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F-stop numbers

It is important to note that the exposure index is not a direct measure of how well your film will be exposed, since it is independent of film speed. However, the exposure index is an absolute measure of the amount of light which will reach your film.

The aperture range of a camera is a series of numbers which each differ a factor 1.414 (the square root of 2). These are called the f-stops and every f-stop is a factor of 2 in light intensity. This is because the aperture is a measure of the diameter of your lens you are using for light transmission, and since the amount of light is proportional to lens surface area, this explains why the f-stop range goes by a factor of the square root of 2.

The exposure index is a measure of the amount of light to which film is being exposed. It mixes the shutter speed and aperture, which together determine the total number of light quanta (photons) reaching the film during the exposure.

The exposure index is also called the exposure value (EV) or light value (LV).

The EI is defined as follows:

EI = 2Log (F2 / t)

F is the f-stop number: for example, using f/11, F=11.
t is the exposure time in seconds.

EI = 0:
exposure of 1 second at f/1 gives 2Log (1) = 0

Example: you are photographing noctilucent clouds. The light meter indicates EI=-2 at 100 ISO. You need a short exposure time, say 16 seconds maximal, because the clouds move fast. Then the f-stop number is fixed:

-2 = 2Log (F2 / 16)

F2 / 16 = 2-2 = 1/4

F = 2

So you would need an f-stop of f/2 for this 100 ISO film and exposure time.

Now imagine you have a wide-angle lens, with lowest aperture of f/2.8. Because it is wide-angle, you want to choose f/5.6 or higher to reduce vignetting at the edges and increase sharpness. Then you have the choice of either using a faster film, or using a longer exposure time. A longer exposure time creates blurriness (moving clouds) and a faster film is lower-resolution. You have to choose what choice is best for this application. Say you stick to the 16 seconds time. Then:

EI = 2Log (5.62 / 16) = 2Log 2 = 1

now you are 3 stops below the indication (1-(-2)=3), since you did measure EI=-2 for 100 ISO. In this case, I would change the 16 seconds to 32, since the lens is wide-angle so any angular movement of the clouds will be relatively small. I would also use a film which is 2 stops faster than 100 ISO, i.e. 400 ISO. This would be a good trade-off between film resolution, cloud movement and vignetting.

The following table lists some exposure indices as a function of exposure time (shutter speed) vertical, and f-stop horizontal. The table can of course be expanded in any of the four directions, albeit that the ranges given below suffice for most weather photography.

f/1 f/1.4 f/2 f/2.8 f/4 f/5.6 f/8 f/11 f/16 f/22 f/32
60 s -6 -5 -4 -3 -2 -1 0 1 2 3 4
30 s -5 -4 -3 -2 -1 0 1 2 3 4 5
15 s -4 -3 -2 -1 0 1 2 3 4 5 6
8 s -3 -2 -1 0 1 2 3 4 5 6 7
4 s -2 -1 0 1 2 3 4 5 6 7 8
2 s -1 0 1 2 3 4 5 6 7 8 9
1 s 0 1 2 3 4 5 6 7 8 9 10
1/2 s 1 2 3 4 5 6 7 8 9 10 11
1/4 s 2 3 4 5 6 7 8 9 10 11 12
1/8 s 3 4 5 6 7 8 9 10 11 12 13
1/15 s 4 5 6 7 8 9 10 11 12 13 14
1/30 s 5 6 7 8 9 10 11 12 13 14 15
1/60 s 6 7 8 9 10 11 12 13 14 15 16
1/125 s 7 8 9 10 11 12 13 14 15 16 17
1/250 s 8 9 10 11 12 13 14 15 16 17 18
1/500 s 9 10 11 12 13 14 15 16 17 18 19
1/1000 s 10 11 12 13 14 15 16 17 18 19 20
1/2000 s 11 12 13 14 15 16 17 18 19 20 21

[Exposure indices (EI) for different shutter speeds and aperture numbers.]