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Re: [Phys-l] fire starter from the sun



To connect this ultra-specifically to the Subject: of this
thread: If you could focus the sun's rays more tightly than
permitted by Liouville's theorem, it would be possible to
create a focal spot hotter than the surface of the sun.

I'm a little confused, particularly on what you mean by "hotter". Are
you saying that if Liouville's theorem did not hold then...

(a) it would be possible to create a spot through which the total energy
flux (energy per time) is greater than the total energy flux that leaves
the surface of the sun,

or are you saying that...

(b) it would be possible to create a spot through which the total
irradiance (energy per time per area) is greater than the total
irradiance that leaves the surface of the sun, or

or are you saying...

(c) something else?

Let me explain my confusion: It seems to me that (a) would violate
conservation of energy, let alone Liouville's theorem. In addition, how
hot the spot gets depends more on the total irradiance not the total
energy flux so I'm guessing you don't mean (a).

On the other hand, if you mean (b) then I fail to see why it is not
possible. I admit that I cannot easily follow the logic you presented
in your note. However, suppose you took an infinite plane surface of
uniform temperature T. This would produce a certain irradiance. If you
place a lens (with optical axis perpendicular to the surface), couldn't
you get the rays to focus to a point with much higher irradiance than
the irradiance at the surface of the sheet?

P.S. I apologize in advance if I am not use the appropriate terminology.
Hopefully my concern is clear enough.
____________________________________________________
Robert Cohen, Chair, Department of Physics
East Stroudsburg University; E. Stroudsburg, PA 18301
570-422-3428; www.esu.edu/~bbq