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On 17-Apr-06 Ludwik wrote:cut
cut
Leigh
I guess my exposition is rusty, Ludwik. I think I said exactly what you said I missed about absorption in the lens. At some absorptivity, given any fixed lens geometry, there must be a crossover from "short"
I wanted to add one more piece of information that will impinge on the answer here, and Ludwik got this one just backwards. If one wishes to minimize spherical aberration in this application (assuming aspheric lenses are not among the unspecified "inequalities" in this problem), he should orient a plano-convex lens with its curved side toward the Sun, not its flat side. That is a much more sophisticated inequality that, I suppose, must be mentioned by the ETS to avoid legal bills. [I see Bernard Cleyet picked up these same points.]
So we see that Larry's simple question (in my opinion a very good question) leads to just the sort of discussion that we as teachers need to nurture among our students or, failing that, between ourselves and our students. I have only just scratched the surface of the discussion here. We still have to work on the fire starting problem at the receiving end of the radiation.
Leigh