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.


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.