Originally posted by normhead I do my own comparisons, I was just wondering, mathematically , how bad is it?
You can only raytrace real lens and tc combinations. There is no general rule applicable. Tcs come in very different varieties, some good, some bad, some rubbish. Some tcs are designed to match particular lenses. In these (rare) cases, the tc designer took into his calculation the design of the lens. These combos are usually quite good. Nevertheless, sometimes a lens and a tc match astonishingly well - just by mere coincidence, I think.
I give you an example: The old T6-2X Pentax 2x tc is mediocre at best. But on the quite as old K 300/4 it was surprisingly good, even better than the more modern Kenko 7-element tc, which worked very visibly better with almost any other lens.
I currently own 8 tcs (the 2 pairs by Pentax - the L's and S's, and the 1.7x AFA, the said Kenko KA modell and the pair of Sigma's matched tcs). Each one works best with certain lenses, but there are also inherent quality differences. For example those tcs which have a very long optical path and a protruding "nose" in general provide much sharper images and negligible loss of IQ - but they can only be used with select lenses, for plain mechanical reasons. So there is a place for the usual shorter tcs, as well, because they will simply fit almost any lens.
Then tcs are very dependent on the lens you use it with. The more parallel the rays coming from the rear lens, the better the tc will work. The misuse of tcs behind wide angle lenses or short fl zooms, will always lead to a regrettable loss of IQ.
But these really very general rules, are not based on maths, but on a mixture of physics and ofcourse simple experience and trials and errors. If you look over the shoulder of a lens designer, you will see, that today he will use software (Zemax, Oslo, whatever) to calculate the lens design. But this is only the first step. With the basic design on the screen, he will use his experience to optimize the design, by changing certain parameters (lens spacing or distribution of different lens curvatures to other elements or changing the glass type), just because "he knows", how these changes will influence the outcome. Lens design is still an empirical science, despite a lot of calculations.
So, yes, do your tests and tell about your findings - but don't get lost in mathematical trials.
Ben