= Solution
For a face of signed slope $s$, conservation of frequency and tangential <wavenumber> gives, on the branch relevant to an incident downward-right ray,
$$
k_r=k\frac{1+s\mu}{1-s\mu},
\qquad
\mu=\frac{|m|}{|k|}=\cot\theta.
$$
At $s\mu=1$, the reflected wavenumber diverges and the reflected <group velocity> becomes tangent to the face. On a supercritical face the denominator changes sign: horizontal propagation reverses and rays from the two faces are directed towards a sawtooth corner. Successive reflections therefore focus energy and shorten the wavelength.
The inviscid ray pattern cannot persist indefinitely. Near-critical focusing amplifies gradients until <kinematic viscosity>, <mass diffusivity>, nonlinear wave steepening, and wave breaking matter; a real corner is also rounded on some finite scale. These effects replace the singular ray construction by dissipative boundary layers, mixing, and a finite-width reflected beam.
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