Exposure and reciprocity
Every camera is a light-proof box with a lens, a shutter that opens for a certain time measured in seconds, and an aperture that opens to a certain size measured in what are called f-stops.
Every scene you photograph requires a certain amount of light reaching the camera’s film or sensor to be exposed correctly. Just as you can fill a glass with water in half the time if you double the flow of water, so too can you shoot a picture in half the time if you double the amount of light allowed to enter. In fact, you can continue halving the time if you continue doubling the amount of light, or doubling the time if you halve the amount of light (and vice versa). This is a reciprocal relationship, and in photography has become known simply as reciprocity.
Modern shutter speeds and modern f-numbers are arranged such that any change of a single step (called a “stop”) will result in either doubling or halving the time or the amount of light. This means that if you wish to, say, cut shutter speed in half, you may then compensate for this change by increasing aperture by one stop, by moving from one number to the next in the sequence.
Shutter speeds are typically measured in fractions of a second, such as 1/500, but are normally marked with the numerator absent. Therefore 1/500 would be listed simply as 500.
Shutter speeds would sequence as follows:
1 second, 2 (ie 1/2), 4, 8, 15, 30, 60, 120, 250, 500, 1000, 2000, 4000
As you can see, some of the numbers are not exact halves or doubles of the others. They are the products of convention, not calculation, and some have been rounded off for convenience.
The International system
No one needs to know this in order to take good photographs, but an f-number is equal to the focal length of the lens divided by the effective (not actual) diameter of the aperture (or “opening” or “diaphragm”). So what does “f” stand for? Nothing, really. It just indicates that it was derived in the manner described in this paragraph’s first sentence.
F-numbers don’t seem to follow the double/half pattern, but that’s only because they are derived from the area of the opening, not its diameter.
Doubling the area of a circle means increasing its diameter by the square root of 2, and that is exactly the step taken by the sequence of f-stop numbers adopted after WW2 (which, incidentally, used 2 as an arbitrary base for the calculation of all the other numbers). This sequence became known as the International system.
1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, 90
Note that, like shutter speeds, some of these numbers are not exactly what they should be, and they too have become accidents of history. Note, too, that since these numbers are ratios, they have no units.
F-numbers are typically written with a slash between the letter F and the actual number, like this: f/4. The letter is normally lowercase and traditionally was also italicized. The slash, contrary to what you may read, doesn’t actually “indicate” division, even if it implies it. The focal length of the lens divided by the f-number will probably not calculate the actual aperture size as one would expect, because, as hinted above, the effective aperture is not necessarily the actual physical aperture. This is because the path of light inside the lens often shrinks, and the aperture may be placed there for convenience.
Alternate f-stop numbering systems
The reason for having a consistent, rational f-stop numbering system is to be able to shoot with two very different lenses, with the same f-stop and shutter speed, and get the same amount of light to the film or sensor. But if every lens and camera maker had a different system, that goal would be lost.
The modern f-stop system is called the “International System”, and before it was adopted, many other systems competed for primacy among manufacturers. One of them, called the Uniform System or “U.S.”, was established by Britain’s Royal Photographic Society in 1881. Kodak used the Uniform System on some cameras up until the 1920s and if you collect old cameras in North America, you will likely run into that one first. But there are others.
- “Calculated modern values” are the numbers derived by the actual calculation (using 2 as a base and 1.414 as a multiplier), before rounding off. This is for comparison purposes with historical sources that may have calculated values as well.
- “Source f-stop value” is the f-number in the source in question. Yellow is an Agfa chart from c. 1900-1920; rose is a chart from a periodical called Photo Miniature, Vol. 1, No. 1, New York, April 1899; and grey is from a source now lost.
- Stolze is after Franz Stolze, 1830-1910. Also known as “European” or “Continental”.
- Zeiss is the Carl Zeiss company, a German manufacturer of optics and instruments founded in Jena in 1846 by Carl Zeiss, Ernst Abbe and Otto Schott.
- The Uniform System was considered obsolete by World War II.
- Goerz is after Carl Paul Goerz, who founded the company so named in 1886. It made cameras, lenses, and tools. In 1926 it merged with other companies to form Zeiss Ikon.
- Voigtlander is an optical company founded by Johann Christoph Voigtlander in Vienna in 1756 and is the “oldest name in cameras”. It produced a lens in 1840 and a daguerrotype camera in 1841.
- Thomas Rudolphus Dallmeyer (1859-1906) was an Anglo-German optician who patented the telephoto lens in 1891, authored a book on the subject, and was president of the Royal Photographic Society from 1900 to 1903. His father, John Henry Dallmeyer, was also an optician who made telescope mirrors (among other things) for markets around the world.
The Uniform System
The Uniform System was defined as follows: the first setting, U.S. 1, gave an aperture equal to one-fourth the focal length; and each step changed the exposure by a factor of two, either doubling or halving it. In the Uniform System, the number itself doubled or halved, also. Given this, then, the Uniform System relates to modern f-stops as follows:
As an indication of how confusing this can become, this is the same table in the ICP Encyclopedia of Photography (Crown Press, New York, 1984, p. 532):
The ICP’s encyclopedia entry skips f/32 and f/64, uses f/90 twice, then introduces f/128 at the end to finish off the table. Grinding through all these numbers makes these sorts of errors understandable. The multicolored table above also clearly has mistakes about the Uniform System (for example, U.S. 2 is not f/6).
What you need to know
F-stops and more generally exposure calculation has led to some of the most pretentious tripe ever found in any vocation. Something about the process brings out the worst elitism in people, usually in the form of undisguised intellectual snobbery. For example, the second sentence in a Wikipedia article about reciprocity used to read as follows:
This relationship is implicitly assumed in most sensitometry, eg, when deriving a Hutter-Driffield curve for a photographic emulsion.
It’s difficult to imagine what kind of self-important pompous ass thinks a layperson needs to read something like that in a basic article on reciprocity (as the second sentence, no less). But this sort of exaggerated and ostentatious behaviour has been around for a long time. The most striking example, and photography’s sacred cow, was Ansel Adams and his zone system. The zone system was a method of determining exposure which seemed to consist mainly of buying many of his books and products, making time-consuming calculations based on subjective criteria while the quality of the light changed, and finally following the advice even novice photographers already knew: do lots of bracketing.
Adams’ technical prowess was beyond dispute, although most of his skill was in the darkroom. His prints are, with more than a little justification, the highest priced of any US photographer. But his supposed methods seem more like convoluted after-the-fact justification for what he’d already decided. Like any fanaticism, of course, this point can’t be argued with any of its followers. Numerology is a black art that doesn’t take kindly to criticism.
What you need to know is best summed up in the photojournalists’ creed of f/8 and be there. This expression was coined in the age of film (it is sometimes attributed to Alfred Eisenstaedt), and still has the ring of truth. In other words, all the theory in the world can’t replace actually being in the right place, at the right time, with equipment you’re intimately familiar with, ready to be used at a moment’s notice, without hesitation. Everything else is nonsense.
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