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This seemingly innocent problem is actually quite tricky. For thermodynamical reasons, it is clear that the answer has to be a "no". Searching the web, it is easy to find this answer, sometimes even together with an explanation of why this is so.

The explanation is that what matters for the temperature at the focus is the solid angle under which one sees the sun when sitting at the focus. If this solid angle were exactly [tex]4\pi[/tex], then the temperature at the focus is said to be the temperature on the surface of the sun. If this solid angle is smaller than [tex]4\pi[/tex], then the incoming power gets scaled down accordingly, and consequently the temperature attained is less.

This reasoning seems faulty too me; for example, an elementary calculation shows that equal equilibrium temperatures endue for the case of a lens which is much smaller than the distances from the lens to the objects. (Just consider how much radiation hits the lens from each object.)

Does anyone know of a reference where this problem is treated properly and thoroughly?

[For I believe to have a solution, and I wonder whether it would make sense to write it up and try to get it published?]