On Sat, 19 Jul 2003 21:11:09 -0400, "Stephen Paul"
wrote:

So, magnification is really a function of the distance of the eye, or film
plane, from the focal plane.

No, not really; though for the eye the effect is "as if" the eye were
a certain distance from the focal plane. For film, the film plane
must be coincident with the focal plane. IOW, the real image must be
placed precisely onto the photographic emulsion (or CCD chip).

It's been a long time since I've dabbled with astrophotography; but
magnification for photographic purposes is *not* the same as
magnification for the visual observer. For photographic and CCD work
image scale is generally more important than any dimentionless
magnification concept. The raw image can always be enlarged provided
it possesses sufficient detail.

Any basic treatise on astrophotography or CCD imaging ought to cover
the simple mathematical details concerning image scale.

I am still missing how we actually determine the "cardinal" (thank you)
ratio of the size of the image in the eyepiece to the size of the image
against the naked eye sky.

(Focal length of objective)/(focal length of eyepiece) *is* that
ratio. Performing the implied division results in the dimensionless
number we call "magnification". That first ratio is equal to this
second ratio: (apparent angular size as seen in the telescope's
eyepiece)/(apparent naked eye angular size).

Be that as it may, allow me to continue to expound upon these ideas. I am
informed that the prime focus photographic magnification is calculated from
the focal length of the lens/mirror, where 50mm is "given" to be 1x, hence
2000mm is considered to be 40x. Does this mean that at 50mm, the image scale
at the focal plane is equal to the naked eye image scale, or is this just an
arbitrary standard value?

To the best of my knowledge the 50mm equals 1x thing is due to
photographic history -- most camera lenses had a focal length around
50mm.

If the former, can we then say that a 40mm eyepiece in a 2000mm focal length
telescope, which provides 50x, is magnifying the image at the focal plane by
50x/40x, or 1.25x??

The standard approach is to treat photographic and visual
magnifications separately.

In the world of astronomy we don't assign a magnification to
individual eyepieces. Instead we label eyepieces by their focal
lengths. The advantage of this comes from the simple formula:
Magnification equals (focal length of objective)/(focal length of
eyepiece).

Nevertheless, there *are* alternative ways of looking at magnification
-- as you've demonstrated in this posting.

Let's consider a second example. If the focal length of the objective is
400mm, the prime focus magnification is 8x, and that same 40mm eyepiece
yields 10x, which is 10/8, or 1.25x. Based on these two examples, it seems
to hold that a 40mm eyepiece magnifies the focal plane image by 1.25x. :-).

Now, given a 20mm eyepiece in the 2000mm scope, we would have 100x
magnification of the naked eye image, which is 2.5x the photographic
magnification at the focal plane. For the 400mm scope, we would have 20x
magnification which is also 2.5x the photographic magnification at the focal
plane.

So, where are we? The image scale at prime focus = focal length of objective
/ 50, hence the magnification of the eyepiece = ((focal length of objective
/ focal length of eyepiece) / (focal length of objective / 50). So, if my
algebra doesn't fail me here, (x/y)/(x/z) = z/y, and we can determine the
magnification of any eyepiece by dividing 50 by the focal length of the
eyepiece.

Not that I'm sure _what_ we gain from this, but is it right?

Your definition of image scale (IIRC) is different from the
traditional (degrees of sky per millimeter at the focal plane)
definition. We don't normally assign magnifications (independent of
any objective) to our eyepieces. Using your formula the magnification
of an eyepiece has the units of "millimeters" -- unless you add
"millimeters" as the unit for the number "50". IOW, your formula is
valid once you add millimeters to 50.

Perhaps on some other planet astronomers have adopted your approach as
their standard for magnification; but on this planet the consensus is
a somewhat different approach.

Now let's drop this and all get outside and do some observing ;-)

Bill Greer