Reflection at intersection of two mirrors
It is overdefined geometry. By most optics ray tracing simulation software it will be treated as absorption.
The intersection point belongs to two interfaces at once. Praxis differs
- Two separate mirrors are likely to produce scattered light, as mentioned by @Carl Witthoft E.g. Glas substrate, which is cemented at the interface to a second mirror. A light ray at the cement will not hit a mirror and produce stray light.
- In manufactured mirrors, like optics injection molding, there will be a curve connecting the two mirror plances. This tiny curve forms a concave mirror.
Depending on your application you should stick either to advance your model with a curved edge or assume this ray is absorbed. In a ray tracing simulation this one ray will not affect simulated irradiance. However you may take a closer look if performing a stray light analysis.
There is no physical beam that is infinitely thin.
In fact in the quantum physical world each free space light beam extends infinitely in space. It falls off rapidly, but there is a probability finding the photon at arbitrarily far distance.
So, since each beam has a certain thickness, even in case we assume the angle is infinitely sharp the behavior is well defined. In the geometrical approximation, by just separate reflection of the two beam parts hitting the two mirrors.
It is not well defined, but that is not a problem because no rays hit the point precisely. If you are a little on one side or the other you know what happens. It is like choosing a uniform random number on $[0,1]$. The chance of each number is zero, which is what it takes to hit the corner exactly.