PhysicsLAB: Inverse Square Relationships

Paint spray travels radially away from the nozzle of the can in straight lines. Like gravity, the strength (intensity) of the spray obeys an inverse-square law.

distance

area

thickness

3 meters

4 meters

Refer to the following information for the next two questions.

A small light source located 1 meter in front of an opening of area 1 m² illuminates a wall behind. If the wall is 1 meter behind the opening (2 meters from the light source), the illuminated area covers 4 m².

How many square meters will be illuminated if the wall is

5 m from the source?

10 m from the source?

Now, hold your bands outstretched, one twice as far from your eyes as the other, and make a casual judgment as to which hand looks bigger. Most people see them to be about the same size, while many see the nearer hand as slightly bigger. Almost nobody upon casual inspection sees the nearer hand as four times as big. But because your vision depends upon an inverse-square law, the nearer hand should appear twice as tall and twice as wide, and therefore occupy four times as much of your visual field, as the farther hand. Your belief that your hands are the same size is so strong that you likely overrule this information. Now if you overlap your hands slightly and view them with one eye closed, you’ll see the nearer hand as clearly bigger. This raises an interesting question: What other illusions do you have that are not so easily checked?

Some of the physics laws that obey an inverse square relationship are intensity of light and sound as well as electric and gravitational field strength.