Re: Private Universe and the Seasons

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 13:27 -0500 9/21/03, Marc Kossover wrote:
> I vote for not.
>
> First, essentially parallel rays that go through a convex lens are focused
> to a very small point. This does not occur with any lenses that I posses.
> All of my lenses focus sunlight to an image that is a disk whose size
> varies appropriately with the power of the lens.

The rays that arrive at the earth are not *exactly* parallel. They
are converging with a central half-angle that is a maximum of about
4.5 milliradians. That will limit the spot size, as will the lens
size, the atmospheric distortion of the rays, and, ultimately, the
fact that a spherical lens in not the optimum lens shape, only the
most convenient. In the final analysis it is impossible to get even
exactly parallel rays to converge to a point. It could create an
image whose temperature was higher than that of the original source,
and I suspect that that violates some law of thermodynamics or
another.

> Second, essentially parallel rays that go through a pinhole (large enough
> to ignore diffraction) creates spots approximately the same size as the
> hole. My pinholes cameras make patterns of light of the sun that vary in
> size, and in fact do a pretty good job measuring the size of the sun if
> you know the distance or vice versa.

Doesn't the size of the spot from a pinhole camera depend on how far
away from the aperture you place the receiver? I would guess that the
clearest image would occur somewhere near the point where the
"umbral" rays cross. If you take the image size at that point to be
the diameter of the penumbra, it will necessarily be larger than the
aperture in the case where the rays are slightly converging, as they
are from the sun.

> Although the sun is very far away, it is also very large.
But even though it is large, it is about 200 times farther away,
which means that for many purposes, among them Aristarchus'
measurement of the size of the earth, or figuring the angle of
incidence of sunlight at various points on the earth's surface, the
rays can be taken as parallel without significant error.

Coincidentally, the moon is about 200 times its radius away from the
earth, which is why we have spectacular solar eclipses. A solar
eclipse is the inverse of a pinhole camera, with the "hole" and the
opaque surface in which the hole is punched exchanging places. I
think we get a pretty good "shadow" of the moon on the earth (which
would be the inverse of the image of the sun in a pinhole camera),
even though the size of that shadow is much smaller than the moon
itself.

Does that make any sense?

Hugh
--

Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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