Download Lab: Inverse Square Law

NGSS HS-PS4-1 and NGSS HS-PS4-3.
The Inverse Square Law of Light
Purpose:


To demonstrate that the brightness of a source of light is a function of the inverse square of its
distance.
To understand how the brightness of light could be used to measure distances, even to stars
and far away galaxies.
Hypothesis:
1. Predict what you think will happen to the brightness of the light as the distance is
increased.
2. Predict what you think the relationship between the distance to the light and the measured
brightness is.
Introduction:
As light travels from a source it spreads out equally in all directions. The brightness of the light is
the power (energy per second) per area. We all know that a light, such as a candle or a streetlight,
looks dimmer the farther away from it we get. But how does the brightness change with distance?
The question of how much dimmer it looks was answered a long time ago. This activity gives an
easy way to repeat that discovery. You will use a simple light source and measure its brightness on
a piece of graph paper at different distances. Then, you will graph the data and discover the
mathematical relationship between brightness and distance.
Materials:
 Mini-Maglite.
 Shade box
 Piece of white paper, 10.5 by 13
 Transparent tape
 Metric Ruler
 Graph paper
 Calculator
Procedure:
1. Set up a data table like the one shown below. The table should have enough rows for at least 9
measurements.
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NGSS HS-PS4-1 and NGSS HS-PS4-3.
Distance from
bulb (cm)
# of Squares
Illuminated
Area Illuminated
(cm2)
Relative
Brightness (cm -2)
2. Set up Shade Box as shown above. The sides of the box are connected. Put the third side on top
and secure it with a SMALL amount of tape.
3. Tape a piece of graph paper to the back wall of the shade box. Please use tape sparingly.
4. On the long sides of the white paper, use a ruler and pencil to measure and mark notches for
each centimeter. Draw straight lines joining the notches at 4, 5, 8, 10, 14, 15, 18, and 20
centimeters. Put this paper on the floor of the shade box.
5. Convert the Mini-Maglite into candle mode by unscrewing the flashlight head to expose the
bulb as shown above. Place the head face down on the table. Put the flashlight barrel into the
head. This is important for stability and to ensure the light is the correct height. CAUTION:
Avoid touching the bulb because it gets hot.
6. Slip the Mini-Maglite into the holder. Place the holder opposite the graph paper in the box. The
square of light made when the light shines through this hole will shine on the graph paper, as
shown below.
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NGSS HS-PS4-1 and NGSS HS-PS4-3.
7. Start with the bulb at a distance of 10 cm from the graph paper (The window card should be
pressed up against the graph paper. Count how many squares on the graph paper are lit and
record the distance and number of illuminated squares in your data table.
8. Continue moving the light assembly farther from the graph paper, to each of the marked off
distances. Record the bulb distance (always add 10 cm) and the number of square illuminated
for each trial.
Tip: Outline the lit region with a pencil and then count the squares. For successive
measurements you just need to add the new number of squares to the previous number of
squares.
9. Reassemble the Mini-Maglite and twist to turn off the light.
10. Measure the sides of the squares in the graph paper to determine the area of each square.
11. Calculate the area illuminated at each distance measured, and record it in your data table.
What we are interested in knowing is how distance affects the amount of light that falls on each
square. The amount of light received per area is called brightness. The amount of light given off
by the bulb and passing through the hole in the card always remains constant. So, what we want
to calculate is the brightness relative to some standard brightness (say the brightness of the bulb
on the graph paper at 10 cm). Let’s look at the relationships mathematically. We call brightness
B, Area A, and the amount of light (also called power or luminosity) L and we can write the
following:
B
L
L
for any distance and B0 
for your standard distance (10 cm)
A
A0
So the relative brightness
B
A
is o (The L cancels out because it is the same for both).
B0
A
12. Calculate the relative brightness for each distance using the formula B/B0 = A0/A, and record it
in your data table.
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NGSS HS-PS4-1 and NGSS HS-PS4-3.
13. Make a graph of the relative brightness as a function of distance putting distance on the x-axis
and brightness on the y-axis.
Questions:
1. What is the general shape of the plot of brightness versus distance?
2. After examining your graph what can you conclude about the relationship between the light
intensity and distance? (Is it directly proportional, inversely proportional, proportional to the
inverse square, etc.?)
3. Do your results support your predictions?
4. Using your completed graph for reference, if the relative brightness is 0.60, what would the
distance of the light source be?
5. If the distance of the light source increased to 40 cm, how would its relative brightness
change?
6. Two stars (A & B) have the same relative brightness. Star A is at a distance of 100 light-years.
Star B is at a distance of 400 light-years. Which star is more luminous and by how much? Show
your work.
7. Two stars (C & D) are the same type of star and have the same luminosity. Star D appears to
have only 1.2% of the brightness of Star C. Star C is known to be 20 light-years away. How far
away is star D? Show your work.
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NGSS HS-PS4-1 and NGSS HS-PS4-3.
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