Shouldn't this cause a fire?
This website shows a telescope projecting the sun onto a blackboard: https://astronomyconnect.com/forums/articles/2-three-ways-to-safely-observe-the-sun.21/
Why isn't the board catching fire? You can easily start a fire on a sunny day by targeting the focal point of a magnifying glass onto something flammable. Why isn't the telescope in this picture doing the same thing?
Photo by Luis Fernández García
That should be Tangentially related xkcd what if Can you use a magnifying glass and moonlight to light a fire?
... A blackboard isn't flammable, is it? The surface is generally made out of slate rock, and you're going to need a lot more focused heat than that little telescope can generate to set it on fire. If you put a piece of paper there you might have a problem, but a blackboard should be fine.
As a matter of fact, that's exactly how my neighbor's house caught fire when he forgot to bring in his telescope (thankfully, they caught it quickly). So it does happen.
I had a similar set up with binoculars, unfortunately I forgot to take the lens cap off the eyepiece I wasn't using. It now has a small hole melted into it.
@DarrelHoffman that's not a blackboard - it's white where it's not in shadow. Compare to the bottom right edge of the paper box that's also in full sun Besides a lot of blackboards are black-painted wood
It's really too bad the temperature argument revolves around photons. It'd be truly spectacular if you could reach -173°C just by focusing on an unlit moon. That'd probably wreck the universe though. It's a good thing that photons are their own anti-particle.
@WayfaringStranger actually if you ensure that your object is able to radiate into space, and not receive radiation from anywhere else, it will cool down to CMB temperatures. (possibly slowly). On Earth we have this atmosphere in the way which may reduce the amount of cooling available. I seem to remember somebody extracting energy from an LED exposed to the night sky.
Compare the telescope’s aperture/light-gathering to the size of the image being projected. They are almost the same size, meaning that there is little if any light-concentration occurring. (Unsurprisingly, solar observations require very little light-gathering power)
The answers below are good at explaining why it doesn’t cause a fire, but please note that if the telescope isn’t aligned properly for the image to be projected by it (i.e. the “projection” stays inside the tube), it may cause heat accumulation on parts of the telescope. This happened to me once, as the focus was on a plastic ring in the eyepiece rather than in the middle of said ring, so the ring started melting and smoke came out. I have also seen photos of a wooden-tube telescope that completely burnt down because of a similar event.
For a magnifying lens or mirror to be able to ignite something with light from the Sun, its surface area must be large relative to the square of the focal length. Solar energy will be spread throughout the projected image, and the size of that image will be essentially proportional to the focal length, making its area proportional to the square of focal length. A typical hand magnifier will have a relatively short focal length, making the projected image quite small. Telescopes, however, are designed to emulate lenses with much longer focal lengths so as to produce larger images. The amount of heating from a telescope will be maximized when it's properly focused, but if the light is spread through a 64mm-diameter image it will be less than 1/1000 as powerful as it would be if it were focused with a shorter lens to produce an image which is only 2mm in diameter.
Incidentally, a factor which makes the "Archimedes death ray" improbable as a means of focusing solar energy to directly ignite ships is that the size of the projected image of the Sun would increase with the distance to the enemy ships. On the other hand, the amount of focused solar energy needed to temporarily or permanently blind people is far below the amount required to ignite things. If the crew of a ship had flaming projectiles they wanted to launch at a town, but sunlight focused by the townspeople's shields were to blind some crew members at an inopportune time, it's not hard to imagine that the ship's crew might accidentally set fire to their own ship or other nearby ships. I think it entirely plausible that people witnessing the battle from shore might have observed that solar energy was being focused on ships, and that the ships subsequently ignited; it's not hard to imagine that such people would conclude that the solar energy ignited the ships whether it actually did or not.