I don't understand the comment about f/stop clouding the issue. It
seems f/stop (i.e. f/ratio) is exactly what people need to understand
(for this case and many other cases).
I think there is a misconception that a positive lens will focus the sun
into a small spot regardless of the focal length. I think this is
because most people who play with lenses always use short focal length
lenses (small f/ratio). I usually poll my class to see who has used a
magnifying glass to start a fire, burn their intials into wood, or
incinerate ants on the sidewalk. Many, if not most, have done one or
more of these. Then, when we discuss the old 12-inch telescope mirror
we have (which isn't in a telescope any more), some guys want to use it
to focus the sun and see how hot they can get something. If I let them
try, they are surprised it doesn't work. Why not? The f/ratio is too
big, i.e. the aperture, although big, is not big compared to the focal
length. The sun does not focus to a spot, but focuses to a fairly large
circle more than an inch in diameter. "Why won't it focus sharper?"
they ask. I point out that it is sharp. If there are clouds, you can
see the sky nicely focused at the image plane. It is sharply focused,
but not small. There's a difference between sharply focused and small;
the words are nowhere near synonomous.
Student's just don't have this knowledge because they haven't played
with long lenses.
Another way to help students see this is to discuss telephoto lenses for
cameras. The longer the focal length, the larger the image on the film
(or CCD). Many students are aware of this because it is obvious that's
what's happening. If the lens diameter is the same, but the image is
larger, i.e. spread out over more area, the brightness will be less.
Thus, to get the same exposure, the telephoto lens needs a larger
diameter. Unless you spend big bucks, the typical telephoto lens does
not have a much larger diameter, hence telephoto lenses tend to have
larger f/ratios. We have to slow-down the shutter and hold the camera
more steady.
If you want to start a fire, you need a small f/ratio. Typical
magnifying glasses that will start a fire have f/ratio between one and
two.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu