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When that happens, though, the camera is using an erroneously shallow depth of focus figure for its calcuations. There would certainly be a slow-down of focusing at the very least because it will be trying to determine a higher degree of precision at a lower level of illumination that the system was designed for. If the lens starts out greatly defocused, it will probably do the in/out rack, fail to find the focus point because it's calculating too slowly, and give up.
OK, so lets say it's an f/4 lens instead of a 5.6 - would focus be significantly slower than it would be with the 2.8 lens the precision sensors were designed for? What about the case of, say, a 200 mm f/2.8 lens on a 1.4x TC? A Canon TC will report the combination as 280 mm f/4 and the camera will focus based on that full dof. A third party TC will report 200 mm f/2.8 but the camera will think there is 1 EV less light. Will it succesfully focus based on 1/3 dof of 200/2.8?
All this AF is new to me - I'm in the process of transitioning from FD to EOS on a budget, so I appreciate these opportunities to learn.