Way back I bought the non-USM version of the Canon 70–200mm f/2.8 over the then new f/4 IS model specifically so I could use it with a 2x teleconvertor to cheaply get the extra reach. Both because the lens quality meant it should work well with a teleconvertor (I think it does) and it would still be able to autofocus on my camera. And being a heavy lens I assumed I would mostly use it on a monopod, if not a tripod, anyway.
It might be that something went slightly awry with your explanation during the two quoted paragraphs?......(it may also be my reading of them and, if so, I appologise)
Bob
No, you are right and that did get rather garbled! Firstly I got confused with the teleconverter factor of 1.4x when obviously the lens in the example should be 320mm because of the 1.6x factor for Canon's APS-C sensors. And obviously you need to move backwards from a 5D with the same focal length lens to increase the ares being captured to take the same image. Which of course flips the depth of field effects from he way I described them. I even got it right for the second one but then changed it because it had to be the opposite of changing position, which it is but not in that reason. And to think I was trying to keep it simple without mention the compression of perspective too. Instead it is a total mess! I am very sorry about that.
Just so anyone reading does not get confused, here it is again hopefully described properly.
Assuming a shot taken at 200mm with a Canon 5D, there are three ways you can use a 7D to capture the same image area:
a) you take a shot in the same location using a 200mm lens then crop the 5D image,
b) you take a shot in the same location using a 320mm lens, or
c) you use the 200mm lens but move further back from the subject so the same area is covered in the 7D viewfinder.
However if you use the second method (b) then although the same image area will be covered they will not be identical. The depth of field is a factor of focus distance, aperture, and focal length. By increasing the focal length of a lens whilst keeping the other two the same you reduce the depth of field. Also longer lenses have a narrower angle of view, so whilst the subject will fill the frame on the 7D the same way it did on the 5D, the background will be more compressed. It will make it seem closer to the subject whilst losing background objects to the left and right of the subject. To be more technical, although perspective is only affected by the distance from the subject so does not actually change, but it is the smaller angle of view that is effectively cropping how much of the background is captured.
The third method (c) has the opposite effect. By increasing the focus distance in being farther from the subject, while keeping the focal length (and aperture) the same as the 5D shot, you increase the depth of field. And although you are using a lens of the same focal length, so it has the same angle of view as the 5D, the greater distance from the subject will widen the perspective. This will make the background appear to stretch farther back and capture more of what is to the left and right of the subject.
Only the first option (a) will produce two identical images, with the same background perspective, and the same depth of field.
This is why a 70–200mm lens is the same regardless of the size of the sensor in the camera, and why it should to be recorded that way. Because a 112–320mm lens will not give the same images on a 7D as a 70–200mm lens on a 5D. In identical shooting positions the 7D will have less depth of field and a more compressed background.
A crop factor is simply that, it relates to the amount of and image that has been effectively cropped from what would have been captured in a 35mm frame. It has does not have any relevance to the lens itself.
And to keep this to the topic, none of this applies to teleconverters as they do effectively change the focal length of the lens. So the 2x factor of a teleconverter on a 70–200mm lens will give the same image as using a 140–400mm lens all other things being the same.
I hope that is better. I have the Vertigo dolly zoom effect on a loop in my head trying to make sure I got it all straight this time!