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The Math would add up
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this post was submitted on 15 Feb 2024
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There is a cool easy-to-show fact that you can never make something hotter than the light source my focusing its light.
Since otherwise you could take heat and divide it into a hotter and colder region, decreasing entropy without using energy.
I'm not sure about the easy-to-show part, but take a look at the Brightness Theorem / Conservation of https://en.wikipedia.org/wiki/Etendue if you want to learn more.
The easy to show part was the second sentence of my comment.
This is really useful physics trivia, because the basic truth is easy to show from a simple law, but the detailed explanations go quite in-depth.
With lenses, you trade bewteen angular accuracy and light density.
For a challenge, try it with LEDs. Where do you find the source "temperature", you can get from focusing an LEDs light?
That's an intriguing question. My first guess would be it corresponds to the diode's band gap?
Thats definitely hugely relevant, yes.