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will a sigma 50-500 lens auto focus on a canon 40d with a tele converter on?


Autofocus relies on a certain amount of light entering the camera, so it can detect what the image is and if it's focussed correctly.
It's just like when it's getting dark, all cameras have trouble focussing, and unless they have a visible/IR illuminator to help, they will "hunt".
Regardless of camera manufacturer, teleconverters reduce the light getting though to the sensor.

Sigma only say that teleconverters work with their f2.8 or wider lenses.  Basically it's because if the maximum aperture is smaller than this, it may not get enough light to focus properly.
Obviously if you're in very bright conditions, it won't be so much of a problem.
At 500mm though, this lens is at something like f6.3.

Some people find focussing works on these lenses but only in very bright conditions.  I wouldn't rely on it though.

Re-design7 years ago
Go to this Canon forum and ask your question there.  I don't have either piece of equipment but I'll bet you get several creditable answers quickly there.