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

[Leigh Palmer <palmer@sfu.ca>]

On 17-Apr-06 Ludwik wrote:

> Another factor that has not been mentioned is absorption of a big  
> fraction of solar energy in the glass itself. Assuming two lenses  
> have the same diameter the one with shorter f would be thicker. To  
> simplify, I am assuming that lenses are flat of the side of the  
> sun. The lens with the longer f will transmit more solar energy.
>
> Ludwik
>
> On Apr 16, 2006, at 1:41 PM, Leigh Palmer wrote:
>
> > On 16-Apr-06 Larry Smith asked:
> >
> > > All other things being equal, would a lens with a short focal
> > > length or a
> > > long focal length be better as a fire starter?
> >
> > All other things being equal, the concentration of radiant energy is
> > greater for a short focal length lens than it is for a long focal
> > length lens. The question is entirely reasonable and, I think, well
> > specified.
> >
> > One would have to contrive a situation in which the correct answer to
> > this question is not that a shorter focal length lens is a better
> > fire starter. The only one that comes to my mind is an utterly
> > unrealistic one in which the lens material is lossy. In that case a
> > thicker (shorter focal length) lens will absorb more energy than a
> > thinner lens.
> >
> > 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"  
to "long" as the correct answer. A detailed calculation may show you  
that your conclusion is incorrect; the result depends upon absorptivity.

I stick my oar in here again to make two comments. The two Johns (D &  
M) think this problem is underdetermined. I feel that is a matter of  
taste, and I'm usually the biggest nitpicker here. I take "All other  
things being equal" to apply to lens diameter and material. If one  
wishes to add lens mass to this list I wouldn't complain too loudly,  
but I would have to do the calculation to obtain the answer, because  
it may not be simple.

What the Johns are saying, if taken in the litigious context of  
standardized testing in the United States, means the item should not  
appear on a multiple choice SAT without further specification.  
However, I think Larry's question is an excellent one to use in class  
physics tests. It meets the criterion that a good student must think  
to answer it, but he will get it right. A mediocre student will get  
it right most of the time. A poor student will get it right less  
often. Making good students think is an excellent idea in my opinion.

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