Stephen Paul wrote:
Magnification - an ordinal value that indicates the number of times the
image at the focal plane is made larger, measured in diameters. Example: 50x
means that the image "in" the eyepiece is 50 diameters larger than the image
at the focal plane.

Bill Greer wrote:
The above definition is inaccurate. This should be clear from the
following: The image of an extended celestial object at the focal
plane of a 400mm focal length telescope is one third the linear size
of the image of the same object at the focal plane of a 1200mm focal
length telescope.

The main issue, I think, is that you can't divide an angular size (the
size in the eyepiece) by a linear size (the size at the focal plane)
and expect to get a dimensionless quantity like magnification. You'd
instead get a quantity in mm^(-1), and that quantity turns out to be
just 1 over the focal length of the eyepiece. (Provided that the
angular size is expressed in radians. If degrees, then it would be
about 57.3 over the focal length of the eyepiece--57.3 coming from the
number of degrees in a radian.)

So clearly, that can't be the magnification, as you point out. Also,
it's not an ordinal value (e.g., "fifth," "forty-second," etc.); it's
a cardinal value. I don't think I've often, if ever, heard anyone
refer to observing Mars "at the two-hundred-eightieth power," for
example.

To expand on what Bill added as a definition of magnification, the
object in the sky has a certain angular size. (You can't measure its
linear size directly, of course.) The virtual image in the eyepiece
has a certain angular size. The magnification is the ratio of the
latter to the former.

Brian Tung
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