Yes, it’s true: If you want to make the background darker, you can usually do this by moving the light closer to the subject. Here’s why.
Let’s assume a subject is 10 feet in front of the background, and the light is 10 feet in front of the subject, and let’s say the correct exposure for the subject at ISO 100 is 1/125th at ƒ/8. If the background is, in reality, a white wall, we know that it will appear darker due to the light falling off as it travels farther from the subject to the background. And, in fact, we can know exactly how much it will fall off: two stops. That’s because of the inverse square law, which says light will fall off in brightness by two stops with every doubling of distance from the source. So the white background at 10 feet behind the subject, with the light 10 feet in front of the subject, will fall off precisely two stops—making it appear light gray. Here’s where it gets interesting.
If you move that light five feet forward, halving the distance between the light and the subject, we know the inverse square law means it will get two stops brighter. So now the correct exposure for the subject will change from ƒ/8 to ƒ/16. And because the background is still 10 feet behind the subject, and the light has fallen off two stops by the time it has traveled five feet beyond the subject (double the distance from the source to the subject), that additional five feet will make the background get another stop darker. (It would need to be 15 feet behind the subject in order to fully double the falloff to four total stops, which would render a white background—actually on the darker side of middle gray.)
I know this is a lot of math to wrap your head around, but it’s such a useful lighting principal that it’s totally worth it.
In practice, this means that when working with a subject and a white wall as a background, with a single light source and enough space to work, you can achieve everything from a bright white background to a dark black one.
To make a white background, position the subject very close to the background—right up against it, in fact. Then, move the light very far from the subject; let’s say 20 feet. With the light that far from the subject, and the subject just a foot in front of the background, the light won’t fall off but a fraction of a stop, rendering the background as it really is—white.
To make a black background, move the subject very close to the light source. In this case, even without moving the light, you could pull the subject all the way up to the light, just a foot away from it, and the background would now be 20 feet behind. The exposure would certainly change with the subject now just 1 foot from the light, and the background will read several stops darker due to the fall-off. Let’s do the math.
With the subject 20 feet in front of the background, and the light just one foot in front of the subject, the light falls off two stops at one foot behind the subject (because that’s now double the distance and two feet from the light). Double the distance again to three feet behind the subject (four feet from the source) and it’s two stops darker still. Eight feet from the source it’s two stops darker again, and 16 feet from the source it’s another two stops darker. That’s a whopping eight stops darker—and then some—by the time the light reaches the background 20 feet beyond the subject. And what does a white wall look like when it’s eight stops underexposed? That’s right: it looks black.
Understand the inverse square law and the way light falls off over distance, and you can use creative lighting techniques to achieve a variety of different looks—even if you’re working with just one light.