The f/stop controls the intensity (brightness) of the light which hits the film. It consists of a variable size opening (diaphragm) adjusted with a scale of numbers representing the relative size of the opening. It is similar to the iris in your eye which opens and closes in response to the amount of light. The series of numbers usually run 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, 90, 128. That is a complete list. No actual lens will have the entire range and the actual numbers may vary from the above list (particularly at the small number end) due to the characteristics of the lens.
Each of the above f/numbers represents double or half the light intensity of it's neighbor. The larger numbers result in less light and the smaller number in greater intensity of light. This may be puzzling to beginners until they understand how the number is derived. The f/stop number is part of a ratio which represents the diameter of the diaphragm opening divided into the focal length of the lens. Thus f/8 means that the diameter of the opening is 1/8th of the focal length of the lens. It then becomes evident that f/16 is less light than f/8, but why is it one fourth the light rather than one half and where did those odd, in between, numbers come from?
The doubling or halving of the shutter speeds is obvious. One quarter second is clearly twice as long as one eighth. The f/stop, however, is not a direct measure of the amount of light, rather it represents the relative diameter of a more or less circular opening. I say more or less because the opening is created by movable leaves of metal. As few as 6 leaves may be used. The opening is actually a polygon of as many sides as there are leaves. It is the area of the opening that determines the amount of light which passes through. Because it is approximately circular the area of the opening is increased by double or half at the intervals in the steps indicated above. If you are a mathematician you can work it out (Pi r squared and all that stuff), other wise it's sufficient to understand the relationship.
The "f" represents the focal length of the lens, therefore the actual diameter of the opening at any given f/stop varies in direct proportion to the length of the lens in use. This relative value of the opening of the diaphragm causes the amount of light on the film to be a constant value between lenses regardless of focal length, ie: as the length of lens increases the light reaching the film is kept constant by increasing the diameter of the opening. Therefore f/8 on a 2" lens is an opening of 1/4" diameter but on an 8" lens the opening is 1". Since light falls off over distance this compensation is necessary to maintain the consistent intensity of light on the film for a given f/setting. If both are used under the same light conditions f/8 with a 50mm lens will produce the same intensity of light on the film as a 10 inch lens at f/8.
So while the scale is initially confusing, it is because it represents a relative value that it a useful measure of light to photographers. If it measured a fixed value, such as the actual diameter in inches or millimeters, you'd have to do all that math stuff yourself for every picture you took.
All the above is based on optical principles for simple lenses. Modern cameras don't use simple lenses. I include this to give an understandable concept of why any given f/stop gives the same relative exposure regardless of the focal length of the lens. The actual measurement of a diaphragm opening used with a compound lens is adjusted to the characteristics of the lens.
If you have lenses of different fixed focal lengths try looking through them (off the camera) when they are both set at the same f/stop and you will see the relationship (longer lens = bigger opening). You may have to hold down a lever on the back of the lens to get the diaphragm to close down if your camera is designed to keep the diaphragm open until the shutter is tripped. Don't use a zoom lens at different focal lengths. They are a special case. Enlarger lenses are good for this exercise if you have them.
Back to Lessons Index
"I was gratified to be able to answer promptly and I did. I said I didn't know." Mark Twain