One of the original designs for the International Space Station was called Solar Dynamics. At Glenn Research Center in Cleveland we built Building 333, the Power Systems Facility, to test the equipment. One of my first tasks as an engineer was to outfit eh building. The SD system consisted of an offset parabolic mirror with adjustable elements. Sunlight was gathered by the mirror and focused on an area about the size and shape of a football. The temperature in that spot was high enough to damage the main ISS structure if it was allowed to impinge on it!
Too late to edit. Here is a link to some photos of the building and the framework for the mirror in place.
The Ordeillo Solar Furnace in France can produce a megawatt of power and melt steel
I hadn’t realized it, but there’s also a solar furnace in Uzbeckistan that is about as powerful as the one in France
Here’s one from the many:
Yes, another way to look at it is that the trick to getting sharper photos is a smaller f-stop - which increases depth of field but also means less light. Also, I wonder at the accuracy of grinding a 100-foot-focal length lens. Not trivial. And as others mention, chromatic abberation is a factor.
Plus the logistics of keeping the “hot spot” at one point. The sun moves 15° an hour or about .26 radians. At 200 feet, the target will move a bit in an hour. In an hour, the focus image of the sun will move about 50 feet… a little less than a foot a minute. (Assuming I can still do trig, which is iffy) so you need to move the lens a decent amount to keep a spot warm. Mirrors are easier to move so seem to be the better choice.
The general term for mirror-based solar focusing systems is heliostat:
I saw a pretty sizable one at White Sands Missile Range which was built to simulate the thermal effects of a nuclear explosion for survivability testing. Here is an article describing its use in a rock-melting experiment:
When I was there last year it had been idle for a while. Maybe they’ll let you borrow it…
Perpendicular to the sun, yes, but which part of the sun? The center?
Imagine you’re part of a team of miniature nanobots working to create the a perfect 200mm x 200mm parabolic mirror array, tasked with creating a solar reflecting death ray to eliminate a pesky rock at a distance of 100 feet. You are individually responsible for articulating one tiny element of that array a nanometer in size- your team has billions of nanobots each with a similar element.
It’s your turn to align your element to the target spot. You radio up a command and an aperture closes in front of the mirror, perfectly aligned to the center of the sun, blocking out everything but a tiny pinhole beam sized just for your mirror. You then adjust your nanomirror right on the target spot 100 feet away - it’s now perfectly focused, a tiny beam of your reflected light exactly on target!
You then wait while all the other billion nanobots each have their turn adjusting their nanomirrors on the focal point, using the pinhole aperture light beam from the center of the sun. They all have perfect focus, right on target. The death ray is almost here! This same method worked perfectly during the trial run when the rock was only a foot away!
Someone hits a button and the pinhole aperture shifts slightly in front of the array, It now just happens to be aligned with your nanomirror and the edge of the sun. You look at the target spot 100 feet away, and find that your mirror is now more than 5 inches off target. Frustrated, you realign your mirror, achieve perfection, but the pinhole then moves to the opposite edge of the sun’s diameter. You’re now more than 10 inches off target.
The aperture starts moving, tracing the sun’s circumference in a circular pattern, still aligned right on your mirror. You find that no matter what you do, depending on the position of the aperture, you can’t align your mirror to one position and guarantee an accuracy of any better than 5 inches from target.
Maybe the others had more luck? Someone hits a button and the aperture now opens fully. The target gets brighter, but everyone else seems to have had the same problem. At that distance, you’ve focused all the available sunlight from your 200mm x 200mm mirror array onto a spot …a little bigger than the size of your original array. The target is about as bright as it would be had someone stood a single flat vanity mirror right next to it.
I gotta ask; why do you need a magnifying glass with a 100-foot focal length? Are you preparing for a real-life Them! (1954 monster movie with giant ants) situation?
This is a thing I don’t understand. Can’t I just track the sun continuously with my mirror, always keeping an optimum angle? It’s not like the sun moves randomly. Motorized telescopes can do it, and I, a very special nanobot, am way smarter than a telescope from Walmart.
The example is assuming a stationary sun. It is trying to provide an explanation about why you can’t focus an extended source - such as the sun - onto an arbitrary point. The system always ends up creating an image of the extended source the size of which is defined by the focal length of the optics and the angular extent of the source.
The way I wrapped my head around this is imagining myself next to the magnifying glass. From that perspective the sun in the sky and it’s focused image are the same size and that remains true regardless of the distance to the focused image. One hundred feet closer to the sun and it doesn’t look any smaller. Likewise, the the projected image stays the same size. When you double the focal length, the focused image takes up four times the area so you need a lens with four times the area to maintain the same light intensity.
Did I get that right?
Doesn’t that Bust™ the broader myth that it was used to repel an invasion. At those distances the ship you set on fire is seconds away from making landfall.
Archimedes really did repel multiple attempts at invasion by the Romans, but a large part of it was just that the weapons he did actually make (catapults and the like) were so far beyond the Romans that most of the troops thought they must be magic. Apparently it got to the point where if they saw a bit of rope on their ship that they didn’t recognize, they’d scream and throw it overboard, for fear that it might be one of Archimedes’ devices.
The reports of Archimedes using concentrated solar light to burn Roman ships come from long after the supposed event. I seriously doubt that there’s any truth to the stories.
My point is that itcould have worked – you can set sails and even ships alight with well-coordinated mirrors. Attempts to discredit the story based on whether or not it could work are, in my opinion, misguided. It could have worked (although at distances so close that more conventional weapons would be better), but it very probably wasn’t even tried.
Better at destroying ships? Probably. Better at convincing the opposing army that you’re a god amongst men and that it’s safer to commit suicide than to try to fight you? Maybe not.
Now, instead of magnifying the sun, a space-based LASER was the source!?
I hope post 35 wasn’t too soon.
I already called solar-powered laser 
Inventor Garrett Brown ( Steadicam, SkyCam, MobyCam, DiveCam, etc. ) set about creating just such a device.
He had someone craft a very large very thin metallic mirror. It spans about 5 ft across. It is a circle and it is mounted into a vacuum pump back.
Then it was attached to the kind of yoke that most movie lights are mounted into so it can be tilted up and down and rotated side to side.
The goal was to be on the dark side or the wrong side of an area in terms of angle of sunlight and use this to reflect the sun back to where you need it. When the Sun hits the 5 ft diameter disc it creates a certain intensity of light when bounced back, but when you turn on the vacuum pump the circle starts getting smaller and smaller and smaller…and brighter and more intense.
Eventually you can set wood on fire. I know this because I witnessed it at his farm. Only the Prototype exists.
It was enormously useful on movie sets because you could be on the wrong side of the location or a building and reflect very bright sunlight into windows. This saves the time and trouble of building scaffolding and putting large movie lights up on the scaffolding to simulate daylight.
On a large film one can calculate the cost per hour and then per minute of production time. If you invent something that can save quite a few hours in every work week of production time well then you’ve paid for itself in the first movie in rentals.
The safety issues coupled with the fact that it’s a somewhat delicate machine stopped him from making anything more than the prototype.
Like a less expensive than crafting several immense pieces of glass to build a focusing lens.
There have been papers proposing building space-based solar-powered lasers, but the big problem, if you want to defeat the Roman Navy, is that you have to get things up into orbit. It’s cheaper and faster to just build a bunchof catapults and things.
Now a solar-powered laser on the ground is another thing. These, too, have been proposed. To the best of knowledge, no one has yet built one (although one has been patented).
Reference #2 on that Wikipedia page is by Geoff Landis, who, in addition to being a NASA scientist, is a science fiction author.
The Martians made one: