Name____________________________
Inverse Square Law Activity
Use the light bulb simulator on the course website to complete this activity.
Dependence of Brightness on Luminosity
1) The simulator allows you to set the luminosity of the light bulb (given in watts)
using the dial to the left of the light bulb. You can also click on and move a
brightness detector toward or away from the light bulb to see how the brightness
changes. We will work with just the top light bulb.
2) Set the luminosity of the bulb to 20 watts and place the brightness detector at a
distance of R = 1 meter away from the light bulb. Record the brightness in the
table below.
3) Now change the luminosity to 50 watts and record the luminosity below. Do this
for all of the remaining luminosity settings.
Luminosity (Watts)
20
25
50
100
400
500
Brightness (Watts/m2)
4) Looking at the numbers in your table, if you double the luminosity, by what factor
does the brightness change? In other words, is the brightness now twice as large,
three times as large, four times? Don’t estimate here; actually divide the higher
brightness number by the lower brightness number on a calculator to see how they
compare.
5) If the luminosity is increased by a factor of four, by what factor does the
brightness change? Give two different examples of this from the table.
6) If the luminosity increases by a factor of 5, by what factor does the brightness
change? Give two different examples of this from the table.
Dependence of Brightness on Distance
7) Now set the luminosity of the top light bulb to 100 watts, and place the brightness
meter at a distance of R = 1 meter. Record the brightness in the table below.
8) Now change the distance of the detector to R = 1.5 meters and record the
brightness below. Do this for all of the remaining distances in the table.
Distance[R] (meters)
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Brightness (Watts/m2)
9) Looking at the numbers in your table, if you double the distance, by what factor
does the brightness change? In other words, is the brightness now half as large,
one-third as large, one-fourth as large? Use a calculator again to determine this.
10) If the distance is increased by a factor of 3, by what factor does the brightness
change? Give two different examples of this from the table.
11) If the distance increases by a factor of 4, by what factor does the brightness
change?
12) If the distance increases by a factor of 5, by what factor does the brightness
change?
Relationship Between Brightness, Luminosity, and Distance
13) We can summarize all of the results above in one equation:
B
L
4R 2
where B is the brightness, L is the luminosity of the light source, and R is the
distance away from the light source. You can see that the behavior you observed
in the previous activities is represented by this equation. If L doubles or triples,
so does the brightness. We say that B is directly proportional to L. On the other
hand, if the distance (R) doubles, then the brightness decreases by a factor of four.
We say that B is inversely proportional to the square of the distance.
14) Let’s try it out. Use the equation to predict what the brightness would be for a
light bulb with a luminosity of 50 watts if you are standing at a distance of 3.5
meters away. Show your calculation below, then check your prediction with the
simulator.
15) Now, imagine that you are standing at a distance of 2 meters from a light bulb and
the brightness you measure is 9.952 watts/m2. Use the equation to determine
what the luminosity of the bulb must be. Show your calculation below, then
check your prediction with the simulator.
16) Now imagine that you are looking at a 100 watt light bulb and the brightness is
0.884 watts/m2. Use the equation to determine how far away from the light bulb
you are standing. Show your calculation below, then check your prediction with
the simulator.