Illumination Problem

Simon studying light reflection as part of the so-called Penrose Illumination Problem: if a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls.

The problem was first solved in 1958 by Roger Penrose using ellipses. He showed there exists a room with curved walls that must always have dark regions if lit only by a single point source. This problem was also solved for polygonal rooms by George Tokarsky in 1995 for 2 dimensions, which showed there exists an unilluminable polygonal 26-sided room with a “dark spot” which is not illuminated from another point in the room, even allowing for repeated reflections.

And what happens if light is shined in the corner of a room with mirrored walls? Will the light escape the room? Simon thinks it will be trapped in the corner through repeated reflections, but he also drew a diagram of how it should “escape”, according to Snell’s law:

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