One for the gurus or, for anyone who has a better understanding of optics and optical design than I (which I suspect is most of you!). A purely hypothetical question but one I find intriguing: A 400mm f/2.8 lens attached to a 1.4 teleconverter becomes, in effect a 560mm f/4 lens. If it were possible, using an APSC sized sensor, to add a `speed booster' would the resulting combination become, in effect, a 560mm f/2.8 set up? And, if it can be, or has been done, what would the I.Q. be like?