The aperture numbers on a lens can be quite confusing and seem rather random at first glance, but there is an explanation as to why this is the case. But let me warn you right away, it has something to do with math.
Lens with aperture ring: f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22
This is my old 28mm lens. A wide-angle lens with an initial aperture of 1:2.8, which means that the lens has a maximum aperture of 1:2.8, which is the maximum amount of light it lets in. For a fixed focal length, that’s not exactly exhilarating, but that’s all I could afford at the time and apart from that, an initial aperture of 1:2.8 isn’t the worst thing either.
Before I get to the rest of the figures, let me quickly clarify how the value of 2.8 comes about.
Calculating the initial aperture of a lens
The initial aperture or speed of a lens is calculated from the focal length (e.g. 28mm here) divided by the diameter of the light transmission (the maximum aperture diameter when looking into the front of the lens):
Focal length / diameter = aperture value
28mm / 10mm = 2.8
The remaining values, which are internationally uniform, are derived from the initial aperture. Each step halves or doubles the amount of light that is transmitted. This is calculated as follows:
Each whole stop is a f-number times or by 2½ = √2 (n = 1 → 2½ ≈ 1.41).
Example: Aperture 2.8 * 1.41 ≈ Aperture 4. Aperture 4 is one stop smaller than 2.8.
It doesn’t get much more mathematical now, because in everyday use nobody has to calculate such values, and why should they, since they are already printed on the lens.
But it is still interesting, because it shows why it is hardly possible to build a small, compact telephoto lens with a high speed. The longer a lens is, i.e. the greater the focal length, the larger the initial aperture must be in order for it to be fast. At the same time, however, this means that the diameter increases, more lenses have to be used and you end up carrying around a few kilograms more.
