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If a parabola reflects parallel lines into its focus, what does a
catenary do? What about non-parallel lines?
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On 2/14/2015 10:25 PM, Mike Horvath wrote:
> If a parabola reflects parallel lines into its focus, what does a
> catenary do? What about non-parallel lines?
I posted a question on Stack Exchange too if you want to look at it.
There is a diagram to look at.
http://math.stackexchange.com/questions/1148679/ray-curve-mirror-problem
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Am 15.02.2015 um 05:13 schrieb Mike Horvath:
> On 2/14/2015 10:25 PM, Mike Horvath wrote:
>> If a parabola reflects parallel lines into its focus, what does a
>> catenary do? What about non-parallel lines?
Um... nothing much of interest as far as optics go, I'd guess. The true
application for caternaries is in statics, where it's the ideal shape
for self-suspending arches and bridges.
> I posted a question on Stack Exchange too if you want to look at it.
> There is a diagram to look at.
>
> http://math.stackexchange.com/questions/1148679/ray-curve-mirror-problem
I think an out-of-focus parabola might indeed be exactly what you need
for that use case.
You could use POV-Ray's photon mapping to test out this hypothesis.
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On 2/15/2015 8:47 AM, clipka wrote:
> Am 15.02.2015 um 05:13 schrieb Mike Horvath:
>> On 2/14/2015 10:25 PM, Mike Horvath wrote:
>>> If a parabola reflects parallel lines into its focus, what does a
>>> catenary do? What about non-parallel lines?
>
> Um... nothing much of interest as far as optics go, I'd guess. The true
> application for caternaries is in statics, where it's the ideal shape
> for self-suspending arches and bridges.
>
>> I posted a question on Stack Exchange too if you want to look at it.
>> There is a diagram to look at.
>>
>> http://math.stackexchange.com/questions/1148679/ray-curve-mirror-problem
>
> I think an out-of-focus parabola might indeed be exactly what you need
> for that use case.
>
> You could use POV-Ray's photon mapping to test out this hypothesis.
>
I will have to do some playing around in geogebra.
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> If a parabola reflects parallel lines into its focus, what does a
> catenary do? What about non-parallel lines?
LOL at the typical response about burning the grass! I assume you are
using a curved mirror like this because you want the light hitting the
grass to be more intense than the light you'd get if you just pointed
the grass straight at the sun. Why not just use a few flat mirrors
angled correctly, that way you wouldn't need to worry about uniformity
and they should be much cheaper to manufacture.
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scott <sco### [at] scott com> wrote:
> > If a parabola reflects parallel lines into its focus,
What if your parabola began to focus those parallel rays, and then intersected a
divergent lens - then you might get back parallel rays, only in the opposite
direction.
Maybe take a look at the construction of a Dobsonian telescope or "light
bucket".
http://en.wikipedia.org/wiki/Dobsonian_telescope
Also, if you simply had flat mirrors mounted to the side of the cylinder, you
could then reflect light straight back onto the grass after it completed its
U-turn.
Allow me to construct athroroughly abyssmal ASCII diagram:
/--\ /--\
^ | | ^
| O |
^ light
|
cylinder
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On 2/16/2015 4:57 AM, scott wrote:
>> If a parabola reflects parallel lines into its focus, what does a
>> catenary do? What about non-parallel lines?
>
> LOL at the typical response about burning the grass! I assume you are
> using a curved mirror like this because you want the light hitting the
> grass to be more intense than the light you'd get if you just pointed
> the grass straight at the sun. Why not just use a few flat mirrors
> angled correctly, that way you wouldn't need to worry about uniformity
> and they should be much cheaper to manufacture.
>
They're not pointed anywhere in general. I guess pointing the mirrors at
the sun might be a good idea.
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