f/stops in Photography

When you take a photograph, there are mainly two elements controlling how much light is sent to the film or digital sensor. One is the shutter speed, which is simply how long the sensor or film is exposed to the incoming light, and the other is the aperture or "f/stop." The f/stop is a measure of the lens opening itself. The larger the opening, the more light comes in (and the faster the shutter can be). The f/stop is actually a ratio of the focal length of the lens (the distance between the lens and the film or sensor) to the diameter of the lens opening. So the larger the opening, the smaller the f/stop. Some of the fancier cameras, like SLRs, let you choose these settings yourself if you wish. Even the pocket digital cameras are using these settings, they are just done automatically for you. In fact, many photo viewing software applications can tell you what shutter speed and f/stop the camera used when it took the photo. 

Each time you take a photo, you or your camera must make a choice between a larger opening and a shorter shutter time or a smaller opening and a longer shutter time. Either way you can get enough light for a good picture. So what is the difference? If you use a long shutter time, a moving object will look blurry. If you use a large opening, the depth that can remain in focus is much shorter. For instance, the first photo of the watering can uses an f/stop of 5.6. The chair behind it is quite fuzzy. The second photo, with an f/stop of 16, has the chair in sharper focus.

If you look at the available f/stop numbers for a particular lens, you might find the numbers mysterious. You will often see a progression like 2, 2.8, 4, 5.6, 8, 11. They almost seem random. In fact, there is logic to it! These are the values of the f/stop ratio where the lens opening doubles in AREA (not diameter!) each time. This lets in twice as much light. Remember that the area of a circle is based on the square of the radius, so if you want the area to double, you can't double the radius. In fact, you would need to multiply the radius (or diameter) by the square root of two. And that multiple, root 2, is exactly where the progression of f/stop numbers comes from. 

Here are some links if you want to learn more:

Wikipedia entry for f/stop numbers

A very detailed (and good) explanation of f/stops and the math involved