What exactly is an f-stop measuring? It's a ratio of what to what?

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f/stops are a bit more confusing because the numbers appear so arbitrary. This is the standard sequence of f/stops from f/1.4 to f/22. Although it doesn't seem intuitive at first, in this sequence the f/1.4 setting lets in the most light while the f/22 setting lets in the least. Also, each of these f/stops has precisely the same halving/doubling relationship as the shutter speed sequence.

1.4 2.0 2.8 4 5.6 8 11 16 22

On the face of it, going from f/4 to f/5.6 doesn't sound like halving the amount of light. What's more, 5.6 is a larger number and sounds like it ought to be more light, not less. Neither does f/4 to f/2.8 sound like doubling the amount of light. In fact, each of the numbers in this sequence is a halving/doubling of the amount of light from its immediate neighbours, just like the shutter speed settings are. Not only that, but it makes sense, as I shall show below.

The reason that both the halving and doubling and the smaller numbers mean more light things make sense is that the f/stop is a ratio. The ratio is between the diameter of the aperture in the lens and the focal length of the lens. The focal length is generally measured in millimeters, so we'll stick with those as our unit of measure. On a 50mm lens, f/2 is saying that the diameter of the aperture is 25mm. The ratio is this 50/25 = 2. A good question might be, what is the area of that aperture? Well, the aperture is usually a set of five to fifteen blades which form a roughly circular hole, so we'll use the formula for the area of a circle, which as you all remember from fifth grade math is π * radius2. For π I'll use 3.14159265. On our 50mm lens, the aperture at f/2 has a diameter of 25mm which is a radius of 12.5mm. The area of the aperture is thus π X 12.52, or 3.14159265 X 156.25, or 490.9 square millimetres.

This fact by itself isn't all that useful. It is useful in relation to the adjacent f/stops. What is the area of the aperture at f/2.8? Well, because the f/stop is a ratio of the focal length to diameter, our 50mm lens at f/2.8 would have a diameter of 50/2.8 = 17.86mm. The area of the circle thus formed would be π X (17.86/2)2, or 250.5 square mm. That's about 250 sq. mm at f/2.8 and 500 at f/2, a double/half relationship. Aha! So that's it! The area of the hole doubles and halves, it's just represented by a ratio on the lens! No wonder it's so darn confusing.

Because you can barely take pictures anywhere with those speeds! Or with any zoom lenses...

I've rarely had problems with 100, but I do mostly landscape and nature photography, so I can manipulate the f-stop and shutter speed accordingly. 200 is easier sure, but 100 and below are so much nicer in enlargements. I never use 400.

The simple version, is the f-stop is lens focal length divided by aperture diameter.

The simple version, is the f-stop is lens focal length divided by aperture diameter.

Even that makes my brain hurt.

I do a fair amount of portraiture, candids and action, so speed is of the essence--when shooting film I'd happily go up to 1600 in black and white. Even sometimes for architecture too.

Because you can barely take pictures anywhere with those speeds! Or with any zoom lenses...

So totally not true! When I used to shoot on film I used tons of 64 and 100 speed film. It's amazing outdoors. I've also done great work with those speed films and a good flash setup. You do have to use higher quality telephoto lenses with slower speed film, and true telephoto and not zoom lenses are also much better with show speed film.

Oooh, this is a timely discussion for me. I lost my camera this weekend, so I'm looking for a new one. It was a Panasonic Lumix DMC-TZ3 which had some good features, but lacked in others. The thing I liked least about it was that it was difficult to take good pictures in low light. For example, I could either take this without a flash, which is grainy and blurry, or this with a flash, which washes out all the stage lights. Compare those to, say this photo, taken by someone else with a Nikon D80.

Are there cameras that will take low light photos near the quality of the D80, but that will fit in my pocket like my Panasonic did (its dimensions are 4.1 x 1.4 x 2.3 inches)?

Given that I'm still on a Pentax K1000 I think we can safely assume speed is not of the essence for me! My only complaint is manually focusing; I hate that.

I do a fair amount of portraiture, candids and action, so speed is of the essence

Huh, I used to shoot indoor theatrical shots with 800 speed film. Very low light. I'd have to be careful to have a stable shooting platform, but I always got lots of very good shots. Certainly not every shot, but that's why I'd always shoot lots of coverage.

dcp had a TZ-3 at the F2F. He was complaining about the poor low-light performance, too.