# Why doesn't exposure change when changing focal length?

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?

It is because the aperture value of f/8.0 actually gives an aperture hole of f/8.0 over the entire focal length range, thereby opening up when the focal length gets larger, whereby the change in the aperture hole exactly balances out the change in wall area that is covered.

So at 18 mm focal length the aperture hole diameter is 18 mm / 8.0 = 2.3 mm, and 270 mm focal length the aperture hole diameter is 270 mm / 8.0 = 33.8 mm, so the aperture hole diameter grows a factor 15 in diameter, or factor of 225 in area, when the focal length narrows down the area on the wall with a factor 15 in both x and y direction, or factor 225 in area, whereby the total amount of light is the same over the focal length range.

The -0.7 change in exposure I saw is probably a result of poor lens design, so some light is lost at larger focal length.

• which is why apertures are usually written as f/8.0!
– ths
Jan 27, 2015 at 13:54
• Actually, the metering change probably has a lot more to do with the fact that the content of the scene changes significantly when you zoom from 18mm to 270mm. Even if you're using spot metering, your 18mm spot is 15X larger at 270mm, so you're only metering a part of it (less than 0.5% of the original spot). Jan 27, 2015 at 16:04
• Aperture should be in mm^2 Jan 27, 2015 at 16:50
• @AlecTeal In some sense it technically is. However, the f/scale is used more frequently because exposure is a more common concern, and here, the exact property in question is incredibly useful. Jan 27, 2015 at 18:25
• @mattdm that's not the point - you've given an area in a linear unit Jan 27, 2015 at 18:52