Someone asked me today why the aperture number on a camera lens gets bigger as the aperture size gets smaller. Some of you no doubt already know why. But for anyone who’s ever wondered the same thing (as I did for many years when I first started using an SLR camera back in the days of film), let me explain.

The aperture is the number you see written as f/2.8 or f/8 or f/22. It describes the size of the opening inside the lens through which the light passes. There’s an iris diaphragm which can open and close to let in different amounts of light. This is useful to control for two reasons:

1. The wider the aperture, the more light you let in to expose your film or digital camera sensor. So in dim light, it’s often better to use a wider aperture. Conversely, in bright sunlight, you can use a narrower aperture to get the same exposure at the same shutter speed.
2. The wider your aperture the narrower your depth of field. This is a measure of the range of distances from your camera within which objects will be in focus. If your depth of field is large, lots of stuff will tend to be in focus, while if it’s narrow, only objects a precise distance from the camera will be in focus and everything else will be blurry. This might sound bad, but in many cases you want a shallow depth of field, such as to make a flattering portrait of someone – it looks better if things in the background are blurry so as not to distract your eye from the subject of the photo. So a portrait photographer will tend to use a wide aperture. On the other hand, a large depth of field is good for landscape photography, where you want everything in focus, so a landscape photographer would tend to use a narrow aperture.

The interesting thing is that to a beginner in photography the numbers of the apertures might seem to be backwards. f/2.8 is a wide aperture, letting in a lot of light, while f/22 is a narrow one, letting in relatively little light. Why is this?

The answer lies in the mysterious “f/” that precedes the aperture number. Although people usually refer to the apertures as “eff two point eight” or “eff twenty-two”, the slash symbol is actually a division sign. The f is the symbol for the focal length of the lens. If you have a standard 50mm lens, the aperture f/2.8 is 50/2.8 = 17.9mm wide. And the aperture f/22 is 50/22 = 2.3mm wide. So you see f/2.8 is quite a bit wider than f/22.

The interesting thing is that the apertures are defined in terms of the focal length of the lens. If you have a 200mm telephoto lens, then f/2.8 is 200/2.8 = 71mm wide and f/22 is 200/22 = 9.1mm wide. So in a physical sense the “same” aperture numbers are actually physically bigger on a longer lens, and physically smaller on a shorter lens.

So you might expect f/2.8 on a 200mm lens to let in more light than f/2.8 on a 50mm lens. But this isn’t the case. The 200mm lens has a field of view 4 times smaller than the 50mm lens – in other words it magnifies things by 4 times compared to the 50mm lens. After all, this is why you use a telephoto lens, to make things look bigger and closer! But the field of view being 4 times smaller means that the lens is gathering 16 times less light (it’s 4 times smaller in the horizontal direction and 4 times smaller in the vertical direction, so it sees an area 16 times smaller). But then the aperture f/2.8 on the 200mm lens is 4 times bigger than the aperture f/2.8 on the 50mm lens, so it gathers 16 times as much light (again, 4 times bigger horizontally, multiplied by 4 times bigger vertically = 16 times the area). So the physically larger aperture exactly cancels the fact that the lens is only seeing a smaller area of the image. The result is that aperture f/2.8 on a given lens gathers exactly the same amount of light as aperture f/2.8 on any other lens! (Assuming an evenly lit subject.)

So that’s why lens apertures are specified in this way. Rather than say the aperture is 5mm, or 13mm, or whatever, it’s much more convenient for figuring your exposure to express the aperture as a fraction of the focal length of the lens. Which explains the odd-looking “f/” notation, and why the numbers get bigger as the aperture gets smaller.

This entry was posted on Thursday, 11 March, 2010 at 22:07 and is filed under Photography, Science. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.