what's with the f/numbers anyway?

Ever wonder why the aperture numbers are like that? Back when dinosaurs roamed the earth, we had aperture rings on lenses, and they had full-stop markings like 2, 2.8, 4, 5.6, 8, 11, 16, 22 on them. The bigger the number, the smaller the opening. Seems backwards, doesn't it? Well, if you must know, it's because these numbers are in the denominator of the formula for the area of the aperture opening. You know, even though 4 is larger than 2, 1/4 is smaller than 1/2 ?

 

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Remember the simple formula for the area of a circle, "pi-R-squared?" or pi times the radius raised to the 2nd power? Well that's it! For the geeky types we write it as

area = pi * r ^ 2

and the radius of the aperture opening is approximately the focal length divided by twice the f/number

r = ( f / 2N)

where f is the focal length of the lens, and N is the aperture number. Another reason why sometimes the aperture number is written as f/5.6 or f/8. The formula becomes

area = pi * ( f / 2N) ^ 2

There you have it, boys and girls. Fifth grade math.

When N is 2.8, you'll get an area that is approximately twice of the area when N is 4, thereby letting in twice the light. Or we say f/2.8 is one full stop wider than f/4.

Now-a-days it's common to have aperture numbers in 1/3 of a stop increments, which involves computing the cubic root of the square root of 2, and who wants to mess with that?? (Ok, fine, it's already been determined, so between f/2.8 and f/4 there's f/3.2 and f/3.5, etc etc).

Just remember, every three clicks on the aperture dial, if your camera is set to 1/3-stop increments, you're either doubling the light (opening up a stop), or halving the light (stopping down a stop)...

Till the next time, this has been Photographic Math Is Fun with PhotoDude, your friendly mad scientist!!