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The Last Lightbender

Element-awry.
 (+1) [vote for, against]

So, I have an idea that's also sort of questions I can't find the answers to.

I want to focus rays from the sun either using a large parabolic dish covered in mirror shards, or ideally through a large Fresnel lens and then direct those rays down the length of a circular tube with a mirrored interior surface to create a portable solar cutting torch/kiln furnace.
Given a perfect lens, a perfectly circular tube and 100% reflection:

Will the rays pass through one another down the length of the tube and refocus at a distant point?
...and if so, would the same hold true for a bent tube? Could focussed light be redirected to distant points, say even underground?

...and why is there absolutely no information to be found on the reflectiveness of natural obsidian?

 — 2 fries shy of a happy meal, Oct 29 2015

Could you use a fiber optic instead?
 — travbm, Oct 29 2015

Why not use total internal reflection?
 — RayfordSteele, Oct 29 2015

Same principal I guess eh? but would the light rays re-converge after bending around corners? I try to visualize it, but it hurts.
 — 2 fries shy of a happy meal, Oct 29 2015

 //Will the rays pass through one another down the length of the tube and refocus at a distant point?//

 You'll need a lens at some point. Think about the point at which the parabolic dish (or Fresnel lens) focusses the rays. They are arriving from all of the dish/lens, and hence at all different angles. They'll therefore bounce down the light-pipe at all different angles.

 For instance, a ray that comes from the centre of the dish will travel straight to the focal point, and straight down the middle of the light pipe (if it's straight). A ray that comes from the edge of the dish will enter the pipe at an angle, and will bounce back and forth along the pipe.

 So, when the rays exit the pipe, they're going to be heading in all different directions.

And, as I recall from an earlier discussion here, you can't focus light down to a point smaller than the source - in this case the disc of the sun as viewed from Earth.
 — MaxwellBuchanan, Oct 29 2015

 hm... I don't want to tighten the focus at all. Because the rays are at an angle to converge when they enter the tube, in my mind I saw them passing through one another at re-convergent intervals down the length of the tube. I get what you're saying though, the straight-line photon will get to the distant focal point slightly faster than the mid-mirror photon, which would arrive faster than the outermost... etc.

Cool.
How about a variation of a Fresnel lens or reflector which, instead of bending concentric rings of light to a focal point, was designed to take the length and curvature of the conduit into account and scatter light accordingly. Could the topology of the lens/reflector needed to do this be figured out by algorithm?
and perhaps even morphed to adapt as needed?
 — 2 fries shy of a happy meal, Oct 29 2015

You can't focus light smaller than the source? I thought it was you can't make it hotter than the source... what if you collimate it first?
 — RayfordSteele, Oct 29 2015

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