It is true that in the optical (high frequency) limit the rays are orthogonal to the constant phase surfaces, the wavefronts, and the optical path length along these rays between any two wavefronts is the same. In other words, the optical distance between two between wavefronts is independent of the ray. This property of wavefronts is sometimes viewed as the manifestation of Huygens's principle in the geometrical optical limit. It can be shown to be essentially equivalent to the various forms the laws of optics are derived including Snell's law of refraction, Fermat's principle, Malus-Dupin law, Lagrange's invariant, etc.
But this property of waveforms does not apply to your question because the extension in the dielectric of the wavefront that is propagating in vacuum is not a wavefront, it is a geometric surface but it is not the one that propagates. Rays may start from a single point and, such as a focus, for example, and then the geometrical optic wavefront may degenerate into a singularity; this is where geometrical optics actually fail to describe real physics and you need physical, ie., wave optics. But in your question you do not have that, in fact the incident wavefront breaks into two planes continuously but not smoothly joined at the interface, kind of bending and propagates while maintaining the optical distance between them.