Beyond the Basics The Inverse Square Law and Depth of Light
The concepts of the inverse square law and depth of light are so essential to lighting that we need to go into them a little deeper. The diagram below shows what happens when light leaves its source. The diagram shows two models. Let’s say that the first is about one foot from the softbox and the second is about two feet, or twice as far, from the light. Notice that the spread of light is much greater at invisible line C–D than it is at invisible line A–B. The light is covering twice the height (approximately, in this drawing) at double the distance. Remember that it is also covering twice the width, so in actuality it is covering an area that is four times as great when the distance from the subject is doubled. Technically, the amount of light has not changed, but it has dispersed a great deal, so the same amount of light must now illuminate a much greater area. Therefore, the exposure value at a given point will be less. The
same amount of light is illuminating more space, so it will be dimmer across the spread, but how much dimmer? The falloff in the exposure value of the light is in the same relationship as its spread. In this case, we doubled the distance and quadrupled the spread. The exposure value at C–D will be 1/4 of that at A–B. This is what the name of the law means: light falls off at a rate of 1/distance2. Here we doubled the distance, so it becomes 1/2, and 22 is 4, so the light value at C–D is 1/4, or 2 stops less than at A–B. It works the opposite way too. The light is illuminating 1/4 of the area at A–B, so it is 4 times more intense, or 2 stops greater, than at C–D. Let’s use actual f-stop numbers to illustrate this further. I will arbitrarily assign the exposure at A–B a value of f/11. The exposure value of the same unchanged light at C–D would be f/5.6. Now, here’s what I think is the hard part about all of this: we know that the light at C–D covers 4 times the area
covered at A–B. What this also means is that the exposure will change more rapidly at A–B than at C–D. As the light expands, its exposure value stays consistent over longer distances because it is covering more space—the intensity is less, but the exposure stays consistent over a deeper portion of the image. On the following page, we will examine three photographs of Flora, our beautiful model who sat in for this demonstration. Flora sat 2 feet from the brick wall for each of these images. A 30x40-inch softbox was set at 2 feet, 4 feet, and 8 feet respectively. The exposure for each image was f/8 at 1/125 second. The exposure is consistent across the three images because we changed the power of the strobes to balance each one. I’ll tell you what the initial exposure was at each distance. Pay attention to three things in each image: the size of the specular highlight, the shadow Light expands in all directions. As we saw earlier, you can control and narrow the direction and beam of light by choosing a light modifier. However, light will begin its expansion once “released.” This diagram, though not drawn to exact measurements, shows how light from a softbox expands. Note that only the vertical expansion is shown here: the light follows the same trajectory along the horizontal plane as well—in fact, it follows the same path along every possible trajectory.