Roger Cicala just posted a great article on TCs at http://www.lensrentals.com. In it, there's a link to a modest article about how auto-focus works and how lens aperture affects AF. Smaller effective apertures (i.e. at 420mm, you're at f/4, at 600mm you're at f/5.6, if you combined them with a tube you'd be at 840mm f/8) give the AF sensor less data to use, and therefore AF will work slower. At f/8, most bodies can't auto-focus.


Some TCs lie to the camera and pretend that they aren't in the path. As such, the camera may still AF when it otherwise wouldn't be able to AF, and may Af with faster motor commands than if the TC was recognized. However it may hunt more, and therefore the end AF result is the same or slower than if the TC had properly reported its presence.