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Understanding why guide number math works

From: Lighting for Photographers: Flash Exposure Fundamentals

Video: Understanding why guide number math works

In this movie, I'm going to take a moment to review how the flash to subject distance and the aperture scales relate to one another. And then we're going to look at how we can use this information to maintain equivalent exposures when we're working with small strobes. Remember, the square root of 2 is an integral part of the Inverse Square Law, which we use to calculate the change in illumination when the flash to subject distance changes. It's also an integral part of calculating the size of an aperture. And an aperture is nothing more than a circle, and you may recall that the formula for the area of a circle is Pi R squared.

Understanding why guide number math works

In this movie, I'm going to take a moment to review how the flash to subject distance and the aperture scales relate to one another. And then we're going to look at how we can use this information to maintain equivalent exposures when we're working with small strobes. Remember, the square root of 2 is an integral part of the Inverse Square Law, which we use to calculate the change in illumination when the flash to subject distance changes. It's also an integral part of calculating the size of an aperture. And an aperture is nothing more than a circle, and you may recall that the formula for the area of a circle is Pi R squared.

Because Pi is a constant that doesn't change no matter how big or how small the circle, we can ignore it while determining the relative change in the size of the aperture. You probably already know that if we double the area of the circle, we'll create a one stop increase in the size of the aperture. And life would really be simple if the formula read area equals Pi times R because each time the radius is doubled, the area of the circle would double. In that world, a one-stop change from a 5 would be f/10 instead of 7.1.

Unfortunately, the formula demands that we use R squared, not R. This means that the area doubles when the radius increases by the square root of 2. If you look carefully, you'll notice that one-stop increments on the aperture scale are separated by a factor 1.4, which you'll recall from our previous discussion of the Inverse Square Law is equal to the square root of 2. As a result, 1.4 dominates the guide number scale, the flash to subject distance scale, and the aperture scale.

When we look at them together, their similarities become obvious and therefore useful. An understanding of how the square root of 2, or 1.4, is used to determine the change in both the aperture size and the flash to subject distance helps you to use the scales to solve problems more quickly, even when shooting in TTL mode or using big strobes. We alluded to this earlier, but now let's demonstrate the results of making offsetting adjustments to flash to subject distance and aperture.

Remember, the guide number for this flash on this camera is 90. So, I started shooting at f/18 from a distance of 5 feet. I opened up the lens in one-third stop increments, while compensating by backing up the flash in one-third stop increments until I got to a distance of 18 feet, and an aperture of f/5. Now, let's review the series of images. As expected, we see the depth of field changes. In addition because I move the flash, the position of the shadows changed and the level of illumination on the background changed.

However, if you focus on her face, you'll see that I was able to maintain equivalent exposures throughout the entire series. This proves that a change in aperture when offset by an equal change in the flash to subject distance results in an equivalent exposure. Once you've learned the scales, and you know your guide number, you'll know exactly where to place the flash to match your aperture. At first, this may sound like a lot of work in a TTL enabled world, but when you get the hang of it, you can really move fast in response to changing circumstances.

So, no matter what your shooting style, there are times when this level of manual control can really save the day.

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