The f-numbers on a lens indicate the minimum and maximum aperture sizes.
Photography combines visual art with science. A lot of the science of photography takes place during the exposure of an image. Part of the science used involves the f-number. The f-number isn't directly part of the camera, but a setting used on a lens to assist in exposure. The f-number system remains constant regardless of the lens or camera used.
The Camera Aperture
Camera lenses contain a diaphragm that opens and closes called an aperture. The aperture regulates the amount of light that enters the camera and reaches the film or digital sensor. The f-number or f-stop means the actual size of the opening used during the exposure process. The majority of people use the terms interchangeably, but in actuality they're not interchangeable. The aperture is the hole that opens and closes in the diaphragm itself, while the f-number equals the size of the aperture's opening.
The F-Scale
If you look around the barrel of a 35 mm lens, there's a scale that represents the minimum and maximum f-numbers for the lens. For example, a 100 mm lens might have a minimum f-number of f/4.0 and a maximum f-number of f/32. Based on that information the f-number sequence on the scale would appear as 4.0, 5.6, 8, 11, 16, 22 and 32. How does each f-number get calculated? The answer lies in the use of the number two.
Square Root of 2
The f-number scale is based on the square root of the number two or 1.41. At any given f-number the previous f-number on the scale allows in twice as much light as the given f-number, while the next f-number on the scale allows in half as much light as the given f-number. For example, if an aperture is set to f/5.6, a certain amount of light enters the camera. If you change the f-number to f/4.0, the aperture size is bigger and the camera now receives twice as much light then at f/5.6 (5.6 / 1.41 = 3.97 rounded up to 4.0). If you change the f-number to f/8.0, the aperture size is now smaller and the camera receives half as much light as it did at f/5.6 (5.6 x 1.41 = 7.89 rounded up to 8.0).
In Use
Although the math behind the f-number can get complicated, in use you must remember two basic rules. The first rule is smaller f-numbers mean a larger aperture size, while larger f-numbers mean a smaller aperture size. The second rule to remember is when moving from one f-number to the next lowest f-number, you'll let in twice as much light as before, and when moving from one f-number to the next highest f-number you'll let in half as much light as before.
Tags: much light, aperture size, f-number scale, given f-number, half much, half much light