Aperture trivia

Things you don't really need to know about your camera's aperture.

HALF STOPS

This comes from our "Department of Knowledge You May Never Use."

If you want to know what the exact halfway point between two ƒ-stops is, add the previous two ƒ-stops together. For example, to find the half-stop between ƒ-4 and ƒ-5.6, add 2 + 2.8, and you will get 4.8. This works for all ƒ-stops. For instance, the half-stop between ƒ-8 and ƒ-11 is 9.6, derived from adding the two previous ƒ-stops (4 + 5.6) together.

ALL THE STOPS THERE ARE

We'll make it even easier for you, and give you the entire scale of full and half-stops from ƒ-1 to ƒ-90. We don't know what you'll do with the information, but here it is:
1, 1.2, 1.4, 1.7, 2, 2.4, 2.8, 3.4, 4, 4.8, 5.6, 6.8, 8, 9.6, 11, 13.6, 16, 19, 22, 27, 32, 38, 45, 54, 64 and 90.

HOW A LENS' ƒ-NUMBERS ARE DETERMINED

A particular lens's ƒ-numbers depend on the focal length of the lens and the diameter of its aperture. The focal length of the lens divided by the lens aperture's diameter is an ƒ-number. For example, a 50mm lens with a 25mm aperture is ƒ-2, whereas a 200mm lens with a 50mm aperture is ƒ-4.

ƒ-STOP NUMBERS DON'T SEEM TO MAKE SENSE. HOW COME?

We said each change in an ƒ-stop number doubles or halves the amount of light, so a change from ƒ-8 to ƒ-11 (the next stop down) lets in half the amount of light. Well, you say, 11 is not half of 8, nor is it two times 8, so where is the relationship?

THE ANSWER IS FOUND IN SQUARE ROOTS

Start with the number 1 and double it, then double that number and so on. You will get the following sequence: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096 and 8192. Now, calculate the square root of each of these numbers, and you will find the standard ƒ-stop number scale.