F/stop Isn't Really an "F" Word
Understanding what f/stops are is fundamental to understanding the theory behind photography, but this is also one of the most confusing things for beginners to get their arms around.
The purpose of a camera lens is to focus the image on the film (or digital sensor these days). In order to do this of course, it has a hole in it. Not much of a revelation, I know, but the important point is that the diameter of this hole has a lot to do with f/stops.
If you take the diameter of this hole and divide it by the focal length of the lens, you get the f/stop number. For example, a 100mm focal length lens with an opening that is 25mm across would be an f/4 aperture. Similarly, a 200mm focal length with a 50mm opening would also be an f/4. As you can see, the f/stop is not a true measure of the size of the opening, but is in fact a ratio. This ratio is generally expressed as a fraction in the form of one over some number. An aperture of f/4 can therefore be considered an abbreviation of "f 1/4." An interesting consequence of this ratio is that as you increase the size of the opening, the fraction gets smaller, whereas smaller openings will give you smaller f/stops. This does seem somewhat backwards, I'll admit, but thats the way it works.
So, moving along with this confusing aperture bit, what's with that crazy series of numbers that's used to mark the aperture scale on lenses? For your reference, the mystical series goes like this:
1.4 2 2.8 4 5.6 8 11 16 22 32
You may already know that a stop is defined as being the doubling or halving of any value. However, the standard series of f/stop numbers doesn't seem to follow that progression, so what gives? If you'll bear with me while I do a bit of math, hopefully I can answer that question.
The amount of light that gets through a lens is proportional to the area of the opening, much as the flow of water into our bucket depends on the size of the opening in our spigot. The aperture (f/stop) is a ratio that depends on the diameter, though, not the area of our lens opening. Here's where we get to pull out our math text books to recall that the area of a circle is given by the formula:
area = (pi) x (radius) 2
And of course the radius is half the diameter. So, if we double the diameter of a circle (which doubles the radius at the same time), we end up with an area that is four times the original area (two squared). If you double the area, though, the diameter only increases by the square root of two. The square root of two just happens to be the magical value of about 1.4. So, the standard f/stop series actually does represent the doubling and halving of something, but that something is the area of the opening, not the diameter. Why they marked things this way, who knows. After a while though, you'll find that you've learned these numbers, and until then, just be thankful that Nikon was nice enough to print them on all your lenses.
One last thing that is helpful to know about apertures is that the term "stopping down" refers to making the hole smaller, which as you now know, results in bigger numbers (f/11 is a smaller hole than f/4 for instance). "Opening up" then means making the hole bigger, which of course gives you smaller f/stop numbers (f/2.8 is a bigger hole than f/16).
Yes, I know it all seems rather backwards, but don't worry, you'll learn it. You'll have to, eventually.