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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.