### F-ing F-stops

#### by F.

Photography is pretty simple: you expose a light-sensitive piece of material to light directed from a lens and the light makes an impression on the material. The end. Whether you have a digital SLR or a pinhole camera or a daguerreotype-maker , the principle is the same. And if you exclude the light sensitive material but keep the rest of this apparatus, you get a camera obscura: a camera without film.

But then the complications start. ISO film speed. Focal length. Shutter speed. Light metering. Focusing. Flash. And my personal bete noire, the f-stop or, as I like to think of it, f-hole.

My understanding of the f-stop has always been blurry. In the old days, there was an aperture ring on the SLR and you would “stop down” the aperture. Or the lens. Or something. My vague understanding of this didn’t prevent me from taking good pictures and get A’s in my college photography classes. But I was always bothered about f-stops. What did that number mean, exactly? Like many things back in that era known as B.G. (before Google), you just learned not to ask too many questions. The cost of finding the answer—the precise answer—was too high. You might ask a teacher or friend, but they would rarely provide a simple explanation.

Where did this strange f-stop concept come from? According to one of my photography textbooks, in the early days of photography, aperture was controlled by metal plates inserted into the camera body (which I picture as a big wooden box). The smaller aperture plates had more material than the larger aperture plates (that is, if you take a sheet of metal and punch a small hole in it, a lot of metal remains around the hole; if the hole is larger, less material remains). This is one way I have thought about f-stops: the greater the f-number, the greater the “non-aperture.” Big number means big non-aperture means small aperture. Big number means small hole, in other words.

But that’s not a very easy way to remember it, at least for my little brain, because it mixes up opposites: big and small. Big means small? Small means big? Sounds like *1984.*

Another way to think about it uses the human eye as an example: the eye as a camera lens that could be “stopped.” The iris, after all, is like an aperture in a camera. Imagine you are looking into a friend’s eye. The smaller the hole (the pupil) the larger the amount of iris you would see. Since the iris is generally colored, more iris means more color. If their pupil is small, more blue shows. This is equivalent to a large f-number. Large f-number means more color, which means smaller pupil (or aperture).

That works a little better for me, but thinking about it numerically may be the easiest way, giving us yet another another way to remember that “low f-number” means “large aperture,” and vice versa. And here it is: the diameter of the aperture is the focal length divided by the f-number, or D = f/N, where D is the diameter (duh), f is focal-length, and N is the f-number.

That makes it sound complicated because I’ve introduced a new term: focal length. But focal length is easy: it is basically the length of the lens, which is often constant. Look at your lens. If you have a short lens, the focal length is short (say, 50mm). If you have a long lens—a big telephoto like wildlife photographers use to take pictures of cheetahs—the focal length is long (say, 200mm). This is more or less what you would expect “focal length” to mean, which is a relief. Given the oddities of camera terminology, I would almost expect a long lens to be short, and a short one long.

So suppose the f-number (which the camera just tells you, thankfully) is 1.1 and you are using a 50mm lens. Then the aperture would be big because 1.1 goes into 50 a whole bunch of times. If you changed the f-number on the camera to 45, then the aperture would be smaller, because 45 goes into 50 a little more than once. And so on. So the more the f-stop goes into the focal length, the bigger the aperture. Small goes into large *more* times, and more means bigger. That, at least, starts to make sense. And if not, maybe this diagram will: