Stephen Paul wrote:
To say that the angular size of an object in the eyepiece is 50x larger than
the angluar size of the unaided eye is also very useful, but I'm now
wondering just what is the correct relationship between the image at the
focal plane and the image "in" the eyepiece.

The linear size in mm of the image in the focal plane, divided by the
angular size in radians of the image in the eyepiece, approximately
equals the focal length of the eyepiece in mm. That's because radians
are dimensionless (except for those eyepieces made by Tele Vue, of
course!)

Essentially, the eyepiece allows you to view the image in the focal
plane as though your eye were at the distance from it equal to the
focal length of the eyepiece (with respect to angular size), except
that naturally, your eye cannot focus at a distance of (say) 6 mm. A
6 mm eyepiece collimates presents a virtual image that is placed at
infinity, so that your eye has no problem focusing on it.

Brian Tung
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