Square roots? …Really??

Why, I am sometimes asked, do the engineers who design cameras make it all so darn difficult? Like using square roots, and stuff.

And I agree, sometimes they do make it complicated. Like by calling “Continuous Focus” (which you might just understand) by a name like “AI Servo” instead, which relies on you knowing that “AI” means “Artificial Intelligence” and that a servo motor is a closely controlled electrical motor with built-in negative feedback loop. Right. And like by making the zoom-in/zoom-out function on my new Canon 1Dx as unintuitive as the one on the old Nikons. Why make it simple, eh?

But sometimes, the engineers are right.

Like in using fractions. f/16 is smaller than f/4 because it is a fraction. Instead of saying “f 16” we should really say “Focal length F divided by 16″, and we certainly would say that way if it weren’t so many syllables. Clearly, 1/16th of a pizza is less than 1/4 of a pizza, and the same is true of aperture.

Anyway – fractions are very useful when a magnitude (like shutter speed or aperture) tends to double or halve all the time. (In contract, ISO is not expressed as a fraction, and hence it can be confusing… 12800 ISO is only a little faster than 800 ISO, but because we do not use fractions here, it looks much faster.)

So get that out of the way. Fractions can be useful.

But why those silly numbers? f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16: why not just f/1, f/2, f/3, and so on?

Ah. There is a reason.

  • You see, those numbers mean something. The “f-number” indicates the size of the lens opening as a fraction of the lens length (so a 200mm lens set to f/4 would have an opening, or aperture, of 200/4 = 50mm).
  • And if you want to, say, halve the light that enters your lens (i.e. reduce it by a stop; a stop means double or half), you would have to halve the area of the aperture (the opening).
  • And to halve the area, you would have to reduce the diameter by… the square root of two. (area is Pi x radius squared, you may recall from high school). And indeed, the square root of two (roughly, 1.4) just happens to be the ratio between those funny numbers.

In other words: hose funny numbers mean that every next number up gives you a stop less light (or when you go to lower numbers, a stop more light). And that, you will agree, is a very convenient thing!

So before you dismiss the engineers and their silly complexities: sometimes it is actually quite useful to see why they do what they do. Confession: I am an engineer (electrical), but unlike other engineers, I do not assume that everyone knows engineering language. I do, however, know when the techie bits are needed. And I will teach you all of then if ytou hang around!


NOTE: In case you missed it: my “Photography Cookbook” eBook is now out! Click here to read about it, or click here to order.



3 thoughts on “Square roots? …Really??

  1. As a fellow engineer I have to agree with you on the user interface design for some of this gear… few things are farther from intuitive and obvious than a DSLR’s ‘custom settings’ list. “Surely”, they must say in committee, “everyone will intuitively know that you must change parameter *A7=True if you want to be able to focus in low light.” Heads nod all around the table. “Next order of business, does anyone remember where we hid the flash sync speed control?”

    Exposure settings are among those wonderful bits of engineering that were thought out once long ago, made exactly right, and never needed to be redesigned again. (Let’s not give them ideas, though…)

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