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.
Comparative Exposures. With lenses numbered this way, and the exposure is given for any one diaphragm, the exposure for any other diaphragm may be easily ascertained. The exposure for a certain stop is one-half that of the size next larger, or double that of the next smaller. Example: U. S. 4 or f/8 will require twice the exposure of U. S. 2 or f/5.6, and on the other hand, it will need but one-half the exposure necessary if stop U. S. 8 or f/11.3 were employed.
680. To Find the U. S. Number When Number is Given for the f System. - When the diaphragm number is given for the f system, and it is desired to find its equivalent value in the U. S. system, square the f value and divide by 16. Example: To find the U. S. number of the diaphragm which may be marked f/20, square the 20, which will give 400. Divide this by 16, and the answer will be 25, which is the U. S. number.
How To Find The Relative Exposure. There may be times when you desire to find the exposure of two different stops, which are not given in the regular scale, and, therefore, you will be unable to find the correct relative exposure. Take, for an example, stop f/7 and stop f/8. The relative exposure is found by multiplying each of these numbers by themselves, and then taking the proportion: 7 x 7=49, and 8 x 8=64. 49/64=3/4. therefore, f/7 requires three-fourths the exposure of f/8.
The Larger The Stop The Better The Lens. It is a mistake to suppose that with any lens made by a good manufacturer, a subject can be sharply focused in all portions with the largest stop; it depends not only on the workmanship, but also upon the design. A simple form of single lens may have to be stopped down to f/22 to obtain a result as good as may be secured with a rapid rectilinear at f/16, or one of the finest modern anastigmats at f/6 or f/8. The largest stop in a rectilinear lens is provided for use when diffusion all over the plate is not so important as rapidity, or when the subject is one which favors the lens. To a great extent this subject has been covered in preceding chapters, and it is, therefore, not necessary to go into detail here regarding these differences.
Subjects Situated At Various Distances Rendered Sharp At The Same Time. No matter how perfect the lens may be it is impossible, when using the largest stop, to secure a sharp image of objects situated close by and far away at the same time. The larger the lens the more marked is its failing in this respect. The better or more costly and skillfully designed and made the lens the more is this noticed, because its definition in part is such that where the image is out of focus this blurring is made all the more conspicuous by contrast. It is this failing which makes hand camera work increase in difficulty with the larger size plate employed.
684. Let us suppose two photographers are standing side by side, each with a camera with an equally good lens, each using the same stop, and each photographing the same subject. The one using a 3 1/4 x 4 1/4 camera and a 5 inch lens may get every detail near and distant as sharp as can be desired; the other, with the 5x7 camera and a 7 or 8 inch lens, will be unable to get foreground and distance sharp at the same time, and must stop down in order to do so. This is quite distinct from any stopping down done to remedy defects of the lens.