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



Jack Uretsky said, "The ray tracing solution may predict an image size
that is smaller than the smallest spot permitted by diffraction. In
such a case, one will not, of course, see the image [predicted by ray
tracing]."

After adding my clarifying words contained in brackets, I completely
agree with Jack. But I still maintain this has nothing to do with the
original discussion about starting a fire with a magnifying lens.

I was speaking to this issue in a previous post when I said, "It is the
sun's angular diameter coupled with the focal length of the lens that
limits the smallness of the spot, and diffraction has essentially
nothing to do with it for any lens large enough to hold in your
fingers."

In that post I was using a 90-mm diameter lens as my example (about 3.5
inches) which is a reasonable size for a common magnifying glass. In
that previous post I said, "For example, with a 90-mm diameter lens, the
Raleigh diffraction limit for 550 nm light is about 4.27E-4 degrees or
2.56E-2 arcminutes or 1.54 arcseconds."

Since the sun's angular diameter is about 30 arcminutes (1800
arcseconds) we can see that a Rayleigh limit of 1.54 arcseconds compared
to an object/image size of 1800 arcseconds predicts no easily observable
diffraction degradation of the sun's image produced by this lens.

In order to get a Rayleigh limit as large as 0.5 degree = 30 arcminutes
= the same as the sun's diameter, we would need a lens with the very
small diameter of 0.08 mm. That does not describe any practical
magnifying lens we would hold in our fingers and with which we would try
to start a fire.

Hence I still do not understand Jack's continued reference to
diffraction phenomena with respect to the topic of starting a fire with
the sun and a lens.

On the other hand, diffraction effects are easily noticed when using a
telescope to view stars other than our sun. The angular diameter of the
closest star (alpha-centauri) is about 0.01 arcseconds which is way
smaller then the 1.54 arcsecond diffraction limit of a 90-mm telescope.
Therefore, when viewing alpha-centauri (or any other star other than the
sun) with a 90-mm telescope, it doesn't matter how good the optics are,
how dry the air is, how dark the sky is... We're not going to see a star
as the small point predicted by ray tracing. I have to admit my
astronomy students are bothered by this even though we have discussed
diffraction problems viewing stars. They remark, "I can't get this in
focus." I keep saying to adjust the focus until the stars look as small
as you can get them. They keep saying that's what they're doing but
they can't get them as small as they want. I keep saying, yeah, I'd
like them smaller as well, but it ain't gonna happen. It's partly
diffraction and it's partly living in Ohio. It's not the fault of a
cheap telescope because we only have good telescopes with very fine
optics.


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu