Understanding

the Inverse Square Law

          • Light
          • Magnetism
          • Gravity
          • Sound

The closer you are, the brighter the light looks!

The stronger the magnet seems!

The harder gravity pulls you!

The louder the sound is!

The Inverse Square Law

     We have all noticed that far off lights seem small and dim, and that distant voices are hard to hear. When we are next to a light source we receive all its brightness, and even very small sounds are audible when we are next to their source.Brightness and loudness grow less as our distance from them grows, and they do so in a way that scientists can measure. Try this activity to get a feeling for what scientists found out.

     Our important measure is one. It might be one city block or one mile or one AU (the distance from earth to the sun). When we get to two, the same thing always happens: the same amount of light energy or sound or magnetism or gravity that we had at one now has to be spread across (2 * 2) times as much area. Therefore light looks fainter and sound intensity drops away. Before we start, let's model the fading away with peanut butter. Watch!

 How Many Slices of Bread

 

This slice gets all the peanut butter!

 
Each slice gets only a quarter of a spoonful of peanut butter

 
One ninth of a spoonful !

Just
a
little
dab
will
do
it!

How Much Peanut Butter

 

 
 Distance

 1

 2

 3

 4

 Multiply the Distance by itself

 1 * 1 = 1 slice

 2 * 2 = 4 slices

 3 * 3 = 9 slices

 4 *4 = 16 slices

Hands-On Activity
 Materials for each person or group 0 one inch squares (with stick-on backing)
an object to represent the light source (a big sequin)
one half sheet of tag board (8.5 x 11 inches)/2
1 inch pipe cleaner
10 inch pipe cleaner
scissors
1. Measure your pipe cleaner. Mark it at one inch intervals. Cut it to make pieces that are one inch long, two inches long, three inches long, and four inches long.

2. Take a pipe cleaner and the one inch squares that are in your packet. Use the pipe cleaner and the squares to lay out a square like this. Do not remove the paper squares from their backing yet.

 

Example:

 

 

 

This is a pipe cleaner.
It is 3 inches long.
 Put three one inch squares along the pipe cleaner.  Turn the pipe cleaner.
Put squares along it.
 Fill in the spaces to make a big square.  Now you have a group of squares (an area) that we call three squared.

3. Do this with all your pipe cleaners. You will have four squares of different sizes.

4. Now find the piece of tagboard that most closely fits each set of squares. Remove the squares from their backing and stick them onto the tagboard. There will be some tagboard with no squares on it in each.
 5. Your tagboard will look like this:

 
  6. Fold the part without squares on it so that your squares will stand up like this:  

7.  Put your little sun marker down on your table.
8. Put the different lengths of pipe cleaners around your sun, like this:      9. Now put the little groups of squares down beside the matching lengths of pipe cleaners, like this:

 

 

   

 __1__
(4 * 4 )

 

 __1__
( 3 * 3 )

 

 __1__
( 2 * 2 )

 __1__
( 1 * 1 )

     You can see how you can use the distance measurement to make the square of the distance. The number of smaller squares tell you how many parts the original light (or sound, or magnetic force or gravity) has been spread over now. Scientists express this as a fraction, dividing the light on the original square by the numbers of squares in the square of the distance.


© 2000. Elizabeth Anne Viau. All rights reserved. eviau@earthlink.net
World Builders Web Site: http://curriculum.calstatela.edu/courses/builders/