While writing another article which contained reference to photographic exposure, a thought occurred to me, one that simplifies understanding the relationship between f-stop, shutter speed, and ISO.

For the purposes of this article, we are going to need some definitions. These are not made up definitions, they are scientific in nature.

Exposure -
Exposure = Intensity x Time

Intensity is how bright, time is how long.

That is pretty simple. We have the luminance of the scene that passes through the lens and the length of time the shutter is open. That’s it. We can regulate the intensity through the use of an iris, or f-stop. Shutter speed is regulated by the shutter speed settings on the camera. Because of the mathematical nature of exposure, these two quantities work together.

These two settings, f-stop and shutter speed, regulate the light passing through the lens. These are located on one side of the camera. On the other side of the camera, usually the back, we have a photo sensitive material.


Sensitivity -
Sensitivity is the degree of response to light, preferably for this discussion within the visible spectrum. This sensitivity is given a rating which is defined by the International Standards Organization (ISO). The greater the numerical value the more sensitive to light the material is. Again, this is pretty simple.


There are a few other related concepts that are important to keep in mind, but we won’t concern ourselves with those, in detail, at present. Those concepts are shutter speed determining how fast the image is captured. If one is trying to capture moving subjects a faster speed is advised. f-stop affects depth of field. The smaller the f-stop the larger the depth of field. Now that we’ve mentioned those, we can put them aside. We are concerned with the relationship of shutter speed and f-stop (exposure), and ISO (sensitivity).

Now, let’s see how the two subjects of our discussion interact with one another. I know we’ve all been exposed to the Exposure Triangle. So, now, let’s forget that we’ve ever seen it.

Again, we are concerned with two items on one side of the camera, and one item on the other. This is the system with which we are going to do some mental exercises.

We are going to imagine this system is a beam balance scale (see below for the illustration). The balance works such that when the weight on one side is equal to the weight on the other, the beam of the scale is horizontal, as shown below.

One the left side, just for a matter of choice, let’s put two weights. One weight is labelled f-stop, the other shutter speed. On the other side of the scale, we are going to put a weight labelled ISO.

The concept is that we have to keep the scale balanced. If we change the amount of weight labelled f-stop, we’re going to have to change the weight labelled shutter speed to maintain that balance. A smaller amount of f-stop requires a larger amount of shutter speed to maintain equilibrium. Conversely, a smaller amount of shutter speed is going to require a larger amount of f-stop.

Now, if we change the ISO side, we have to change either one or the other, or both f-stop and shutter speed to compensate. That is actually how simple the relationship is. It’s not complicated at all.

The additional matters that one needs to keep in mind are, as mentioned earlier, depth of field, stopping motion, etc. This is why taking a photograph becomes more of a system management exercise than just pointing a camera and clicking a shutter. There are trade offs to be made. You, as the photographer, manage these trade offs. And that is the essence of photographic exposure.
--Bob

Bob, that is an interesting spin. And useful if it helps others understand with a different picture in their mind. I find the "term" exposure triangle a bit misleading or useless. Though I am pretty sure your balance(ing) model is not new. In fact I have probably been thinking that all along as I learned Chemistry and Physics before Photography. Balancing methodologies are fairly common to Science. And you are correct including time the way you did even though a couple people were trying to slip around it somehow.

I found this and it seems to make sense to me, units (in the metric system) are m^2/(sec-cd) in other words meter squared per second-candela. This is derived from the exposure equation (N^2/t) = LS/K, where N is your f-stop value (focal length divided by iris diameter, unitless), L is luminance in candela per square meter, S is your film speed (ISO) and K is a unitless constant. If you just solve for S you end up with units of area divided by (time x light).

Might be time to check the old Physics Textbook or the CRC Handbook of Chemistry and Physics.

If you just want to give yourself a headache, take a look at this, or try to read it. https://en.wikipedia.org/wiki/Exposure_(photography)