I have a theoretical question for any of you with a working knowledge of lenses/optics.
If an extender works by taking the central part of a lens's image circle and enlarges it to cover the whole sensor(thus magnifying and reducing brightness), shouldn't it be possible to create an adapter for crop sensor cameras that uses the entire image circle of a full-frame lens and reduces it to the size of the cropped sensor to gain the full angle of view? Would the resulting smaller light circle also be brighter since it's focused onto a smaller area?
Yes, it's technically possible. But Kodak owns all of the patents, so nobody's going to make one. As well, there's no "universal" adapter possible; they'd need to make different versions for different exit pupil locations.
And one last thing: because of physical limitations, f/2.8 is probably the brightest one of these adapters can do. Possibly f/2.0.
As an aside; that's exactly how Olympus makes their 35-100 f/2.0 lens. It's optically a 70-200 f/2.8 with a .5x converter built-in. In theory, it should be a 35-100 f/1.4 -- it's certainly as big, heavy and as expensive as one.