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We all know that the farther away we get, the dimmer a light will look. The question of how much dimmer it looks was answered a long time ago. Here’s an easy way to repeat that discovery.
If you are using metric units:
Keep the distance between the bulb and the card with the square hole constant at one inch. (If you are using metric graph paper, we recommend a distance of 2 cm.) Put the graph paper at different distances from the bulb, and count how many squares on the graph paper are lit at each distance (click to enlarge diagram below). The results will be easier to understand if you make a table of “number of squares lit” versus “distance.” Be sure to measure the distance from the graph paper to the bulb each time.
As you move the graph paper, light from the Mini Maglite spreads out equally in all directions. As the distance from the bulb to the graph paper increases, the same amount of light spreads over a larger and larger area, and the light reaching each square becomes correspondingly less intense. For example, adjust the distance from the bulb to the graph paper to 1 inch. At this distance, the graph paper touches the card. A single square (measuring 1/2 inch) will be illuminated. When the graph paper is moved 2 inches from the card, four squares will be illuminated on the graph paper. When the graph paper is moved 3 inches from the card, nine squares will be illuminated. At 4 inches, sixteen squares will be illuminated, and so on. The area illuminated will increase as the square of the distance. (If you are using metric graph paper, try moving the graph paper at 2-cm increments.)
The intensity of light is the power per area. Since the energy that comes through the hole you cut is spread out over a larger area, the intensity of the light decreases. Since the area increases as the square of the distance, the intensity of the light must decrease as the inverse square of the distance. Thus, intensity follows the inverse-square law.
The inverse-square law applies not only to the intensity of light but also to gravitational and electrical forces. The pull of the earth’s gravity drops off at 1/r2, where r is the distance from the center of the earth. The attraction or repulsion between two electric charges also decreases with the distance at 1/r2, where r is the distance between the two charges.
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Attribution: Exploratorium Teacher Institute