Ed,
I don't know of a special treatment of the focusing lens, but I am certainly not into it enough to think that one doesn't exit. The focusing lens can be either positive or negative, and common binoculars use both. I hope you won't mind some random thoughts.
I get a lot of mileage out of a couple of simple page-1 type forumlas which I'm sure you are familiar with. Where f is focal length and o and i are object and image distances,
there is the "lens equation",
1/f = 1/o + 1/i
and one for linear magnification of a lens (image height/object height),
m=f/(f-o)
Then there's also the fact that combined power (inverse focal length) of stacked lenses is the sum of the individual powers.
Although these are strictly correct only for "thin" lenses, which the modern binocular certainly isn't, conceptually they are useful for figuring out how things generally work, with a little boldness, which is to say, no worries if it's not quite right!
By the third relation, the power of the objective is not changed by the motion of the focusing lens. Therefore, what is being changed is the effective location of the origin of focusing. Moving the focusing lens is equivalent to moving the entire objective back and forth. For various object distances, the image can be made to fall at the field stop of the eyepiece.
The variation in magnification then can be seen to result purely from the variation in the object distance, as described by the second equation.
The next step I think would be gravely major: get a copy of ZEMAX, get the precise optical layout, and go to town on a genuine ray trace.
To qualify my wisdom, I must admit to having taken optics as a sophomore in 1969, but had usually drank so much beer the night before that I was kind of in a daze during most of the classes. I actually absorbed the above information, Snell's law of refraction at a boundary, and the basic bit about thin film refraction and reflection (how coatings work) but buddy that's "IT". Just enough to make me a prime victim for consumer optics!
Ron
