Re: Light gathering cone?

"Paul Ciszek" <nospam@xxxxxxxxxx> wrote in message
news:epbevc$66j$1@xxxxxxxxxxxxxxxxxxxx

One way to concentrate light on a device without lenses (or the need to
aim precisely) is to build a narrow cone (frustrum, actually) with a
reflective interior surface. If the cone is made of solid glass and
silvered on the conical surface, then Snell's law works in your favor--
any light that makes it into the glass at all will be less than the
critical angle away from the axis, making it easier to reflect back
towards the center. I tried to work out how narrow the angle needed to
be to capture all the light, and saw there really was no such thing.
Eventually the light will start ricocheting its way back out of the
cone. So now I am wondering:

1) Does this device have a name?

2) Has anyone analyzed the problem?

See this recent sci.math Google thread:
http://tinyurl.com/2s9ng2


That's actually a math Olympiad problem. Quite hard to prove it, but
eventually any ray that enters the cone will escape.
--
I.N. Galidakis
http://tinyurl.com/ye57yc

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