Leonard Shepherd
Forum Pro
I would be more than surprised if that were true.I think you will find that the 2x TCIII focuses faster and locks on easier than what you are experiencing with the 2x TCII version.
Neither converter plays any direct part in auto focusing and each stops a similar amount of light.
The light falling on the in camera AF detectors and the information sent to the focus motor in the lens does not change.
It follows there is no change likely to affect AF speed.
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Leonard Shepherd
Good photography is mainly about doing simple things well. The challenge is doing simple things well enough for good results.