With a Canon 550D camera and a Tamron 18-270 mm zoom lens, I tried to fix shutter time, aperture (f/8.0 to cover all zoom range), and ISO, so the exposure meter read 0.0 with 18 mm focal length and while focusing on a uniform white wall. Then I changed to 270 mm focal length, but the exposure reading did not change significantly (only to -0.7).
However, I had expected exposure to change, since only (18 mm / 270 mm) ** 2 = 1/225 of the wall is now covered in compare the coverage when focal length is 18 mm, thus only 1/225 of the light gets to the sensor after the change of focal length.
Why does exposure not change when narrowing the field of view with change of focal length?