Les Jones: Where Do Aperture F Values Come From?

May 16, 2008

Photos > Where Do Aperture F Values Come From?

So in photography class we memorized the standard whole-stop aperture numbers. 1.4, 2.0, 2.8, 4, 5.6, etc. We also learned that going from one whole aperture stop to the next represents a doubling or halving of light. We didn't get into the formula those numbers are based on, but it was mentioned that they were related to the area of the circle of light projected through the lens diaphragm.

What I didn't realize is that those number are square roots. Specifically, they're the square roots of the power of 2. The ones that aren't multiples of 2 are rounded for simplicity.

Apterture f-stop	Is the square root of	Which is also known as
1.4	2	2¹
2	4	2²
2.8	8	2³
4	16	2⁴
5.6	32	2⁵
8	64	2⁶
11	128	2⁷
16	258	2⁸
22	512	2⁹
32	1024	2¹⁰

See also:
- Aperture (Wikipedia)

Posted by lesjones | TrackBack

Comments

1+1=2 (except for very large values of 1).F/nums are ratios of the focal length (F) divided by the size of the lens opening in same units. Since its a ratio, the value of F is irrelevant to exposure. Using this system, different lenses will give, closeto, the same exposure using only the same F/# and time. If you will notice, every other F/# is a power of 2! 2,4,8,16,32,64,128. Reducing the lens opening physically by half cuts the exposure to 1/4 its former value, so some smart people provided more stops halfway in between. This is a fine system, provious systems were all a plate of hash by comparison. And yes, there are lenses that go down to F/128, sometimes more. Just not on 35mm SLRs. Hope this has been of some illumination.
(8^))

Posted by: Ritchie at May 17, 2008

"Since its a ratio, the value of F is irrelevant to exposure."

I'm guessing you meant to add some qualifications to that statement. Clearly a 200mm/F2.8 lens is going to provide different exposure options compared to a 200mm/F5.6 lens.

Posted by: Les Jones at May 18, 2008

Ok, let me qualify. At the same f/setting. Clearly your example is correct, but I neglected to clarify, at the same f/setting. A 25mm lens at say, f/8 will give substantially the same exposure as a 100mm lens, at f/8. At the same exposure time. Sorry for the unclarity, I'm told this happens. Let me mention a quibble, individual systems and components vary. My Pentax 6x7 requires an extra stop of exposure, +1. With the normal 105mm and 75mm wide angle, with 2 different meters and "sunny 16". Shutter has been checked, lens irises checked. No one has an explanation. I handle it by de-rating the film 1 stop, 400 is used at 200, etc. Chalk it up as part of the charm.

Posted by: Ritchie at May 18, 2008