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The amount of illumination falling on a subject is a function of two variables, the power of the flash, and the flash to subject distance. We can control the amount of light falling on the subject by adjusting either one of these variables. We're going to talk about the power output of small strobes in great detail when we discuss guide numbers and power ratios, but first let's tackle the Inverse Square Law and learn how to predict the effect that changing our flash to distance has on illumination. At first this may seem like a lot of math, but stick with me and you'll see how this pays off once you understand how it works.
Intuitively, we know that the closer we move the light to our subject, the more illuminated the subject becomes. Unfortunately, this is not a linear progression. On the face of it, it seems that if you cut the flash to subject distance in half, you would double the amount of light falling on the subject. Unfortunately, this is not true. Instead the change in illumination is inversely proportional to the change in the flash to subject distance. As you can see by looking at this graphic, the light illuminates in ever larger areas that spreads out from the flash.
But the intensity of the light diminishes the further it gets from the source. The underlying formula that is used to describe this change is the Inverse Square Law. It reads intensity equals 1 over the flash to subject distance squared. If we want to reduce the exposure by one stop, we know we have to reduce the light falling on our subject to one-half of the original amount. To achieve this, we have to move the flash back from our starting point by a factor that when squared is equal to 2.
Let's start by assigning a theoretical value of 1 to our current flash to subject distance. When we apply the Inverse Square Law, we see that the difference in intensity between our theoretical value of 1 and 1/2 in the formula is indeed equal to the square root of 2. Because the square root of 2 equals approximately 1.4, the resulting formula to achieve a one-stop change is 1/2 equals 1 over 1.4 squared.
Therefore, an increase in the flash to subject distance by a factor of 1.4 times the original distance creates a one-stop change in the amount of light falling on the subject. This allows us to multiply or divide any flash to subject distance by 1.4 to determine how far to move our flash for a one-stop change. If instead we want to make a two stop change, we know we have to reduce the intensity of light to one-quarter to the original amount.
By applying the Inverse Square Law, we know that we have to double the distance to achieve our goal. Because 1/4 equals 1 over 2 squared. Let's look at the visual effect of this in a series of images. I took these with my flash at full power, my ISO at 100, and my aperture set to f/8.0. I started the series with my flash 5.6 feet from the subject and moved the flash back in full stop increments. I applied the Inverse Square Law and multiplied 5.6 by 1.4.
This gave me 7.84 feet, which gets rounded to 8. So I moved the flash back to 8 feet, took a shot, and the resulting exposure was indeed reduced by one stop. I then multiplied 8 by 1.4 to get 11 feet. I repeated the process to get 16, and once again to get 22 feet. Notice that when I double the distance, I got a two stop change. Understanding this simple phenomenon allows us to work very efficiently and determine our flash to subject distance.
As expected, as I move the flash back, the amount of light falling on the subject decreased. What's exciting is that it decreased in a predictable manner as governed by the Inverse Square Law. It should also be clear from this series that the flash to subject distance clearly affects the flash exposure. You probably also notice that the flash to subject distance scale looks an awful lot like the aperture scale. This realization is really powerful. Once you understand that you can create equivalent flash exposure simply by making off setting moves in your aperture and flash to subject distance, you're well on your way to mastering the fundamentals of flash photography.
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