Is there a physicist in the audience who can tell us what happens at sharp corners? I would assume things happen as the distance between the two mirrors becomes comparable to the light's wavelength.
You get diffraction - the wave spreads out in a range of directions, like a water wave bending around a harbour barrier.
Presumably the light must reflect properly, otherwise corner reflectors wouldn't work.
That is not the only issue, mirrors don't really work the way one naively imagines. See for example this video [1], mirrors have their appearance between about 10 and 15 minutes into the video. Reality won't match the simple mathematical model even ignoring the corners and having a door is the correct solution in practice.
The Feynman lectures on physics has a great explanation, too.
It's really a question about geometry, and uses light to illustrate it. What actually happens with light isn't that important.
> Is there a room which is so fiendishly complicated that wherever you hold the match there are some dark spots in the room? Nobody knows the answer...