In this article I will explain f-stops as used in photography, on my way to a brief sketch of the history of aperture control in SLR lenses. This is a backgrounder so that when I come to present you with some old lenses in future articles I don't need to explain each and every term. I won't go into much detail here, just the basics. Any good photography reference can help you further.
I also present my handy f-stop guide, in the hopes it is useful as a reference. As usual you can click through that image to get to a full-size download from Flickr.
The aperture is the opening in the lens through which light passes to get to the film or sensor. A diaphragm is used to open and close this hole. We are used to our SLR cameras having the diaphragm as part of the lens mechanism, but it is entirely possible to instead have it as part of the camera body. As SLRs have evolved, how we control the aperture has become more automated, to the point that we now take this function for granted. But it's worth giving a thought to the process, especially if you are interested in hunting out old lenses that might use a different mechanism from what you are used to. Some of these require a bit more work to use, but they are not terribly complicated.
I will start by discussing f-stops. Knowing how many stops there are between different f-numbers helps in setting exposure. I will remind you that the smallest numbers correspond to the largest f-stops, since when we say f/2.8 we are talking in terms of an inverse ratio, and really mean 1/2.8. That's what the slash in "f/2.8" is there to remind us of.
As the number gets higher the f-stop gets smaller, meaning the aperture is being made smaller by the lens diaphragm. f/32 is the smallest aperture you are likely to find on a lens, and practically speaking, image quality degrades long before that (due to an unavoidable physical reality called diffraction -- but that is another article).
Each stop specifies a doubling in light intensity, which is why it is such a handy measure. The f-number is related to this through the root of 2, approximately 1.41, which explains the rather unusual sequence of numbers we have become accustomed to. In my table I have rounded these off to two significant digits. (This introduces a lot of error in the smaller numbers but it's not of practical import.)
By the way, the "fastest" lens I own is f/1.2, but there are certainly lenses out there in the world faster than f/1. However, if you own one I doubt you need this chart!
In my next article I will discuss the development of aperture control mechanisms from completely manual to completely automatic systems.