## Saturday, August 21, 2010

### Effective Aperture

Ever wondered what the numbers on an SLR camera's lens meant? My Nikon D80 has an 18-135mm 3.5-5.6 zoom lens. At the shortest focal length - 18mm - the maximum effective aperture is 3.5 f/stops; at the longest focal length - 135mm - the maximum effective aperture is 5.6 f/stops. Why the difference? And what does it mean?

A stop (note: a stop is not an f/stop) is an important measure in photography: it describes how much light reaches the device inside the camera that captures the image. Increasing the light by 1 stop is a two-fold increase in light; decreasing by 1 stop is a halving of light. Modern cameras control the amount of exposure by varying the shutter speed and/or the aperture size.

Ignoring shutter speed for now, we look at aperture size for the rest of the post. The diameter (and radius) of a circle are functions of the circle's area. Double the area (increase aperture by 1 stop) and the diameter goes up by SQRT(2). Halve the area and it comes down by 1/SQRT(2), which is the inverse function. Taking the first 10 stops (starting at 0 not just because I like programming), let's see what the areas and diameters (unitless ratios of the starting values) would be.

Stop=>Area=>Diameter
0=>1=>1
1=>2=>1.4
2=>4=>2
3=>8=>3.5
4=>16=>4
5=>32=>5.6
6=>64=>8
7=>128=>11
8=>256=>16
9=>512=>22
10=>1024=>32

Does the sequence on the right look familiar? Notice that it has both 3.5 and 5.6 in it: both numbers are stamped on the lens. These numbers are f/stops.

Here's a definition: the f/stop is the ratio between the diameter of the aperture and the focal length of the lens.

Starting at the longest focal length for this lens - 135mm - we discover the maximum effective aperture is f/5.6. As you know, things that are further away appear smaller, so to maintain a constant effective aperture as while shortening the focal length, the lens must shrink the real aperture. At the shortest focal length - 18mm - the same effective aperture of f/5.6 has a much smaller real aperture than at the longest focal length (18/135 to be precise) yet it's letting in exactly the same amount of light. At this focal length, this lens (but not all lenses) will allow us a bigger effective aperture of f/3.5.

The average zoom lens (with a range of focal lengths) will also have a range of maximum effective apertures. A 400mm lens with a f/2.8 aperture will be very wide (and heavy) while a shorter lens with the same aperture might fit (figuratively) in your pocket.