Originally posted by pathdoc Would you be willing to explain this in a few short sentences?
The amount of light captured by the lens is proportional to the physical area of lens' aperture which is proportional to the square of the focal length. But then, the amount of light arriving on each pixel of the sensor is decreased by the square of the focal length because each unit of captured light is spread more.
For images of illuminated areas, the increased magnification effect of a longer focal length exactly cancels the increased light gathering effect of a longer focal length. Thus, a uniform wall looks just as bright in an image taken with a 12 mm lens at f/8 as it does with a 1200mm lens at f/8. Think of it this way: the 1200 mm lens gathers 10,000X more light per unit area of wall but sees 1/10,000 as much wall as the 12 mm lens. That's why a standalone light meter can work - giving an accurate exposure that works regardless of the focal length of the lens.
For images of a point light source, all that matters is the light gathering effect. Magnifying a true point of light with a longer lens still produces just a point of light. But the larger focal length lens will have gathered more light. A 1200mm lens at f/8 gathers 10,000X more light from each star than does a 12 mm lens at f/8. This is why larger telescopes can see fainter stars even if the larger telescope has the same relative aperture as a smaller one.