides the reflection by geometrical optics

a lateral wave contribution must be included for the region of total reflection.To simplify the calculation

a paraxial approximation is employed when the observer is located near the beam axis. However

the above-mentioned analytical methods all fail in the transition region which is determined by a parameter called "numerical distance". The uniform solution in the transition region is generated by means of a parabolic cylinder function with a complex argument. Detailed numerical comparisons assess the validity of various formulations.