
Mathematical mysteries: How unilluminating - todayiamme
https://plus.maths.org/content/mathematical-mysteries-how-unilluminating
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adrianN
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.

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danbruc
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.

[1]
[https://www.youtube.com/watch?v=NumSE2LvSmQ](https://www.youtube.com/watch?v=NumSE2LvSmQ)

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adrianN
That's a really cool video. Thanks!

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spacehome
The Feynman lectures on physics has a great explanation, too.

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nilkn
> 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/)

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shasta
More 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.)

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lubujackson
I feel like this problem is sitting on some big important concept, kind of
like how topology expanded into a rich area of mathematics.

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stuxnet79
I agree. But I have only a superficial and rough understanding of the big
ideas that underpin topology. What practical applications does it have?

