Originally posted by wtf_cowboy
I see, I have much to learn. Math was never my strong suit anyway...
Here is the simple, basic equation:
SPEED = MONEY
The faster you want a lens to be, the more you pay for it. And the less you pay, the slower it will be, usually. A telextender / teleconverter / TC is a cheap way to get a longer lens, but the cost is speed.
Keep in mind that all telephoto lenses have a TC built into them. This "telephoto group" makes the lens physically shorter than its actual focal length. For instance, 100mm is about 4 inches. I have two 100mm lenses. The Meyer Trioplan 100/2.8 is a plain long lens, about 3 1/2 inches long. The Enna Sandmar 100/4.5 is a short telephoto, only 1 3/4 inches long. I suspect that internally it is a ~72/2.8 lens with a 1.4x TC optical group in back. When you add a TC to a lens, you are similarly 'shortening' the resultant lens. An actual 400mm long lens is over a foot long! A 2x TC on a short 200mm prime is half that length. But it is slow...
As mentioned above, changing sensor or film size does not change the focal length of a lens. A 100mm lens is still a 100mm lens whether it sits on a 4x5 view camera or a 110 Instamatic or anything in-between. It's just that smaller sensor or film frames see less of the projected image -- the area it sees is called the "field of view" (FOV). A 100mm lens on a full-frame camera has a wider FOV than the same lens on a crop-sensor camera like most dSLRs, but the optics remain the same.
Here's how this works. Cut out a picture from a magazine. Draw a rectangle on it that is 60x45mm - that's about the size of frame on many medium-format (MF) cameras. Inside that, draw a 36x24mm rectangle - that's the size of a full-frame (FF) 35mm camera frame. Now, inside that, draw a 24x18mm rectangle - that's the size of a 35mm half-frame (HF) or APS-C dSLR camera frame. And, just for LULZ, inside that you can draw a 18x12mm rectangle - that's the frame size of m4/3 (Panasonic, Olympus) cameras. In each case, THE PICTURE REMAINS THE SAME. The focal length and other optical characteristics remain the same. But smaller sensors see less of the picture, that's all.