t4i and 1.4 extender

[neuroanatomist]

The camera isn't necessarily the issue. It's more the lens, and the max aperture of the combo. A 1.4x TC costs 1-stop of light - an f/2.8 lens becomes f/4, an f/4 lens becomes f/5.6, an f/5.6 lens becomes f/8. A 2x TC costs 2-stops - an f/2.8 lens becomes f/5.6, f/4 becomes f/8, etc.

Your camera is needs an f/5.6 lens or faster for phase AF (viewfinder) to work (live view works to f/11 at least). The 1D X and 5DIII can AF with an f/8 combo, although only with the central point with 4 expansion points.

So, you can use a 1.4x TC with an f/2.8 or f/4 lens on your camera and still have AF. Note that I'm referring to max apertures, it doesn't matter what aperture you select for the shot (AF is always done with the lens wide open). The 300/4L + 1.4x (II or III) gives a very good 420mm f/5.6. The 400/5.6 + 1.4x is an optically decent 560mm f/8, which won't AF on your camera (it will on the 1D X/5DIII). You get better results whenever using a TC with a non-supertele if you stop down from max (300/4L + 1.4x shot at f/8).

The other issue is that with the Canon TCs only certain lenses are physically compatible. The TCs have a protruding front element, and the lens needs space for that. Only a subset of L-series lenses work with Canon TCs - zooms starting at 70mm and longer (except the 70-300L, which is technically partially compatible but don't go there), and primes starting at 135mm.

If you use a 3rd party TC (e.g., Kenko), they are physically compatible with any EF or EF-S lens, but the optical results may not be worthwhile (although the Kenko 1.4x DGX Pro with the 100L macro, results are decent; with the 70-300L, too, but that combo won't AF on your body).

Hope that helps...