BlahBlah, I think I know what you're getting at here, and I have kind of an answer, but not a very good one because I don't really understand it either.
Let's take a 70-200mm f/2.8 constant max aperture lens. Obviously there is a single diaphragm mechanism within this lens; it is a fixed maximum size, no matter what the zoom level. But an f/2.8 aperture at 70mm would be 25mm in diameter, while an f/2.8 aperture at 200mm would be 71mm in diameter. So if the physical size of the diaphragm mechanism is all that matters, this lens should be a variable-aperture lens, approximately f/1.0 at 70mm, and f/2.8 at 200mm. But we know this is not the case. Now what is the reason for this?
It is because the aperture that matters is the "apparent aperture", not the real, physical aperture. How the apparent aperture is calculated is beyond my knowledge and probably requires a lot of arcane optical equations. There is part of an answer here:
http://photo.net/bboard/q-and-a-fetch-msg?topic_id=23&msg_id=0000Wf
along with a recommendation for a detailed optics book.
To expand on this line of thought, is the light on the sensor the same, at the same apeture regardless of focal length, or does it change?
i.e. if I have a 17-200mm f/2.8, and I point it at a graycard at 17mm apeture, and proper exposure is 1/100th, then I zoom it in to 200mm, is the proper exposure for 18% gray still going to be 1/100th, or will it change with focal length?
The aperture value is supposed to be constant for level of light, across all focal lengths (although the physical aperture size changes with the focal length).
50mm f/2.0 = 25mm aperture
50mm f/4.0 = 12.5mm aperture (1/4 the light of 50/2.0 => 4x shutter speed to keep same exposure)
100mm f/4.0 = 25mm aperture (same size as 50/2.0, but same light as 50/4.0)
50mm f/2.0 = 50mm aperture (same light as 50/1.0)
So, to answer your second question, yes, your exposure will stay the same at 17mm f/2.8 as at 200mm f/2.8. This is the great thing about constant maximum aperture lenses. Variable maximum aperture lenses are hard to use in manual mode because you constantly have to adjust when you zoom (if you are at or near maximum apertures, that is).
no, you've got that wrong. for equivalence purposes, a 50 f/1.4 on full frame would be roughly equivalent to a 31 f/0.9 on APS-C. for equivalence you need the same angle of view (so divide 50 by the 1.6 crop factor to get 31.25) and the same absolute aperture (50/1.4 = ~35.7 = 31.25/0.875).
I think he meant a 50/1.4 lens becomes the equivalent of an 85/1.8 lens on a crop body. I know this is true from a DOF point of view, but when it comes to exposure, I'm not so sure (and would welcome a lesson on this). It seems to me that, when using a 50/1.4 on a crop body, you are only using the middle part of the image circle, which will be, on average, brighter than the entire image circle, i.e. what is used on full-frame. Also, it seems that I have never noticed a difference between my crop an full-frame bodies when it came time to set exposure. I can set my 5D and my 20D to the same exposure settings (ISO, aperture, shutter speed) and get a photo with roughly the same apparent brightness. Of course this could easily be something that the camera makers compensate for by making the ISO equivalents different for crop and full-frame bodies, but I have no idea whether this is the case. I would love to hear more info on this.