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



You can't discuss diffraction phenomena in terms of rays. When dealing with wave phenomena, the concept or "ray" is sometimes useful when a short wavelength approximation is appropriate. That approximation is
never appropriate when discussing phenomena that are essentially "wavelike".
To help Bernard with his perevious misunderstanding of my remark:
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.
Regards,

Jack


On Wed, 19 Apr 2006, Michael Edmiston wrote:

I'm sorry, but I just can't figure out what Jack and Bernard are saying
because it doesn't make any sense with respect to what I observe
experimentally and what I observe when I do ray tracing.

I suggest the following two things.

(1) Get a long lens 500 to 1000 mm focal length. Take it outdoors in
the sunlight and see how small of a spot you can get on a piece of
paper. The smallest spot you can get will occur when the sun's image is
in focus. Any out-of-focus image will be a larger spot than the
in-focus image.

The smallest spot will be sin(32.5')*(focal length) where 32.5' is the
approximate angular diameter of the sun. Since the sun is very far
away, its in-focus image will be at the focal length of the lens.

I challenge you to get a smaller spot than the spot you obtain when you
have a sharp image of the sun projected on the paper.

(2) Click on the link below to get a PDF file of a drawing I made.

www.bluffton.edu/~edmistonm/sun_lens_image.pdf

(there are underscores between the words sun_lens_image)

The red rays from the top of the sun come to focus at the focal plane as
shown. The blue rays from the bottom of the sun come to focus at the
focal plane as shown. The spot at the focal plane where the sun's image
is in sharp focus is the smallest spot you can get.

This drawing was made using regular ray-tracing rules for a thin lens.
To fit everything on the paper, the sun is too close to the lens. The
primary thing that changes when the sun moves further away (to the left)
is the focal plane on the right moves toward the focus (F). At
93-million miles away the sun's image (i.e. the focal plane) will be at
the focus of the lens for all practical purposes. But the spot will not
be a point because the sun is not a point. It's angular diameter is
about 32.5 arcminutes. The rays through the center of the lens will be
diverging at 32.5 arcminutes. When these rays have reached the focal
plane they will have spread to a circle of diameter sin(32.5')*(focal
length) and that is how you can calculate the minimum diameter of the
spot.


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


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