| 1 | ||
| 1 | * 1.4 = | 1.4 |
| 1.4 | * 1.4 = | 2 |
| 2 | * 1.4 = | 2.8 |
| 2.8 | * 1.4 = | 4 |
| 4 | * 1.4 = | 5.6 |
| 5.6 | * 1.4 = | 8 |
| 8 | * 1.4 = | 11 |
| 11 | * 1.4 = | 16 |
| 16 | * 1.4 = | 22 |
| 22 | * 1.4 = | 32 |
Did you ever ask yourself why the shutter speed numbers make sense and the aperture numbers don’t? Did you ever try to get a good answer from the photography experts and they didn’t know either? Well put on your thinking caps, remember back to high school geometry, and get ready.
The standard shutter speed series goes like this: 1 sec, 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000, etc… These numbers make sense. Each shutter speed is twice as fast as the one before it (OK, a couple of these are fudged to make them easier to use). And each one will let pass half as much light as the one before it. So much for shutter speeds. But the aperture series is strange: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, etc… They’re all related by a factor of 1.4, not 2. Why?
What does f -stop even mean? Remember that we measure light in units called stops. A change of one stop of light means that we have either twice as much or half as much light. It doesn’t matter if we are talking about apertures or shutter speeds, a stop is a stop.
An f -stop is defined as ratio of the focal length of the lens to the diameter of the lens:
| f -stop = | focal length of the lens |
| diameter of the lens |
OR
| diameter = | focal length of the lens |
| f -stop |
So if we have a lens with a focal length of 200 mm and the diameter of the front element is 50 mm, the maximum aperture or f -stop is:
| f -stop = | 200mm | = f 4 |
| 50mm |
OR
| diameter = | 200mm | = 50mm |
| f 4 |
The actual series of numbers comes from high school geometry. The area of a circle (the aperture is a circle) is related to the numerical constant π (pronounced “pie”, π = 3.14) and its diameter:
Area of a circle = 1/4 * π * [diameter] 2
Since a stop is twice as much light, each succeeding aperture has to have twice the area in order to let in twice as much light. So a circle with twice the area is:
2 * Area = 2 * 1/4 * π * [diameter] 2
Taking the factor of 2 inside the square, gives:
2 * Area = 1/4 * π * [(square root of 2) * diameter] 2
The square root of 2 is 1.414, which is plenty close to 1.4. What all this means is that in order to let in twice as much light, each aperture has to have a diameter that is 1.4 times bigger than the previous aperture.
The series starts with 1. The next aperture would be 1 * 1.4, which is 1.4. The next aperture would be 1.4 * 1.4, which is 2, and so on, as shown in chart 2.
The best part of all this is that you don’t have to remember it. The camera designers did all the work so you can simply count stops. If you open the aperture by one stop, just compensate by adjusting the shutter speed one stop faster to get the same exposure. It doesn’t matter where you start, because a stop is a stop. Simple.