Exp 32
Light, Brightness and Distance
You probably have noticed that a light appears to be brighter when you are close to it, and dimmer
when you are farther away. If you are reading this page illuminated by a single light bulb, the amount
of the light that strikes this page will increase as the page is brought closer to the light source. Using a
Light Sensor, you can determine how the brightness of light varies with distance from the source and
compare that result to a mathematical model.
There are several ways to measure the brightness of light. Since this experiment can be performed with
any of several different light sensors, each of which measure slightly different quantities, we will just
use the word intensity to describe the relative brightness of the light, although the term may not be
strictly appropriate for your sensor. Regardless of the way light is measured, the same relative changes
with distance are observed, and that is what you will study today. In this experiment you will measure
light intensity at a variety of distances from a small source of light, and see how the intensity varies
with distance.
Figure 1
Be gentle; don’t overtighten the light sensor clamp. You break it, you buy it!
OBJECTIVE

Determine the mathematical relationship between intensity and the distance from the light source.
MATERIALS
Power Macintosh or Windows PC
LabPro or Universal Lab Interface
Logger Pro
Light Sensor
Physics with Computers
81901823
meter stick
clear glass light bulb (1.5 V penlight type)
battery (1.5 V)
Graphical Analysis or graph paper
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Last printed 8/1/2017 12:23:00 AM
Experiment 32
PRELIMINARY QUESTIONS
1. Suppose a small light source is placed at the center
of two transparent spheres. One sphere has a
radius R, and the other a radius 2R. An intensity I
passes through the surface of the inner sphere. If
no light is absorbed, so that all of the light emitted
by the source passes through the inner sphere and
reaches the outer sphere, what is the intensity at
the outer sphere? Solve this problem by
considering the following:
2R
light
source
R
a. How does the rate of photons striking the inner
sphere compare to the rate at the outer sphere?
[Rate = number of photons per s]
inner
outer
b. How do the surface areas of the two spheres
sphere
compare? [Ratio]
sphere
c. In general, then, how will the intensity vary
with distance from the source? Sketch a plot of
Figure 2
intensity vs. distance, letting the intensity at R
be Io. Use distances of R, 2R, 3R, 4R, and 5R. Label the intensities of the other distances as
multiples of Io.
2. Since most light bulbs that you use are not true point sources of light, how do you think the answer
to Question 1 would change if a typical light bulb were used? First, define “point source”.
3. The LoggerPro file has example data. Answer Analysis questions 1 and 2 using this data.
INITIAL SETUP
1. Connect the Light Sensor to Channel 1 of the LabPro or Universal Lab Interface. If your sensor has
a range switch, set it to the 6000-lux range.
2. Make sure that the filament axis of the light bulb is horizontal and pointing directly at the Light
Sensor. This makes the light bulb look more like a point source of light as seen by the Light Sensor.
3. The filament and Light Sensor should be at the same vertical height (Figure 1).
4. Using the scale on the track, record the position of the end of the filament (not the glass).
5. Open the Experiment 32 file from the course outline webpage. A graph will appear on the screen.
The vertical axis of the graph has intensity in units for your sensor. The horizontal axis has distance
scaled from 0 to 20 cm. The Meter window will display light intensity.
6. Turn down the lights to darken the room. A dark room is critical to obtaining good results. There
must be no reflective surfaces behind or beside the bulb. The sensor should be aimed away from the
windows and lit computer monitors.
PROCEDURE
1. Place the Light Sensor 3 cm from the light bulb filament and note the value of intensity in the
Meter window. Make sure that the intensity changes as you move the sensor, otherwise you may
need to switch to a less sensitive scale or use a less intense light source. Move the sensor away
from the bulb and watch the displayed intensity values. What is your prediction for the relationship
between intensity and the distance to a light source?
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Light, Brightness and Distance
2. Click
to begin data collection. Place the Light Sensor as close as possible to (but at least 2
cm from) the light bulb filament. Important: The distance must be measured carefully. Be sure
you measure from the filament of the lamp to the sensor on the Light Sensor.
3. Wait for the intensity value displayed on the screen to stabilize. Click Keep , then type the distance
between the Light Sensor and the light source and press ENTER to record the value of intensity. A
point will be plotted on the graph.
4. Move the Light Sensor 1 cm farther away from the light source and repeat Step 3.
5. Repeat Step 3 moving the sensor in 1-cm increments until the Light Sensor is 10 cm from the light
source. Then move the sensor by 2 cm increments until the separation is 20 cm.
6. Click
when you have finished collecting data. In your data table, record the intensity and
distance data pairs displayed in the Table window (or, if directed by your instructor, print a copy of
the Table window).
DATA TABLE – IN LAB MANUAL
ANALYSIS
Include the graph (with dialogue box(es)) and data table in your lab report.
1. Examine the graph of intensity vs. distance. Based on this graph, decide what kind of mathematical
relationship you think exists between these two variables. On the same graph printout show
dialogue boxes for each of the following and comment on which is the best fit for your data.
If the relationship is inverse, then I = k • 1/d where k is a proportionality constant.
If the relationship is inverse square, then I = k • 1/d2 where k is a proportionality constant.
 If the relationship is inverse square, then I = k • 1/d2 + B where k is a proportionality constant and
B is the vertical translation.


2. Does the function that fits the data best agree with your model of intensity using the concentric
spheres? Explain. Modify your explanation if necessary. Hint: What is the equation for the surface
area of a sphere?
3. List some reasons why your experimental setup might not match the relationship you predicted in
the Preliminary Questions between intensity and distance. An answer of “Human Error” or similar
will result in the deduction of 6.022 x 1023 points from your Physics grade.
EXTENSIONS
1. Confirm the relationship between intensity and distance by finding the linear plot of I = k • 1/d2.
Create a modified column of data with the heading “Distance^-2” to represent 1/d2. Graph intensity
vs. distance^-2. A straight line that passes through the origin would verify the inverse square
relationship.
2. Use the Light Sensor to examine sunglasses. By what percentage is the sun’s intensity reduced
when sunlight passes through the lens of sunglasses?
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Experiment 32
POSTLAB READING
1. http://imagine.gsfc.nasa.gov/YBA/M31-velocity/1overR2-more.html
http://imagine.gsfc.nasa.gov/YBA/M31-velocity/gravity.html
§5.6 – 5.7 [review connection]
2. Define, compare, and contrast the following pairs of terms. Hyperphysics is a good source.
Wikipedia may not be.
a. radiometry vs. photometry,
b. radiant flux vs. luminous flux,
c. luminous vs. illuminated,
d. illuminance vs luminous intensity.
APPLICATION PROBLEMS – KNOW HOW TO DO
1. A lamp is moved from 30 cm to 90 cm above the pages of a book. By what factor does the
illumination change? [1/9]
2. A 150 W bulb emits a luminous flux of 2275 lm. What is the illumination on a surface 3.0 m below
the bulb? [20 lx]
3. A 64 cd point source of light is 3.0 m above the surface of a desk. What is the illumination on the
desk’s surface, measured in lux? [7.1 lx]
4. The illumination on a tabletop is 20.0 lx from a lamp mounted 4.0 m above the table. What is the
intensity of the bulb? [ 320 cd]
5. A design requirement for a new school is that the minimum illumination of 160 lx on the surface of
each student’s desk. The lights are to be mounted 2.0 m above the desks. Determine the minimum
luminous flux of the lights. [8000 lm]
6. http://imagine.gsfc.nasa.gov/YBA/M31-velocity/1overR2-quiz.html
7. Questions, Chapter 5: 11, 13
Problems, Chapter 5: 28, 29, 30
ADVANCED PROBLEMS – KNOW HOW TO DO
1. A screen is placed between two lamps such that they illuminate the screen equally [this is called a
photometer]. The first lamp emits a luminous flux of 1445 lm and is 2.5 m from the screen.
a. What is the distance of the second lamp from the screen if it’s luminous flux is 2375 lm? [3.2]
b. What is the distance of the second lamp if it’s luminous flux is half that of the first? One-third?
Double? Triple?
2. Two lamps illuminate a screen equally. The first lamp has an intensity of 101 cd and is 5.0 m from
the screen.
a. Determine the intensity of the second lamp if it is 3.0 m from the screen. [36 cd]
b. If the screen is 3.5 cm by 2.0 cm, determine the illuminance of the screen for each lamp.
c. Determine the luminous flux for each lamp.
3. Questions, Chapter 5: 12
Problems, Chapter 5: 31, 32, 33, 37, 41
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