5 ms·
Mathematical mysteries: How unilluminating
- adrianN 11y agoIs 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.
- Ono-Sendai 11y agoYou get diffraction - the wave spreads out in a range of directions, like a water wave bending around a harbour barrier.
- lmm 11y agoPresumably the light must reflect properly, otherwise corner reflectors wouldn't work.
- danbruc 11y agoThat 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. [1] https://www.youtube.com/watch?v=NumSE2LvSmQ https://www.youtube.com/watch?v=NumSE2LvSmQ
- empath75 11y agoIt's really a question about geometry, and uses light to illustrate it. What actually happens with light isn't that important.
- nilkn 11y ago> 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... Yes, if you allow walls to be curved: http://blog.zacharyabel.com/tag/unilluminable-rooms/ http://blog.zacharyabel.com/tag/unilluminable-rooms/
- shasta 11y agoMore at http://mathworld.wolfram.com/IlluminationProblem.html http://mathworld.wolfram.com/IlluminationProblem.html. (If curved mirrors are allowed the problem was solved by Roger Penrose and there are rooms that cannot be illuminated - see link.)
- lubujackson 11y agoI feel like this problem is sitting on some big important concept, kind of like how topology expanded into a rich area of mathematics.
- stuxnet79 11y agoI agree. But I have only a superficial and rough understanding of the big ideas that underpin topology. What practical applications does it have?