Okay, I finally managed to figure out the equations to describe the angle of any particular part of the surface of an ideal fresnel lens relative to the distance of that part of the surface from the centre of the lens, for any given focal length or material.

The angle at the surface is theta.

theta = sin^-1 z(r-1)^-1

where;

z = tan^-1 xd^-1

where;

x is the distance from the part of the surface to the centre of the fresnel lens and d is the distance between the lens' focal point to the point where the central axis of the lens crosses the lens' plane.

and where;

r = n(2) / n(1)

where;

n(2) = the refractive index of the lens' material

and where;

n(1) = the refractive index of air, at 1 atm and O degrees celcius.

The refractive index values for ice and air are as follows, for wherever the wavelenth of light, lamda, is equal to 589nm.

Ice= 1.309
Air=1.000293

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Since I'm crap at calculus, this took me fucking ages to work out, many hours. I'm pleased with myself, but have no way to confirm my results, unless I actually finish making the mold and make an ice lens, and test it out experimentally. So I guess I'll continue with this in the morning.

I made a works spreadsheet to calculate the angles for various surfaces across the lens. The left hand column represents centimetres from the central axis across the plane of the lens, the right hand column the angle of the surface of the lens at that point. The formula holds for a vanishingly small seperation between the inclined surfaces of the lens. In actuality, the separation will be about a centimetre; if the seperation is too great, it will be a lens, rather than a fresnel lens, the geometry of which is governed by different rules that as far as I can tell are more complicated than those for an ideal fresnel lens.

I couldn't find a decent way of molding the mold out of plastacine, and then I had to go to sea for a month. So, I haven't made much headway. I bought a plastic ruler and cut notches into it shaped like the lens, and tried to use that to shape the mold, but it didn't work because the plastacine was too sticky and clumpy. The idea might work better if I were to get some actual clay, and a potters wheel, but that might be too much effort. Still thinking about it, but will have to wait until I get home to do anything about it.

You may as well use another lens as a mold.

Crafting your own lens would be very difficult to do correctly, depending on how precise you want it.

Still interested to see how you do though.

I've just moved into my new place now, so I've got the space to do this properly, but I've been super busy lately so I've returned to my earlier dream of making a parabolic reflector dish. I've been thinking of making one out of cardboard an tin foil for a long time, just as a prototype before making a 'serious' one. As I've just bought a new house I've got shitloads of carboard lying about, and the materials are cheap, so I did it.

As you can see from the pic, it looks like shit. I'm just waiting for a sunny day to give it a test, see if it works at all. This is more of an update to remind everyone I'm still thinking about optics.

By the way, you can make a 'fresnel' parabolic reflector, but it's not as efficient as a regular one or a lens, because the design necessitates gaps in the light rays recast by the mirrors which increase in width with distance from the centre.

>>75

Ah, can't use another lens as a mold... because there are no fresnel lenses made out of ice. The material changes the optical properties.

>>78

The makeshift parabolic reflector worked... poorly. I could feel it illuminating and warming my hand, but it didn't have the capacity to focus the sunlight to any useful degree. I suppose, under certain circumstances, it could be used to intercept and otherwise weak radio signal. The lesson, I think, is that good mirrors and/or a perfectly smooth paraboloid are necessary. Back to the drawing board!

>>82
wood might work better, provided you cover it with something.

>>83
The model 2 is probably going to be wood and aluminium sheeting. Probably not going to get around to it this leave, probably next leave.

I got some clay to make the mold for the ice fresnel lens. I'm saving up can be bothered points at the moment, when I've got enough I'll get on with it.

>>79
Only the focal length changes. You should be able to use any fresnel as the example.

http://en.wikipedia.org/wiki/Focal_length


For the case of a lens of thickness d in air, and surfaces with radii of curvature R1 and R2, the effective focal length f is given by:
[a function which depends on the focal length, with any (spherical in this case) curvatures you choose.]

>>90

It's more sciencey if you do the math yourself.

I've thought about a way to mathematically work out the shape of a parabolic reflector with a focal point to the side of the dish, so that the shadow of anything placed at the focal point doesn't impede the functioning of the reflector. This isn't exactly hidden and arcane information, but I've found useful resources on the subject scant sur l'internet.

Haven't done the math yet though. Will update again probably when I go back on leave and have moved the project onwards.

SAGE has been used.

Set of equations to plan the construction of your own parabolic reflector. (It doesn't look like a dish so that the object being held at the focus doesn't cast a shadow on the dish. Focus is offset out of the way.)

Quick design I made for the reflector I intend to build. The 'dish' has to be able to pitch and yaw so that it can be aimed at the Sun.