THE F SYSTEM It can easily be demonstrated that if a circle be drawn on the surface of any sphere equal in area to one half of one of its octants above re ferred to, the diameter of this circle will equal approximately the radius of the sphere and there fore the altitude of the corresponding cone. Now, as is well known, the usual method of denoting the light admitting property of a photo graphic lens, is to express the ratio of the dia phragm diameter to the focal length of the lens; hence the focal or f system.
Thus in the accompanying diagram if ab cd represent a bundle of parallel light rays incident upon a lens, o, the light will be concentrated at the point e called the focus and situated at the distance oe from the lens known as its focal length. The focal length for a lens of any given diameter is evidently dependent upon the curva ture, the refractive index of the glass, etc., but the amount of light per unit area of the spot at e is directly proportional to the area of the lens opening or to the square of bd, and inversely proportional to the square of the distance oe.
The intensity of the effect at e therefore is pro portional to the square of the ratio of bd to oe.
This ratio bd/oe is called the relative aperture of the lens and is the basis of the f system for indicating lens speeds. For example if a lens of 16 inches focal length is used with a diaphragm opening 2 inches in diameter, the former is eight times the latter and the relative aperture is expressed f / 8 ($). If the full opening of this lens be 4 inches in diameter the focus is only four times this diameter and the relative aper ture will therefore be f/ 4. As the base of the cone of light admitted with the f / 4 opening is four times the area of the base of the f/ 8 opening, the altitude or focus being the same, the illumi nation at e will be four times as intense with the former as with the latter and the necessary ex posure for taking a picture one fourth as great.