Lens to make sun shine at a same spot

[AndreiRS]

Hi. I have been observing some curious stuff in some trees here. The branches which take sun all day, "pop" a lot of new branches. So I was thinking about some shape of lens that would make the sun light hit always a same spot on the tree during almost all day. But then I remembered that concentrating light this way, I will just make the tree light up like a torch. I think I need a lens that gets light from various directions and make it come strait from the other side. But without focusing it too much. Just a little more intense than normal sun light.

[profdc9]

There is a field of study of solar concentrators that try to accomplish just that, especially for concentrated solar energy.  The simplest kind is a parabolic trough which focuses in one direction.  A pipe with a heat transfer fluid is heated by the sun.  The trough forms an image of the sun as a line, so as the day progresses, the line moves, but stays mostly focused on the pipe.  There are also designs of "aspheric" concentrators which start with a parabolic dish and then distort it so that the aberrated images of the sun tend to stay focused on a multijunction solar cell. 

There is a theorem called Liouville theorem, or the law of etendue, which states that it is not possible to concentrate a light source to a higher radiance than the source (in this case the Sun).  Radiance is a measure of the amount of power per unit area per unit of "solid angle."  At the surface of the Sun, the Sun is approximately a black body at 5800 K.  If you could concentrate all of the light in a hemisphere on an isolated, heat insulated target, it would heat up to 5800 K, but any real object would melt or vaporize first.  The same law makes it so that it is not possible to design a refracting or reflecting optic to always focus rays from any direction to the same point.  So any design of a solar concentrator is always a compromise that maintains a certain level of concentration given the various positions of the Sun in the sky.

So the answer is that strictly speaking, it is impossible to make a lens to focus the sun to the same spot no matter what position the sun is in, but there are good compromise designs used for solar collection.

Dan

[Mads Barnkob]

You should search for Fresnel lenses, as Dan mentions they have been used for experiments with upping the effectiveness of solar panels.

[AndreiRS]

Hi profdc9. Thanks for all the info. I think I can manage to do something like that pipe heater. Ah I think I got the idea, with a simple lens I was already imagining it would not work just like that. Maybe with some electronics and motors moving the parts.

I will try to find some small Fresnel lens. It need to be small, less than 5cm would be good. Thanks Mads. First I will try with some simple lens just to see what happens.

[profdc9]

Sometimes you can obtain Fresnel lenses from hobby or camping stores, because they can be used to start campfires.  Also, old overhead projectors have a Fresnel lens to concentrate the transmitted light into the projection lens.  A real find is an old projection TV.  Many have huge Fresnel lenses behind the screen that concentrate the source metal halide lamp to be viewed in the forward direction.  You can melt concrete with it!  Watch this:

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Another good lens for concentrating the sun is a simple glass globe. These form a tight focus on the far surface of the globe which can easily burn things as well.

Dan

[Uspring]

@profdc9:
Funny, that you mentioned Liouville. It was my first thought, when I read the OP.

@AndreiRS:
A consequence of Liouvilles theorem is, that you can't focus an object down to a point with e.g. a camera. The best you can do, is to have a little image of it on the focal plane. If you focus sunlight, you will optimally get an image of the sun somewhere. Liouvilles theorem holds for any arrangement of lenses, mirrors or even yet uninvented contraptions.

Since the sun moves around the sky, its image consequently will move, since the sun basically becomes a more spread out object. The image turns into a line of light, so your tree won't always be illuminated. You still can have the tree lit all day by setting up a set of mirrors, each one angled for a particular time span. Liouville bites you here in the sense, that you will need large mirror areas in total and will also put light, where you don't need it. You can try lenses, but they also need to be big.
A moveable mirror helps there.