I think the question is more like "why isn't f/8 the next f-stop number after f/4 if everything is half or double?"

The f-number doesn't double (it increases by (2)(sq.rt. of 2), actually) but the area of the iris opening does double.

I'll try to explain the math as concisely as possible. Each stop, as you know, is either half or double the light from an adjacent stop.

On a 50mm lens an f2 will have an entrance pupil diameter (the iris opening diamater as seen from the front of the lens, essentilly) of 25mm and an f2.8 will have an entrance pupil diamater of 17.86mm.

Since the whole c ircle opening is allowing light to enter, we should consider the area of that circle. The 25mm circle (f2) would have an area of (pi)(12.5^2) or 490.63 square mm. The 17.86mm c ircle (f2.8) has an area of (pi)(8.93^2) or 250.4 square mm.

Notice the approximate relationship between the areas. The f2 area is about double the f2.8 area. They would work out perfectly except for my rounding off of numbers (both on my part and on the part of lens makers. for example f22 doubled to get f45 vs. f44) and my use of 3.14 for pi instead of a greater number of digits, both done simply to save time.

**Edited by Christopher D. Keth, 06 January 2007 - 05:50 PM.**