Reciprocity and Exposure Math in the Digital Age
Basic exposure theory states that there is a reciprocal relationship between shutter speed and aperture. Increase one and you have to decrease the other by the same amount to compensate. That's how I learned it back in the day at least. But it's time to rethink reciprocity in the digital age.
Long ago, in the land of film photography, there were indeed just two primary variables that together determined exposure. The analogy was often given of a water faucet controlling how much water made it into a bucket. That bucket was your exposure. To achieve the same net volume of water in that bucket, you could open the spigot all the way for a short amount of time, of only open it partway for a longer time. The size of the opening in the spigot stood for the size of your aperture opening in this analogy, and the time you left the faucet running corresponded to the time you left the shutter open.
Any combination of opening diameter and time that together resulted in a given amount of water making it into the bucket could be considered equivalent. Any combination of aperture and shutter speed likewise that resulted in the same amount of light reaching your recording medium would result in the same exposure. If you increased one, you had to compensate by decreasing the other by the same amount. In the world of photography, the units we use to measure these amounts is of course the stop. Doubling or halving either aperture or shutter speed results in a change of one stop. Add a stop to one by doubling it and you have to subtract a stop from the other by cutting it in half.
This all makes perfect sense and constitutes the foundation of exposure theory. But it's never told the complete truth.
For one thing, there have never been just two variables. On equal footing with aperture and shutter speed, ISO sensitivity has equal weight in determining exposure. This holds true regardless of whether the recording medium is film or digital. Even though it is obviously easier to change ISO with digital today than it was with film back in days of yore, it's always been possible to change the ISO. Today, all that is necessary is to rotate the ISO dial. Back then, you had to open up the camera and change to a film with a faster or slower ISO speed. The ISO sensitivity was an inherent aspect of a given film stock. That was a pain. I generally only considered shifting ISO when I finished each roll of film, although it was possible to rewind a partially used roll and then later use a little device known as a film leader retriever to reach inside the cartridge in order to catch the film sprockets and pull the end back out so the roll could be reloaded into the camera. Yes, that was a pain.
I presume the fact that changing to a different film ISO was such a pain that it was often neglected as a variable when teaching about exposure. It really doesn't fit well with the water faucet and bucket analogy either, but I think I'm on firm ground in assuming somebody would have come up with way to do so if changing ISO weren't such a pain. The ease with which it is possible to change digital ISO today though means it's time to rethink reciprocity. If you open up the lens aperture by one stop you don't have to cut the shutter speed in half to keep the exposure the same. You can decrease the ISO by half instead.
Back in the film era there used to be a think called "reciprocity failure" that affected really long exposures. In terms of the faucet and bucket analogy, you could think of reciprocity failure as being evaporation. Over a sufficiently long exposure time, not only did water flowing out of the spigot make its way into your bucket, some portion of the water already in that bucket would be lost due to evaporation. The amount lost was negligible at normal shutter speeds, but over progressively longer exposure times, that amount could no longer be ignored. To compensate, it was necessary to artificially add extra exposure time to make up for the loss. Different film emulsions suffered from this problem to differing degrees, but no film was completely immune. Thankfully, digital sensors don't really suffer from reciprocity failure at all, and we can safely ignore this quirk.
But long digital exposures can adversely be affected by another factor: noise. Unless the temperature of your camera sensor is down at absolute zero, whatever thermal energy it does possess can result in random electrons "leaking" out and being recorded on your media. Early digital cameras suffered horribly from noise, but from long exposures and from raising the ISO too high. Fast ISO speeds meant that the camera sensor was capable of exposing an image quite quickly, but the small amount of light that could reach the sensor in such a short time could be easily overwhelmed by noise. As such, digital photographers were initially hesitant to shoot at high ISO settings, preferring instead to keep the ISO dial pegged at the slowest setting their camera natively supported.
This hesitance was both understandable and generally well warranted in order to achieve the best image quality possible with early generation digital cameras. Nobody liked noise, and those photographers converting from film were accustomed to fine grained films having slow ISO speeds. Everyone could continue to ignore ISO speed for the most part, only even considering raising it as a last resort to avoid noise. And so discussions of exposure as being a reciprocal pairing of shutter speed and aperture continues, and the analogy of the faucet and bucket continued as the clearest way to teach exposure theory.
But today, all three exposure variables are on equal footing. Current digital cameras do remarkably well at ISO speeds higher than we could ever consider back in the days of film or early digital. Nowadays, the fact that the ISO dial is so easy to rotate matters. Today, it makes more sense to think of these three variables as each controlling something different. You can pick an aperture based on the depth of field you are looking for, select a shutter speed as needed to freeze or blur motion the way you want, and then balance things out by selecting the ISO you need for your desired exposure. Thinking in terms of reciprocity tends to perpetuate the myth that you have to increase exposure time if you close down the aperture, and vice versa.
I don't really have an analogy for teaching exposure that works any better than the faucet and bucket model, but I think we need one. The idea of reciprocity in terms of just two variables doesn't tell the full truth.
It's time to rethink reciprocity in the current digital age.