Rik wrote:
"at exactly 1:1, changing the bellows extension only changes magnification, not focus!"
This sounds like an oxymoron.
Nonetheless it is correct, at least if you believe in calculus.
Assume thin lens model, 1/f = 1/o + 1/i, and start differentiating. What you will discover is that exactly at 1:1, the derivative of i+o with respect to i is zero, while the derivative of m=i/o is not.
In other words, the image of the subject remains stubbornly focused on the sensor, even though its size is changing!
You can easily set up a physical experiment to confirm this result. Simply place a lens between subject and sensor and adjust the distances such that the magnification is exactly 1:1 and the subject is focused. Then move the lens back and forth. What you will see is that you can move the lens quite a large distance and hardly change the focus at all.
People who spent a lot of time in darkrooms working with enlargers around 1:1 quickly discovered the practical implications of this surprising result. When you're at 1:1, and you turn the "focus" knob on the enlarger, the image doesn't change focus, it only changes size. To focus, one has to leave the focus knob alone and move the whole enlarger head up and down.
Modern macro lenses avoid this problem by changing focal length, not by just extending a fixed focal length lens. The result is that you can still crisply focus a typical macro lens at 1:1 just by turning the magnification/focus ring, while leaving the camera and subject in fixed positions. If the lens focused entirely by extension, this would not work.
--Rik
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