Focusing light using a pyramidal mirror setup

[CaptainZappo]

Hi, I was wondering if it would be possible to focus light down to a small point using the following method:


Construct a pyramid from four identical triangular mirrors (three would also work), with the mirrored side facing inwards of course. Do not put a base on the pyramid, but instead use the open end of the pyramid to gather light (point it towards the Sun). A small hole should also be made on the opposite side of the pyramid (where the focused light will emerge).


Would the light be focused down by the mirror setup or would the light simply bounce around inside and come back out the top?

I have come to the conclusion that the walls of the pyramid must be fairly steep for this to work, but I'm not sure if this assumption is correct. I can't seem to convince myself either way.

All help will be greatly appreciated.

 

[Mentz114]

I suggest you draw a ray diagram. I doubt if there will be any focusing because curved surfaces or varying refractive index are required to get a focus.

 

[AlephZero]

The idea doesn't seem to work in 2D, for any angle between the mirrors. Every reflection increases the deviation of the beam from the target and after a few reflections the beam is turned round. (See angles a, b, c in the attachment).

In 3D, the idea certainly doesn't work for corner-cube reflectors, which are widely used as "omnidirectional mirrors". http://en.wikipedia.org/wiki/Corner_reflector

 

[Danger]

Captain, is this just a matter of curiosity, or are you trying to build something? If the latter, I would seriously recommend that you stick with regular lenses. As Aleph said, the pyramid idea is pretty much a bust.

 

[CaptainZappo]

Captain, is this just a matter of curiosity, or are you trying to build something? If the latter, I would seriously recommend that you stick with regular lenses. As Aleph said, the pyramid idea is pretty much a bust.

I have purchased a large Fresnel lens (about 1 square yard) and I am trying to build something that will focus the light into a tighter spot; the focal point is currently a blob roughly four inches in diameter. I am trying to concentrate this light down to a spot roughly one square inch (or less). I originally thought another Fresnel lens (or even a magnifying glass) could be used to accomplish this, but I could not get this work because all the light rays are hitting the focal point at different angles.

 

[Danger]

Well, if it's that big it isn't really a focal point. Have you tried moving the second lens away from that focal area, either toward or away from the Fresnel lens? That's all that I can think of, unless you use a parabolic reflector as your secondary. That should solve your problem handily, as long as the 'collector' isn't in the way of the original Fresnel output.
I'm done here; optics is a very complicated subject that I know nothing about, so you'll have to wait for someone more qualified to answer.