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I thought this would have been asked before but it seems not.

I don't understand how f-stops are numbered. From what I read, the lower the f-stop number, the larger the aperture. That is, f/2 is larger than f/22.

This seems odd to me. The maximum aperture width is (at least theoretically) infinite, while the minimum is 0 (i.e. the lens is completely closed and not letting in any light).

The way the numbering system is set up, it allows for infinitely tiny apertures but a limit on how large they can be (i.e. I guess the largest is f/0)

Can someone clarify why the aperture is numbered in this way?

The f stop is a comparison between the physical size of the focal length and the aperture.

If the aperture is 25mm and the focal length is 100mm, then you'd have f/4 because the aperture value is 1/4 the focal length.

So, the f stop is the fractional representation of this comparison. As with fractions, 1/2 is bigger than 1/22.

/ is division.

A number divided by 22 (f/22) is smaller than the same number divided by 2 (f/2).
As simple as that.

Now, WHY?

f is the focal length. Describing the aperture as a fraction of the focal length has one advantage: it immediately reveals the image brightness.

Example:

20mm aperture can be...

• Telephoto lens, 200mm f/10 - pretty dark


• Wide angle lens, 30mm f/1.5 - pretty bright

It's no accident that f-stops are written with a "division" slash.

You say, "f/2 is larger than f/22". Here, "f" stands for the focal length, and the result of the expression gives the physical size of the aperture opening. So, let's take a 50mm lens... At f/2, the aperture opening measures 25mm. At f/22, the aperture opening measures ~2.3mm. Obviously an opening measuring 25mm is going to let in more light than one that measures ~2.3mm.

You say, "I guess the largest is f/0". No. You can't divide by zero. Or in other words, there is no lens such that the ratio of the focal length to the size of the aperture is f:∞.

Because the lens operates much like a funnel in that it gathers light, the greater the working diameter of the lens, the brighter the projected image. How bright this image will be is dependent on the brightness of the scene and the magnification realized by the lens. The longer the focal length, the more the lens magnifies. The deed of magnifying to produce an image, takes its toll on image brightness. In other words, the longer the focal length, the more the lens magnifies. This higher magnification result is a larger but dimmer image of objects.

Another way to say this, image brightness intertwines the working diameter and the focal length. Because these two factors are so interwoven, gauging image brightness is demanding. We are forced to fall back on a mathematical ratio that will take the chaos out of figuring out image brightness. This is true because a ratio is dimensionless. If I tell you the ratio of boys to girls in a 6th grade class is 3 boys for every 4 girls, I have given you a ratio that works independent of the number of students. For example if the class consist of 28 kids, then 12 boys to 16 girls is the breakdown (ratio is dimensionless).

For the camera lens: if the working diameter is 4 inches and the focal length is 4 inches, then the focal ratio (f-number) = 4 ÷ 4 = 1 (written as f/1 (f/1 is produces a very bright image). If the working diameter is 2 inches and the focal length is 4 inches, then the f-number is 4 ÷ 2 = 2 (written as f/2.).

The splendor of using a ratio is, any lens operating at the same f-number as another lens, yields the same image brightness regardless of the dimensions (diameter or focal length), for an identical scene. It’s complicated; but the f-number system actually takes away the chaos.

The "why" is that f/stop number is focal length / aperture diameter.

So a 100 mm lens at f/4 has an effective aperture of 25 mm. This is not exactly the physical diameter opening, but is the effective diameter, specifically the front entrance pupil, as seen by the magnification of the front lens elements.

Because of this definition, as aperture diameter becomes larger (and exposure increases), f/stop number becomes smaller. f/2.8 is wide, and f/22 is narrow.

It may seem backwards at first, but we get over it easily, and the huge advantage of the f/stop number system is that it applies for any lens, of any size and focal length and aperture, so then we all know what we mean when we say f/8. f/8 is f/8 exposure on any lens. This is a plus. It wasn't that way in the early beginning. And of course, light meters meter with the same meanings.

My site has more about this at https://www.scantips.com/lights/fstop.html