What the F-Stop, Indeed!

As many of you know, I enjoy listening to podcasts on my drive to and from work, and this afternoon was no different. On one of the podcasts I listened to today, I happened to hear what had to be the most convoluted, confusing, and downright confounding explanations of the f-stop that I've ever heard. I'm pretty sure that at least one crucial part of the explanation was even wrong. Very wrong. WTF-stop, indeed! So, let's go ahead and take a look at the term "f-stop" to see if I can make some sense of it for you, as it's actually deceptively simple. Maybe.

f-stop: In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens's focal length to the diameter of the entrance pupil (in photography, the aperture or iris).

Being a ratio, or fractional number, the f-stop is usually expressed as something like f:4 or f/5.6.

So there you have it. Makes perfect sense now, doesn't it? No? Read on, then.

F-stops control the amount of light passed through the lens

To put some concrete numbers behind this, a 50mm f/2 lens, has a maximum aperture of 50/2, or 25mm. When set to f/2, this particular lens would be said to be "wide open," meaning the aperture is at its maximum opening, allowing the maximum amount of light to pass through the lens. If we set this particular lens to f/4, as an example, the aperture will be closed down (or "stopped down") to 50/4, or 12.5mm. This, obviously, reduces the amount of light that can pass through the lens. By applying this same concept, we can figure that a 25mm aperture on a 100mm lens works out to f/4.

Oh, Lawdy, we've used algebra!

If this is still confusing, think of the aperture or iris like a very precise valve in a water pipe. Closing the valve makes a smaller opening, restricting the amount of water that can flow.

Now, here's where the math can get hinky, and where people start to get confused. The math involved is weird because we're dealing with the area of a circle, and that makes some of the numbers start to look funny. I say that someone else figured out all this math (using algebra and geometry and physics and stuff), and handed us the results, and they work, so let's just go with their results from here on out.

With that said, there's a sequence of numbers that are the "full f-stops," and they are the numbers that set up the ratios that are the key to understanding the whole thing. Here's the sequence for our hypothetical 50mm lens:

2, 2.8, 4, 5.6, 8, 11, 16, 22

These are arranged from the largest opening to the smallest, and I think this is where people start to get confused -- the bigger number let's in less light? What? But remember, it's a ratio that describes how far the aperture is open with respect to the focal length of the lens. Getting back to our 50mm f/2 lens, the numbers break down like this:

f-stop aperture diameter
2 25mm
2.8 17.86mm
4 12.5mm
5.6 8.93mm
8 6.25mm
11 4.55mm
16 3.13mm
22 2.27mm

The next bit that's important to know is that each full f-stop you stop down cuts the amount of light passed through the lens by half. In other words, the f/2 lens transmits 100% of the available light when set at f/2 (wide open). Setting the aperture to f/2.8 passes half the available light. Stopping down another stop cuts the light in half again, passing only one quarter of the available light. Going down to f/11 passes just 1/32 of the available light through the lens.

Conversely, each stop you open up doubles the amount of light passing through the lens. So, if you're at f/11 and open up to f/8, you go from 1/32 of the available light passing through the lens to 1/16 of the available light passing through the lens -- double the amount of light.

So, to re-cap the subject, the f-stop is the ratio of the focal length of the lens to the diameter of the aperture. The aperture controls the amount of light that can pass through the lens. Smaller apertures mean less light, larger apertures mean more. Each full f-stop step down cuts light in half, each full f-stop up doubles the amount of light.

The guy on the podcast rambled on about this for at least five minutes!

F-stops control depth of field

Wait, what? It does more than just control light? 'Fraid so.

I'm not going to dive too deep into this right now, but the aperture can also be used to control something called "depth of field." What's that all about?

Depth of field: In optics, particularly as it relates to film and photography, depth of field (DOF), also called focus range or effective focus range, is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image.

We've all seen brilliant landscape photographs in which everything from the rocks in the near foreground to the distant mountains appear to be in sharp focus. A photo like this is said to have a deep or large depth of field. On the other hand, a portrait where the subject eyes are in sharp focus, but the background is nothing but a fantastic blur of color, is said to have a shallow depth of field.

There's a lot of math involved in figuring out exactly what will appear sharp and what won't, but the basic gist is that a small aperture will cause more depth to appear sharp (our landscape), while opening the aperture up will cause less to be sharp (our portrait).

The podcaster took another five minutes to describe this.

There's something called "hyperfocal distance" that can tell you what will and won't be sharp, but we'll talk about that another day.