This section is from the book "Complete Self-Instructing Library Of Practical Photography", by J. B. Schriever. Also available from Amazon: Complete Self-Instructing Library Of Practical Photography.
670. The opening in a lens is its aperture. Anything that will give various sizes of openings for the admission of light may be termed a stop or diaphragm.
671. Stops and diaphragms, while used in the same manner, are differently located. A stop is placed in front of the lens, and a diaphragm is placed between the lenses. The former is almost always used with single lenses, while the latter is employed with doublets. For general use there are three forms: The iris, waterhouse and rotating stops or diaphragms.
672. There are three distinct uses to which stops may be put. Unless the photographer realizes this and forms some idea of the way in which each purpose is achieved by the use of stop or diaphragm, he will be working in the dark and not secure the results which might have been easily produced if proper consideration had been given to this subject.
The Three Uses Of Stops. The first distinct purpose to which the stop is put is to overcome the optical defects of the lens should there be any; second, it is to bring objects located at various distances from the camera into sharp focus at the same time, and third to accent the shadows or give more contrast in flat scenes.
Comparative Sizes. In order that it may be an easy matter to figure the required amount of exposure for any particular stop, when the exposure is given for another stop, it is necessary to have a system of numbering the different sizes. In common use there are two such systems, one known as the f, or focal length system, the other U. S., or uniform system. The f system is a comparison between the focal length of the lens and the diameter of the stop, while the U. S. system is simply a comparison of the exposure values of the different size stops.
To Find The Focal Value Of A Stop. To find the focal value of a stop or diaphragm, first ascertain the equivalent focus of the lens, and divide this by the diameter of the stop. Example: If the focal length of the lens is 8 inches, and the diameter of the stop is 1/4 inch, the result of 8 divided by 1/4 is 32. The number of the diaphragm is, therefore, 32, and should be expressed f/32.
Systems Compared. In the U. S. system No. 1 is 1/4 the focal length of the lens, which is written in the f system, f/4. The diameter of No. 2 must be such that the area of the opening will be half that of No. 1.
To Secure The F Value. To secure the equivalent value of U. S. 2 in the f system, square the f value of U. S. No. 1, which is 4 (this will give 16); then multiply by 2 (result 32), and finally extract the square root, which will give a result of 5.6. Therefore, f/5.6, is equivalent to U. S. 2.
678. First, the volume of light that passes through the diaphragm is proportionate to the area of the aperture. Second, the areas of circles are proportionate to the square of their diameters. By working out the remainder of the figures the complete series will be as follows: