Strange Number Sequence in Photography

In my last photography post, I shared three sets of numbers: Film (sensor) speed, Shutter Speed, and Aperture (f-stop).  The sensor speeds and shutter speeds made sense; each one was roughly double or half the preceding number.  The aperture series of numbers, however, was rather odd.  If you’d like to know why that set of numbers is so odd-looking compared to the other two sets of numbers, read on, this post is for you!

The numbers in the aperture series represent the ratio of the focal length of the lens to the diameter of the aperture.  That’s why it’s called an f/number, and why in my last article you saw me refer to an aperture as f/11 instead of f11.  By using a ratio, photographers avoid having to memorize a different sequence of numbers for each focal length lens they own.  Imagine what would you have to do for a zoom lens!  Thus f/8 on a 100mm lens lets in the same amount of light as f/8 on a 28mm lens which lets in the same amount of light as f/8 on a 500mm lens.

But why aren’t the numbers doubling or halving as you step through the sequence?  Because the amount of light that passes through a given aperture is dependent on the area, not the diameter of the opening.  In High School Geometry class, we learn that the area of a circle is equal to pi times the square of the radius.  So for a 100 mm lens, f/2 would have a diameter of 50mm.  The area of this aperture on this lens is 3.14 x 25 x 25 is about 2000 square mm.  The next number in the sequence, f/2.8, would have a diameter of approximately 35.714 mm.  3.14 x 17.85 x 17.85 is about 1000 square mm.

Instead of memorizing the whole sequence, there’s really only two numbers you have to remember: 1.4 and 2.  Double 1.4 and 2 and you get the following two sequences:

  • 1.4, 2.8, 5.6, 11, 22
  • 2, 4, 8, 16, 32

Merge the two series together in ascending order and you get the whole series:
1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32.

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