I'm trying to wrap my head around the math/physics of how illuminance on the film/sensor plane remains equal for a given f-number regardless of the focal length of the lens. Since a longer lens will have a larger entrance pupil at a given f-stop than a shorter lens at the same f-stop, how can the light falling on the film/sensor be equivalent?
Empirically, I know this to be true. Say I take an incident meter reading (not reflected/TTL) off my subject, and get f/5.6 at 1/100s, I'll get proper exposure at the point at which i took the meter reading with that setting whether I use a 50mm lens or a 200mm lens (obviously composition will be different).
Wikipedia's f-number article reads:
A 100 mm focal length f/4 lens has an entrance pupil diameter of 25 mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of 50 mm. The 200 mm lens's entrance pupil has four times the area of the 100 mm lens's entrance pupil, and thus collects four times as much light from each object in the lens's field of view. But compared to the 100 mm lens, the 200 mm lens projects an image of each object twice as high and twice as wide, covering four times the area, and so both lenses produce the same illuminance at the focal plane when imaging a scene of a given luminance.
I'm not sure I agree with the explanation on wikipedia. The film/sensor doesn't care how big the image is that falls outside the bounds of the sensor; the film/sensor "sees" what it sees, and that's it.