The "aperture" is the opening in your camera's lens that allows light to travel through it. The aperture controls two fundamental things about this light: (i) how much of it enters (per unit time), and (ii) how parallel (or, “collimated”) the rays are. The larger the aperture, the more light enters and the less collimated (more cone-like) it is; the smaller the aperture, the less light enters and the more collimated (straight line-like) it is. The quantity of light entering is a primary determinant of exposure, and the degree of collimation affects depth-of-field, both of which are topics for other articles.
The size of the aperture is mechanically controlled by the blades of the "iris" (also known as the "diaphragm") inside the lens; you can set this manually, or allow the camera to set it for you. The figure at left shows the operation of a 9-bladed diaphragm.
More specifically, the quantity of light entering the lens is directly proportional to the area of the aperture: if the area doubles, the quantity of light doubles; if it halves, the quantity of light halves, too. In photography, the word "aperture" is typically used as a shorthand for the "area of the aperture." This is how I'll use it from now on.
Photographers measure light in buckets called “stops.” It’s important to realize that a stop is not a fixed quantity, like a litre, but rather a ratio of quantities. If the quantity of light entering the lens is increased from x to 2x, it has been increased by one stop. If it’s subsequently increased to 4x, it has again been increased by one stop. A stop up or down refers to doubling or halving, respectively, the quantity of light entering the lens, and therefore to doubling, or halving, the aperture.
In photography, aperture is not measured absolutely (in square millimetres, for example.) Instead, it is measured relatively, specifically with respect to the focal length of the lens. The f-number, N (also called f-stop, focal ratio, f-ratio, or relative aperture) describes the ratio of the focal length of the lens, f, to the diameter of the aperture, d.
Because the equation at right describes a reciprocal relationship, the smaller the f-number, the larger the aperture. When the aperture and focal length are equal, the aperture is described as f/1.
If we assume that the opening is circular, its area will be proportional to the square of its diameter. Therefore, in order to reduce aperture by one half from f/1 (that is decrease exposure by one stop), we must decrease d by a factor of 1/√2; this gives us f/1.4. To reduce aperture again by one half (decrease exposure by another stop), we must decrease d again by a factor of 1/√2; etc. This gives us the following geometric progression of f-numbers, where f is an arbitrary, constant focal length:
If you don’t follow the math, don’t worry. Just remember the fact that each of these values differ by one stop. That is, an aperture of f/2 is double an aperture of f/2.8 and admits double the light; f/2.8 is double f/4; etc.
Therefore, absolute measures of the aperture and focal length are irrelevant for determining exposure. The photographer can always rely on the fact that an aperture of f/2 lets in twice as much light as one of f/2.8 and four times as much as one of f/4, regardless of the lens. This is the huge advantage to specifying apertures relatively; it makes it trivial for the photographer to switch between lenses of different focal lengths.
The diagram at left shows the relative sizes of a series of apertures. The human eye is not good at estimating area, so it's difficult to see that the aperture f/1.4 is in fact double the size of f/2.
f-Numbers are typically marked on the barrel of a lens. The figure at right shows a Nikkor 35mm f/2 lens. The f-number scale is clearly shown (in duplicate) at the bottom of the barrel. For this lens, it ranges from f/2 to f/22 in full stops. The position of the white dot on this scale indicates that the lens is currently set to f/11. The thick white strip above the dot indicates the focal distance, which in this case is just shy of 5 ft, or about 1.5 m. On either side of this strip is a series of three lines connected to the numbers 11, 16, and 22. This is the depth-of-field indicator. What it means in this case is that at a focal distance of 1.5 m and an aperture of f/11, objects ranging in distance from 1 to just over 2 m will be rendered in acceptable focus. (Depth-of-field is a lot more complicated than this; I'll cover it in detail in a forthcoming article.)