Teaching Tips: Inverse Square Law

Have you ever noticed that a campfire illuminates the faces of all who sit around it quite well, but when you go off to your tent for more marshmallows the light dwindles down to almost nothing? You've probably observed the same with sound—your headphones seem to be loud enough when up against your ears, yet you can only barely hear them when you rest them against your neck. This is all due to an effect known as the Inverse Square Law, and it applies to many natural phenomenon including light, sound, radiation, and gravitation.

The Inverse Square Law can be explained in several ways, but it is probably best to take a step-by-step approach with something simple like a light bulb. You can try this with your class.

Cover a light source with some opaque material that lets no light escape. Then, put a small pinhole in the material to let out a one-dimensional beam of light. Now, whether you put your hand an inch from the light source or a few yards away, the light intensity in your palm from the small beam escaping from the pinhole is about the same.

Add a second dimension by cutting a slit in the material so that a fan of light escapes. The light now has another dimension to spread out into. If you put your hand a few inches from the source and slowly back away, you'll see that the intensity changes quite a bit. While you will see the entire slit on your hand when it is very close to the source, at a large distance you will see that your hand only covers a small part of the arc of light and therefore only receives a small part of the energy. The light's intensity is inversely proportional to the distance, I = 1/d or I = I0/d.

Finally, if you cut a square from the material to allow a third dimension, you'll see even more spread. Now the light, and thus its energy, can spread in two directions. Again, if you place your hand near the cutout you will see the full bright square in your palm, but as you move away, the intensity drops quickly and the square no longer fits in your hand. Since it is spreading in two directions and s throughout a square area, the intensity falls in inverse proportion to the distance squared, I = 1/d2 or I = I0/d2.