I wrote this article about exposure many years ago. I've updated it to reflect the change from film to digital which has happened since it was written, but that's about all the changes it needed. What was true then, is still true now
Shutter speed is, of course, measured in seconds or fractions of a second, and these are familiar units needing no explanation. Aperture, however, is measured by means of f-stops, and though I'm sure everyone is familiar with numbers such as f2.8 and f8, probably not everyone is clear on what these numbers actually mean.
The simplest way to explain f-stops is to consider a very simple lens system in which a single element lens is placed one focal length away from the film. Let's say we have a lens 75mm in diameter and 300mm in focal length. Now another term for f-stop is f-ratio, and the ratio referred to is the ratio of the focal length of the lens to its diameter. In this case the ratio is 300/75, or more simply 4.0! Thus such a lens has a photographic "speed" (also called "f-stop", "f-ratio" or "f-number") of f4. If we use a lens of only half the diameter (37.5mm), but the same focal length (300mm), it would then be an f8 lens. I think it's clear that the smaller diameter lens will collect less light than the larger one, and so the image formed by the smaller diameter f8 lens will be less bright than that formed by the larger diameter f4 lens.
Now real photographic lenses are complex designs which use many lens elements. Clearly they don't change their f-stop by varying the physical size of their lens elements. Instead an internal, variable diameter, iris (also called a "stop") is used to regulate the effective aperture. As the iris closes down to a smaller diameter, less light is allowed through the lens and the image formed by the lens becomes dimmer. Thus the brightness of the image formed by a complex 300mm f2.8 lens with a front element 107mm in diameter, when that lens is used at f4, is exactly the same as that formed by a simple, 75mm diameter 300mm focal length f4 lens. Moreover, the image formed by any f4 lens, whether 300mm, 50mm or 20mm in focal length will be the same brightness.
So, starting out from f1.0 (which is a nice round number!) decreasing the image brightness by a factor of two gives us f1.4. Decreasing the image brightness by another factor of two gives f2.0, and so on to f2.8, f4, f5.6 and the rest. Changing the image brightness by a factor of two in this manner is called changing the exposure by "1 stop". Opening up the aperture to give a brighter image (and a smaller f-number) is called "opening up by one stop", while decreasing image brightness by a factor of two (and so going to the next larger f-number) is called "closing down by one stop".
Thus a full stop sequence would be : f4, f5.6, f8 etc.
a 1/2 stop sequence would be : f4, f4.7, f5.6, f6.7, f8 etc.
a 1/3 stop sequence would be : f4, f4.5, f5, f5.6, f6.2, f7.2, f8 etc.
Thus a full stop sequence is : 1/125, 1/250, 1/500 etc
a 1/2 stop sequence is: 1/125, 1/177, 1/250, 1/354, 1/500 etc.
a 1/3 stop sequence is: 1/125, 1/158, 1/198, 1/250, 1/315, 1/397, 1/500 etc.
Many modern cameras with electronic shutters are essentially "stepless", i.e. when used in automatic modes the shutter speed can be changed in very small steps of 1/10 stop or less, however the shutter speed displayed under these conditions is normally the nearest full, 1/2 or 1/3 step unit, depending on the camera.
Of course that doesn't mean that you have to shoot at 1/125 and f16. If we open up to f11, we increase the image brightness by a factor of two, and if we change the shutter speed to 1/250 we halve the time for which the film is exposed to the image. These two effects cancel, and so 1/125 @ f16 and 1/250 @ f11 are the same exposure, as are 1/500 @ f8, 1/1000 @ f5.6, 1/2000 @ f4 and so on. There is, in fact, a single number which represents all these values. It is called the "Exposure Value" or EV. In this example, 1/125@f16, 1/250 @f11 and all the equivalent combinations of shutter speed and aperture can simply be represented by EV 15. A change of 1 EV unit is the same as a change of 1 full stop of aperture or one "stop" of shutter speed, thus if 1/125 @ f16 is EV 15, then 1/250 @f16 is EV 16 and 1/125 @f11 is EV 14. Higher EV numbers mean less exposure, lower numbers more exposure.
In order to relate EVs to absolute brightness levels, you have to define film speed. Thus using the sunny f16 rule, exposure at ISO 64 would be 1/60 @ f16, which is EV 14 ("EV 14 at ISO 64") while at ISO 125 it would be 1/125 @f16, which is EV 15 ("EV 15 at ISO 125"). You will see EVs used in this way in camera specifications where the operating range of the autofocus system and/or the built in exposure meter are expressed in terms of EV units. A range to EV 1 to EV 18 would be fairly typical. For reference, EV 15 at ISO 100 is a typical of a clear bright, sunny day. A brightly light office is usually at EV 7 or 8 at ISO 100 and a typical living room under artificial light is around EV 5 at ISO 100.
You can easily calculate EV from shutter speed and aperture using the formula:
EV = AV + TV
Where AV is the aperture value and TV is the time value as shown below:
The ISO setting is a linear function of sensitivity. By that I mean that if you double the ISO setting (say from 100 to 200), you only need 1/2 the exposure. So if the exposure was 1/100s at F8 and ISO 100, at ISO 200 the exposure would be 1/200s at f8 (expose for 1/2 as long) or 1/100s at f11 (reduce the amount of light by a factor of two). Each doubling or halving of film sensitivity is still called a change of one stop. So ISO 200 is 1 stop faster than ISO 100 and ISO 400 is one stop slower than ISO 800.
By tradition, fractional stop changes in ISO are done in 1/3 stops, never in 1/2 stops. The 1/3 stop sequence of ISO changes is a sequence based on multiplication by the cube root of 2 (1.26), though the numbers are rounded. Thus 1/3 stop faster than ISO 100 would be 100 x 1.26 = 126. In fact this is usually given as 125. Similarly 2/3 stop faster is 100 x 1.26 x 1.26 = 159, usually given as 160. Here's the sequence from ISO 50 to ISO 1600 in 1/3 stop steps.
50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1250, 1600
|Optical (Neutral) Density||0.3||0.6||0.9||1.8||2.6||3|
If you buy an "ND2" or "2ND" filter, just be sure whether that "2" is a filter factor (in which case it's a 1 stop filter), a stop factor (in which case it's a 2 stop filter) or an OD factor (in which case it's a 6 and 2/3 stop filter).