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Is there something like an entropy law for light rays?

I came up with the following experiment: A black box has two circular holes in it, a small and a large one. I don't care about there placement. Now I like to build something into the box that any ray entering the large hole will exit the box through the small hole.

However, I could not imagine any combination of optical tools like lenses, mirrors and so on that would do that.

It seems possible to concentrate a parallel bundle of light to a small spot or hole, but not unordered rays.

Is there a law written in ink that forbids such a contraption?

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There is indeed, excellent intuition! This is called conservation of etendue. en.wikipedia.org/wiki/Etendue –  user2963 Apr 8 '12 at 12:43
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Thanks! If you post that as an answer, I will accept it. An addition: If I would use a solar cell and an electrical lightsource both highly effective, it should be possible to build the box. Is this possible becuase it's by non-optic means, or is there a deeper law that would limit the effectivenes of the cell or the source to impede this? –  dronus Apr 8 '12 at 23:42
    
@dronus It is possible because transfer entropy somewhere else. In fact you need some energy to erase information, but its negligible. –  Piotr Migdal Apr 9 '12 at 10:21
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Perhaps @zephyr should submit an answer to this question so that this moves out of the 'unanswered' section? –  Kitchi Nov 12 '12 at 13:08
    
BTW Because the entropy of light is entropy like any other, you can trade it for other kinds of entropy. So if you don't mind producing some heat as a side effect, you can concentrate light further than you can with lenses and mirrors if you interpret 'concentrate' liberally enough. See: en.wikipedia.org/wiki/Luminescent_solar_concentrator –  Dan Piponi Sep 24 '13 at 18:27

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up vote 3 down vote accepted

(I'm copy-pasting from @user2963's comment into this community wiki.)

There is indeed, excellent intuition! This is called conservation of etendue. en.wikipedia.org/wiki/Etendue

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