f-stop Confusion: Mystery Solved and Explained!

F-stop Confusion

Every once in a while someone makes a choice that causes confusion forever after, and such is the case with “f-stops.” I know of no other concept that causes as much confusion for photographers. It certainly confused me, but the concept is so important to getting correct exposures that I dug into it. What I discovered that a little arithmetic explains it all, and as always, understanding conquered confusion.

Need to cut to the chase? Less is more for f-stops. A bigger f-stop number means a smaller aperture and less light entering the camera. Continue reading if you want to know why.

F-stops are sometimes called “f/stops” or “f-ratios,” or “f-numbers.” The terms are equivalent and all refer to the same way to talk about the amount of light of any given brightness that a lens will allow into a camera. Each full f-stop change allows twice as much light into the camera as the next smaller one. One of the two reasons this can be confusing is that small f-stop values mean big openings and vice versa, a difficulty that began the very moment f-stop was defined as the focal length of a lens divided by the area of its opening

f = (lens focal length)/(area of lens opening),
or
f=L/A

So you see that a big diameter results in a small number because the f-number is actually a ratio. How simple life would be if only they had switched the numerator and denominator when they defined the f-stop! Then a big aperture would have had a big f-number!

Now that we’ve conquered that mystery let’s go to the other source of confusion – – how come going from f/4 to f/2 lets in 4 times as much light? Why doesn’t this change mean only twice as much light entering the camera? Once more, the answer lies in the math. The defining equation includes the area of the lens opening, and of course every night we lie awake thinking about the fact that a circle’s area is equal to pi (3.14) multiplied by the square of the radius. NOTE: (If you are reading this on an aggregation site such as “Inside Word” you probably are not seeing all of the graphics and other information. You need to see everything, so click the link to go to the complete article at theDigitalPhotoCoach.com.)

f-stop

The r-squared part of the equation means that we have to take the square root of the change in the amount of light we want in order to arrive at the f-stop number. If we decide that we’re going to base our f-numbers on f-1, then each time we reduce the amount of light to some fraction of what an f-1 aperture will admit, the f-number becomes the square root of that fraction.

For example, the f-stop that lets in half as much light as f/8 is f/11. That is because 1/8 squared is 1/64; half as much light is 1/128, and the square root of 1/128 is 1/11.

f-stop

f-stop

So it does make sense after all, and here’s the really good news. Unless you are taking a test, it will be enough to remember that

in f-stop lingo, less is more.

When comparing one f-stop with another f-stop, the lesser one will allow more light into the camera.

Please leave a comment if you’ve figured out an easy way to keep this straight. The world is waiting for your help!

I recommend that you make a point to learn how to adjust your camera’s aperture settings. If all else fails, look in your manual — the information is there. There is information about how to manage aperture, shutter speed, and ISO rating in this discussion: Speed, Aperture. and ISO Simplified

I hope to see you back here soon.

Curtis

Decreasing aperture diagram courtesy CBuckley

© 2011, TheDigitalPhotoCoach.com. All rights reserved.

© 2011, TheDigitalPhotoCoach.com. All rights reserved.

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