Having always been mathematically inclined, I "picture" (pun intended) the exposure triangle as a mathematical formula something like:
A x B x C = P
Unfortunately, P is an 'indefinite' or non-specific number that I think of as ‘the Perfect Picture’, and depends on the eye of the beholder.
Let me explain:
If A x B x C = 1000 (a constant value), then it’s easy to see that as A increases, then B and/or C must decrease to compensate to get the result of 1000. Likewise, decreasing B, for example, would require an increase in A and/or C. Unfortunately, the exposure triangle not this ‘simplistic’ of a math formula, and there’s intended and sometimes unintended consequences to altering any of the values.
Let’s say A = f-stop value. If a larger f-stop (aperture) is used (numerically smaller value), then, increasing f-stop increases the exposure and therefore shutter speed and/or ISO must be lowered to get the same result. Similarly, if B = Shutter Speed, increasing the shutter-open time (1/x th second, where x is numerically smaller) requires that ISO be decreased and/or aperture must be decreased as well to get the same result.
So, for you mathematicians out there, the formula would actually be something like:
(100 - f/stop) x (1000 - shutter speed expressed without the fraction) x ISO speed = P
Note: I chose 100 as a max f-stop value as I don’t know if f/100 is possible (pinhole, perhaps?). Similarly, I chose 1/1000[SUP]th[/SUP] second as a ‘max’ shutter speed, but in reality it is probably more like 32,000 or something equally as large. 1000 used here for simplicity sake.
The 100 - f/stop calculation is there to give a larger number from smaller f-stop numbers. f 22, for example, would result in a value of 88, and so on. Shooting at f 4 (96 value in the calc) instead of f 22 will result in more light hitting the sensor if nothing else is changed.
Similarly, 1000 - shutter speed is used to give a smaller number the faster the shutter speed (eg, 1/100 sec speed would use only the 100 number in the calculation, giving a result of 900). Longer shutter open times result in larger numbers in this calculation. Decreasing shutter open time (eg, 1/30[SUP]th[/SUP] to 1/100[SUP]th[/SUP]) would therefore result in a smaller number in this calculation, lowering the total exposure value “P”.
Lastly, increasing ISO speed would necessitate a reducing one of the other numerical values in my equation, but in actuality, you'd be increasing the shutter speed (less time open) or going to a smaller f-stop like f 16 or f 22 to still get a good exposure.
Before everybody’s head starts spinning, know that I don’t do any of these ‘complex’ calculations in my head when I go to take a picture. I’m too old for that kind of stuff. Instead, I simply think of it in the simplistic A x B x C = P. Changing any of the three will require compensating (opposite) changes in either or both of the other two to get the same result. I’m not really saying ‘A = f/stop, etc.’ It’s simply A x B x C, without assigning meanings or values of any kind to them.
As mentioned at the top, there’s additional, intended and non-intended consequences when changing ANY of the values.
On the intended side, simply increasing the aperture size and changing nothing else will result in a ‘brighter’ picture, due to more light hitting the sensor. But there’s a limit to how bright is ‘right’. If the picture gets too bright, the highlights wash out. And at the other extreme of under exposure, what’s in the darker areas have no visible details recorded.
Increasing aperture size also DECREASES the depth of field, that portion of the picture where everything is in focus. At f 32 (smallest aperture), almost everything will be in focus (depth of field) that’s farther away from the lens than its closest focal distance. At f1.2, the depth of field is frequently measured in inches, even fractions of an inch for some lenses. Note that narrower depth of field is desirable in some shooting situations to ‘bring out’ the subject of the photo, while making everything else a little or a lot fuzzy, also known as bokeh. Some lenses produce better bokeh than others, depending on their construction and quality (and price). Of course, increasing aperture size requires decreasing either/or shutter open time or ISO.
Making shutter speed adjustments either increases or decreases the total amount of light hitting the sensor. Shutter speed variations are good for making long (often, minutes!) night exposures when the camera is on a tripod. But in most situations, long shutter open times are more like ¼ or 1/10 or 1/30 of a second. The long open time lets in more light, and is useful in situations where nothing is moving. People shots are almost always blurred at these speeds, even if they are sitting down and smiling. Yours (and mine, too) hands will move slightly with every heartbeat as well, and at 1/30[SUP]th[/SUP], there could be a blur. Speeding things up to 1/60[SUP]th[/SUP] can stop ‘slower’ human movement (like holding a pose), but for most people pictures, 1/100[SUP]th[/SUP] or faster is required to stop them for sure. Indianapolis race cars, on the other hand, need shutter times of 1/500[SUP]th[/SUP] second or even faster to ‘freeze’ them in the picture. So, by increasing shutter open time, more light hits the sensor. But subject movement can end up in a blur if too slow. Too fast, and the pictures get dark, unless compensating increases are made to aperature and/or ISO. Shutter speed synchronization with flash units is a lengthy subject in itself, has various added effects, and not a part of this epistle.
ISO is probably the easiest to understand. Think of a bird pecking at seeds on the ground. Some birds peck seeds faster than others. Of course, me armed with a Shop-Vac can clear the ground of all the seeds in a heartbeat or three. ISO is the same. Lower ISO settings are like birds pecking away to gather the necessary light to make the picture. With a Shop-Vac (high ISO setting), all the light is gathered in less than a heartbeat. The problem with using a Shop-Vac in the above example is it also picks up a lot of dirt with the seeds. This is comparable to noise, ie, odd, multi-colored pixels in the resultant picture, mostly visible in darker areas. Slower ISO speeds closer to 100 or 200 rather than 3200 reduces the ‘dirty’ noise in the pictures. How high is ‘high ISO’? It varies from camera maker to camera maker, and even from camera model to model, as well. Generally, the newer the camera, the better the handling of faster ISO speeds…How big is YOUR Shop-Vac?
Of course, there’s even more to the ‘exposure triangle’ adjustment consequences than discussed above, like color density, edge focusing, and other generally pro-level issues. But for me, and for most non-professional photographers, I suspect, the simple A x B x C = P and the consequences described above is more than enough to keep our heads spinning!
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