*First a disclaimer: I **KNOW** that viewing the sun through a telescope will burn my eyes, so no need to convince me of that. I'm not going to try it. This question is about the optics and physics of **why** that is true.*

A friend and I were discussing ways to safely view the upcoming solar eclipse, and I discovered a huge gap in my understanding of optics theory. Namely, these two truths:

 1. Telescopes cannot increase the *surface* brightness of an image, they can only increase *total* brightness by making the image bigger at the same surface brightness. No point in the bigger image will be brighter than it is with the naked eye, due to the [conservation of étendue][1].
 2. If you look directly at the sun through a magnifying telescope, you will quickly burn and permanently damage your eyes. However you can get away with looking at the sun with the naked eye for a second or two and not immediately go blind.

I accept both of these as true and am not challenging them, but seem to me to be in contradiction to each other, even from a purely optical and physical standpoint (the biology of the eye and human visual system being irrelevant). What am I missing?

To further clarify my question / confusion, consider this thought experiment. Let's construct a camera out of a closed cardboard box, with a small hole + lens on the front, and a simple sheet of paper on the back (inside) acting as the "film". **Scenario 1**: We point this camera at the sun, and it makes a tiny bright circle on the paper (a tiny image of the sun), but not bright enough to ignite and burn the paper because the aperture and lens are too small. **Scenario 2**: Next, we place a telescope in front of our camera, which magnifies the image and creates a larger circle on the paper.

**The key question**: Will any point of the paper in Scenario 2 become hotter than it was in Scenario 1? Is it possible cause the paper to ignite?

Truth 1 would indicate that the answer is no, while truth 2 would indicate that the answer is yes. What am I missing?


  [1]: https://en.wikipedia.org/wiki/Etendue