Photography

Exposure value

A camera's exposure value, both for film and digital, relates to the amount of light entering the camera, and is determined by a)aperture and b)shutter speed. For film there's also a sensitivity factor (ISO number), but that does determine the amount of light required by the film, not the amount of light entering the camera.

Aperture

Aperture is indicated by a number related to the diameter of the aperture. I have to say “related to” because it's not the diameter directly, rather a number inversely proportional to it. It's expressed as $$ f:n $$ where $f:$ means “focal length divided by”, and $n$ is the number indicating the diameter. $f:2$, for instance, means that the diameter is the focal distance of the lens, $f$, divided by 2. So for a 50mm lens the aperture diameter will be 25mm. The important thing here, and something which may confuse a beginning photographer, is that the aperture number is in the denominator, which means that a higher number will result in a smaller aperture. So, for instance $f:2$ is a wider aperture than $f:4$.
What complicates things even more is that the amount of light depends on the aperture area, not its diameter. Since the area is proportional to the diameter squared, doubling the diameter will result in 4 times as much light. For instance $f:2$ gives you 4 times as much light as $f:4$; if you want twice as much light your diameter has to go up by a factor $\sqrt{2}$, or about 1.4. That explains the weird numbers in the column headers of the table below: each number is about 1.4 times the previous one.

Every doubling of the amount of light is called “a stop”, and in the table each column you go left or right is 1 stop. For instance $f:2$ is 2 stops more than $f:4$. Likewise, $f:22$ is 3 stops less than $f:8$.

Shutter speed

Shutter speed is easier to understand: if you expose the film or digital sensor only half as long it receives only half the amount of light. Again doubling the shutter speed agrees with one stop. In the table you go one stop up (or down) by moving one row up (or down).

Exposure values

So, both aperture and shutter speed can be used to move one stop up or down, and certain changes will cancel each other. For instance changing your aperture from $f:8$ to $f:5.6$ (one step up) will be cancelled if you also decrease you shutter speed from 1/125" to 1/250" (one step down). To find the relationship between two aperture/speed combinations the concept of “exposure value” was introduced. Each aperture/speed combination has its exposure value, and by comparing exposure values you can tell how many stops difference there is between the two. Since the exposure value scale is a relative one it doesn't really matter where the reference lies. The value $f:1$ at 1" was chosen as exposure value 0. (It's worth noting that $f:1$ is exceptional, and such lenses are prohibitively expensive.)

The table gives the exposure value for different aperture/speed combination. On the diagonals from bottom left to top right you'll see equal exposure values. That's because a one stop lower aperture is compensated by a one stop higher speed.