Continuing the discussion on whether the smaller spot has higher losses
to surrounding material... Let me describe an experiment you can do.
You can do it for real, or you can do it mentally.
Assume the calculations in the earlier post are correct. The power
density from 144 1-ft^2 mirrors all converging on a target of 1-ft^2
area is about 9 kW/m^2. The power density from a 100-mm f/2 lens at
sharpest focus is a spot of area 0.008 m^2 with a power density of 200
kw/m^2.
If the smallness of the spot is a problem, such that too much thermal
energy is lost to the material surrounding the spot, just move the lens
closer to the target so as to spread the spot over a larger area. Did
this work? Did the center of the larger spot char more quickly than the
highly focused spot? No? So the "thermal protection" that the larger
area provided for the central portion of the spot was not sufficient to
make up for the reduced power density of the larger spot. Wouldn't that
say that getting the power density higher is more important than
providing a ring of thermal protection around the central area.
I realize the previous paragraph is not exactly the experiment Brian
might want to conduct. That experiment would go like this. Get a
100-mm f/2 lens, and get a 400-mm f/2 lens. The 100-mm lens will
provide a focused solar image of 1.75-mm diameter and the 400-mm lens
will produce a focused image of 3.5-mm diameter. The power densities in
the spots will be the same. Will the center of the spot from the 400-mm
lens char more quickly (reach higher temperature) than the center of the
100-mm lens? It's raining today, so I can't try this. I don't have
those exact lenses either, but I might have something close.
Also remember we are trying to start a fire. That's a molecular-scale
process, i.e. chemistry. Consider the size of molecules compared to the
size of the spot. A spot that that is roughly 2-mm diameter is still a
very large spot compared to molecular sizes. The molecules in the
center of the 2-mm diameter spot are still surrounded by many molecular
layers around them that are still heated by the spot.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu