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.
Influence Of Focal Length On Depth Of Focus. The influence of focal length on depth of focus is often either not at all understood, or entirely misunderstood. The idea is very prevalent that longer focus means, or should mean, greater depth, while in fact it is just the reverse. The distance between the principal focus and the sharp image being a certain fraction of the focal length, it is plainly evident that the longer the focus, the greater must be the variation in distance of the focal planes for objects situated at different distances from the lens. For instance, two objects situated respectively 50 feet and 100 feet from the lens, will have their images about 1-32 inch apart with a 6 inch focus lens, and about 1/8 inch apart with a 12 inch focus lens. It is therefore plain that the range of distance - or the space - throughout which different objects may be distributed and yet appear sharp at the same time (in the same plane) is greater, the shorter the focus of the lens is, and vice versa. In other words, the shorter the focus of the lens, the more depth; the longer the focus, the less depth.
621. With the same relative aperture, depth varies inversely as the square of the focus. Thus, of two lenses of the same rapidity (that is, having the same ratio of aperture to focal length) the one having double the focal length of the other will have only one-fourth its depth. Take for example one lens of 2 inches aperture and 6 inches focus, and another one of 4 inches aperture and 12 inches focus. The aperture ratio (ratio of diameter of aperture to focal length - relative aperture) is the same (1-3) in both lenses; therefore, their relative depth is inversely as (6x6) 36 and (12x12) 144, or directly as 144 and 36, or as 4 and 1. Two lenses of respectively 2 inches aperture with 8 inches focus and 3 inches aperture with 12 inches focus, will also have the same relative aperture, and their relative depth will be inversely as 64 and 144, or directly as 9 and 4; that is, the 8 inch focus lens will have fully twice the depth of the 12 inch focus lens.
622. To sum up: Depth varies inversely as the diameter of the aperture, and inversely as the square of the focus; therefore, 1 - With the same focal length and the same relative aperture in any two or more lenses, the depth is the same; 2 - With the same focal length but different relative aperture, the depth is inversely proportionate to the diameter of the aperture; 3 - With the same relative aperture but different focal length, the depth is inversely proportionate to the square of the focus.
Speed Of Lenses - How Determined. The term speed, or rapidity, as applied to a photographic lens, refers to the energy or intensity of light action on the sensitive plate. The stronger, or more energetic that action is, the more rapidly it produces the desired effect on the sensitive silver salts, and the greater, we say, is the speed of the lens. It is needless to say that the volume of light here plays an important part. It is quite plain that the greater the volume of light acting on the plate, the more rapidly must the result be obtained; consequently, the more light the lens transmits to the plate - other conditions being equal - the greater is its speed. The volume of light, therefore, is one of the factors which determines the speed of lenses. Another factor is the concentration of the light, or, as we generally term it, its intensity when it reaches the plate. Other conditions, such as quality of material, perfection of workmanship, etc., being equal, those two factors determine the relative speed in all lenses, regardless of type or make.
624. The volume of light is regulated by the aperture of the lens - the opening (diaphragm) through which it must pass in order to reach the plate. The larger the area of this opening, the more light it will admit. Thus, if we have two circular openings of different size, it is evident that the larger one will let through more light than the smaller one, in proportion as its area is larger - in other words, the volume of light is directly proportionate to the area of the opening. If we know how much larger in area one opening is than the other, we also know how much more light it admits.
625. From geometry we know that circular areas compare as the squares of their diameters; consequently the volume of light transmitted through the two openings respectively must be directly proportionate to the squares of their diameters. In Fig. 20 we have two circles in which for easier comparison the larger is twice the diameter of the smaller. Inspection shows the square of the larger diameter to be equal to four times that of the smaller. Since the areas of the two circles are proportional to these squares, it follows that the larger has four times the area of the smaller and consequently transmits four times as much light. If the diameters are one inch and two inches respectively, the proportion of light is as l x l and 2x2, or as 1 and 4. In the same manner diameters of two inches and three inches give us the proportion of light as 2x2 and 3x3, or as 4 and 9.
626. If the distance between lens and plate is the same, the intensity of the same volume of light is also the same; there is no variation in intensity, and speed depends on the volume of light alone. Thus, in one and the same lens, or in several lenses of the same focal length, but different types, when used under the same conditions, speed is proportionate to the square of the diameter of aperture. If we have one lens with, say four stops, 1, 2, 3, and 4 inches in diameter respectively, the relative speed of the lens with those stops will be as 1, 4, 9, 16. If we have several lenses, all of the same focal length and with stops as just mentioned, their speed will be the same with the same diameter of stops, and different with different diameter of stops. In short, with the same focal length and same diameter of aperture in any two or more lenses, their speed is the same; with the same focal length but with different diameter of aperture, the speed is proportionate to the square of the diameter.