Could an armchair optical engineer and DIY lens grinder craft a homemade magnifying glass capable of incinerating a pile of leaves from a distance of, say, 100 feet? Would the ideal configuration consist of one gigantic lens (basically a supersized desk magnifying glass) or a series of lenses similar to a camera lens or telescope? Could both versions achieve the stated goal, given a skilled and dedicated hobbyist?
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Not sure how big such a lens would need to be, but there were incredible challenges to casting and grinding the 200-inch mirror for the Hale telescope, though admittedly that was years ago.
If there was any reason to do such a thing, the right solution would probably be an array of smaller lenses.
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You’d need a huge lens to ignite anything from 100 feet away, no matter how perfectly ground it is. Lenses can’t produce temperatures any hotter than the light source they’re focusing. You get hotter by making that temperature fill more of the target’s field of view.
Anyone on Earth can look up, on a clear day, and see a 6000 K heat source, filling a spot of the sky a half a degree across. That’s not enough to set things on fire. An ant under a magnifying glass sees a source of that same temperature, except filling half the sky: Now, that can burn things.
Yeah, don’t do that 
There are YouTube videos of people who’ve taken the fresnel lenses out of old projection style wide-screen televisions and use them to melt steel and rock. Setting leaves on fire would be trivial; the greater challenge would be making the optical elements flatter so the focus length was increased to 100 feet. You might need a secondary mirror to allow the beam to be horizontal, but the lenses are iirc about 3×5 feet and mirrors that size are common.
Besides the difficulty in grinding such a large traditional lens, it would deform from its own weight when supported by the edge. This is a major problem for lenses used in telescopes, which is why large telescopes almost universally use mirrors instead of lenses (a mirror can be supported from the back; a lens can only be supported from the edge because the support would get in the way of the optical path). Lens sag might not be a major problem if the only purpose is to start a fire; an amount of distortion that would ruin a telescope image might have only a small effect on fire-starting ability.
If the goal is setting a pile of leaves on fire mirrors are the way to go: just add more and more of them until the fire starts. Archimedes is credited with burning enemy ships in Syracuse, though this is likely apocryphal, but today solar thermal energy is used for a whole range of purposes: from cooking to electricity generation.
The mirrors don’t even have to be parabolic, flat ones will do if you use enough of them, and spherical mirrors are good too, the spherical aberration should not be a problem with a 100 feet focal lenght.
But if you insist on lenses (where, as Lumpy has noted, you will probably need mirrors anyway to orient the beam) I believe plastic will be easier to work with.
And most leaves don’t really burn that well acording to my experience: paper is better. Crumpled newspapers were the best in my pyromaniac youth’s recollection.
Traditionally, the problem with refracting lenses was chromatic aberration. Eventually achromatic lenses were developed that corrected for this. The solution until then was to have lenses with very long focal lengths, more than 100 feet. The other solution was the reflecting telescope, which had the additional advantage of allowing the objective to be considerably closer to the eyepiece.
Anyway, the apparent size of the sun on Mercury is about 1.5°. That’s big enough to raise surface temperatures to the ignition point of paper. A lens with an apparent size of 1.5° at 100 feet would be ~30" in diameter. That’s roughly the size of the largest lenses in astronomical use.
So I would say, yeah, maybe a very, very dedicated DIYer could.
There is the story about the Archimedes death ray using mirrors to set enemy boats on fire, and Mythbusters did a bit on this and came up with some interesting results that didn’t outright dismiss the idea of using the sun as a weapon.
How much of the field of view of the rock was taken up by the fresnel lens? The sun takes up about 0.2 deg^2 in the sky- the fresnel lens likely takes substantially more area in the sky from the perspective of the rock by several orders of magnitude.
If the original melted rock was 1 foot away from the lens, the only way you could duplicate the same effect on a rock from 100 feet away is to get a giant fresnel lens that takes up the same area of sky - this would require the lense to be 100 times bigger in diameter (10,000 times larger in area) It is not physically possible to use the same size fresnel lens and “just change the focal point 100 feet away” and get the same beam intensity at the focus spot.
I’m trying to understand what field of view has to do with the intensity of the beam.
The link below has two versions of a fresnel lens. Both are 200mm \times 200mm, but one has a focal length of 100mm and the other a focal length of 210mm. An observer at 100mm will see the lens blocking more of the field of view than the observer at 210mm.
Both lenses are collecting 0.04m2 of light. Does the intensity of the beam traveling an extra 110mm decrease in the same ratio as the relative blocked field of view?
I guess my question is does the covered field of view have to do with transmission losses? Because it doesn’t make sense to me that it can have to do with the amount of energy originally striking the lens, because that should be the same for two lenses of the same size.
Both lenses are collecting the same amount of light, but the more distant one is putting that light onto a larger (less concentrated) spot. The spot projected by the lens is an image of the Sun, which has a finite diameter. For any good lens, the angle formed by going from one edge of the bright spot, to the lens, to the other edge, is always going to be a half a degree.
To put it a different way - sunlight is not a collimated beam. Its the same reason why shadows are less crisp the further from the object you’re casting them are.
From the perspective of anywhere on the surface of the fresnel lens, it is getting light from a 0.5 degree spot in the sky, from edge-to-edge of the sun. You can’t design a lens that can perfectly focus that variation in angle - Even with a perfect mirror or lens, the incoming sunlight from the center of the sun will be focused right on your target spot, but the incoming sunlight from the edge of the sun will not be - as it came in at .25 degrees off axis. You can’t send photons at two different angles to the exact same spot on a lens and expect that same spot on the lens to magically put them in the same place.
The farther away your target is from the lens, the more relevant this off-axis angle becomes. The lens close to the target with a short focal length can concentrate all of its energy (even the off-axis edge-of-sun light) onto a narrow spot, but the same size lens with a 100 ft focal length ends up dispersing it over a gigantic area, with barely any of it exactly on target.
The only workaround to get the same intensity on your target spot at that distance is to make a gigantic lens - its still going to be dispersed over a wide area, but you’ve made up for it in “volume” of light collected.
I assume the OP already knows about these solar power towers?
As for death rays for burning stuff at a distance, perhaps one could construct a solar powered infrared laser…
XKCD’s Randall Munroe wrote an interesting What If article about sunlight, moonlight and giant magnifying glasses:
Thank you, that was the bit I needed to understand it, and it makes sense.
@YamatoTwinkie I think I understand what you’re saying, but I wanted a simpler description than the angles and degree stuff. The third grade talk, not the 12th grade physics talk. I think after the first explanation I was ready to digest yours.
I think I’ve been down this road of thinking before, because it caused me to remember an idea I’ve had before on similar topics. Perhaps I’ve even asked the question before. Obviously I’m wrong, but I’m not exactly sure why (debunk my perpetual motion machine!)
If instead of one large 200mm \times 200mm lens I have an array of 100 20mm \times 20mm lenses, would that gain anything? Each of the small lenses could be adjusted/ground/tilted to have the same focal point. Would the off angle light be less dispersed(?), because the off angle is less for each mini-lens, than for the large lens?
I guess I’m imagining that each mini-lens is angled so they are all perpendicular to the sun (is that mostly flat at these distances?), but then the lenses are formed in such a way that the light is bent coming out of each to all focus on the same spot.
You are essentially reinventing a Fresnel lens. You gain in terms of mechanical limitations on lens size, but nothing else. The light only cares about the geometry of changes in refractive index. How you hang those in space is an implementation problem. If you give up a requirement for a perfect focussed image, you can mess with relaxing the geometry a lot. But it doesn’t change the underlying etendue problem.
No matter what, the requirement of reversal of the optical path always holds. Doesn’t matter how you break up the optical elements. In particular you don’t reduce the off axis angles. They are fixed by the location in space of that part of the optics. Running the optical paths back from the target is a great way to see this is so. Indeed it is a used thing to do when trying to understand any optical train.
That works, but your array of lenses still needs to be just as large as the original single lens would have been. You’re basically just cutting the lens up into a bunch of pieces.
Mythbusters did three episodes on this, but I don’t think they did a very good job. In the first they used a very clumsy method of focusing that didn’t even get them as tight a focal spt as they should have. I talked to the MIT professor involved in the second case, and he agreed that, although Adam did a god job with rapid mirror alignment, there were some problems with the way things were done. For the third try they finally came up with a focusing scheme (although ironically not the simple method that was the one proposed back in the early 1970s that fe-ignited interest in this topic). The still didn’t succeedci setting fire to their target ship.
Which is ironic, since two other groups replicating th experiment DID set fire to a ship. In 1973 Ioannis Sakkas set fire to a ship at a distance of 48.8 meters (160 feet, so farther than your stated 100 feet). He had a crew of 60 students holding mirrors with an area about 1.6 square meters each. In Osnabruck, Germany in 2002 a similar experiment was successful at a distance of 50 meters (164 feet). They used 500 mirrors with average size of 0.2 sq meters. So it’s certainly possible. Buffon’s origina experiments with this in 1747 were 65 feet away, and he set fire to tarred hemp and melted tin. You can find YouTube videos of people setting fire to things with collections of mirrors at various distances.
I calculated the approximate solar flux for a lot of these. The Mythbusters ought to have been able to set fire to an appropriate target, provided their focusing was good. See the second chapter in my book How the Ray Gun Got Its Zap!
It’s a lot easier to make and aim a big mirror than a big lens, even a fresnel lens.