Abstract

Objective

To determine how the intensity of a point source of light, like a star, changes with distance from that source.

Introduction

Do you love looking at the stars? No, not the Hollywood kind—the ones in the sky! For thousands of years, people have looked up at these faithful pinpoints of light and wondered about those "diamonds in the sky." They've used stars as centerpieces for religions, fuel for legends and myths, tools for navigation, and as predictable calendars for planting crops. In 1584, though, Giordano Bruno suggested that the stars were objects, much like the Sun, just farther away. This idea upset a lot of people, and he was actually killed for this and for other beliefs. It would take more than 250 years for people to accept that Bruno was right and take their first distance measurement from Earth to a star.

Figure 1. A photo, taken by Science Buddies founder Kenneth Hess, of 100 billion stars in the Milky Way at the Golden State Star Party. (Kenneth L. Hess, 2009.)

To find out just how far away a star is, scientists first had to figure out how the brightness or intensity of a point source of light, like a star, changes with distance. They experimented and predicted that the relationship between brightness and distance would follow an inverse-square law. This means that as the distance from a light source doubles, its brightness decreases by a factor of four, (which is the square of the distance). This is illustrated in the drawing below, where the red dot, the point source of light, has a brightness we'll name L₀ for this example, at one unit (it could represent any unit) away from the light; but as you double the distance to two units away, the brightness goes down by a factor of four. At three units away, the brightness goes down by a factor of nine, and so on.

Figure 2. This drawing shows how light follows an inverse square law. Notice that as the distance increases from the light source (the red dot), the light must spread out over a larger surface area, and the surface brightness decreases by the distance squared. (NASA, 2006.)

In this astronomy science project, you will set up an experiment that will allow you to test whether light from a point source, like a star, follows the predicted inverse-square law.

Terms, Concepts, and Questions to Start Background Research

• Intensity
• Point source
• Inverse-square law
• Square
• Factor
• Lux (lx)
• Linear
• Inverse

Questions

• Why do you think stars are approximated as point sources, even though they are much bigger than Earth?
• Based on your research, how is it possible to measure distance and velocity of stars from changes in the brightness of a point source?
• Can you think of any other laws that follow an inverse-square relationship?

Bibliography

This source provides a history of stars:

• Cain, F. (2009, February 10). History of Stars. Retrieved March 17, 2010, from http://www.universetoday.com/guide-to-space/stars/history-of-stars/

These sources explain the inverse-square law for light and how changes in brightness can be used to measure distance and velocity (speed and direction) of a star:

• Newman, P. (2006, January 30). More on Brightness as a Function of Distance. Retrieved March 17, 2010, from http://imagine.gsfc.nasa.gov/YBA/M31-velocity/1overR2-more.html
• Newman, P. (2006, January 30). Observing the Light Intensity of M31. Retrieved March 17, 2010, from http://imagine.gsfc.nasa.gov/YBA/M31-velocity/1overR2-intro.html

Materials and Equipment

• Lux meter, also known as a light meter, such as the Light Meter LX1010B,50,000 Lux Luxmeter with lcd display, available at Amazon.com.
• Measuring tape
• Music stand
• Packaging tape
• Lamp with a round lightbulb (any wattage)
• Room that can be darkened well and cleared of objects in a 6-foot x6-foot area
• Lab notebook
• Graph paper
• Optional: Stool, heavy books, or sturdy box
• Optional: Camera

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Experimental Procedure

Note: A light meter is an instrument that measures the intensity of light, as perceived by the human eye, and is measured in the units of lux (lx). Before starting your experiment, read the instructions that come with your light (lux) meter so that you know how to use it. Practice taking light measurements around your home from different sources. For example, see what kinds of light measurements you get from a lamp (both close to and far away from it); a TV; beside a window, both with and without its blinds; and outside.

Setting Up Your Experiment

1. Clear the room, or push aside any objects in the room, until you have an empty area that is approximately 6-feet (ft.) square.
1. Try to keep very shiny things that can reflect light out of the room.
2. Try to set up your experiment near the middle of the room, away from walls that might reflect light.
2. Attach the sensor (the light detector part) of the light meter to the middle of the music stand with a piece of packaging tape, so that it does not wiggle around. Do not cover the sensor itself with any tape.
3. Remove and set aside the lamp shade from the lamp so that the lightbulb is exposed.
4. If the lamp is short, set the lamp on a stool, heavy books, or on a sturdy box to raise it up so the top of the lamp is at least the lowest height of the music stand.
5. Position the measuring tape so that is directly under the lamp, and extend it 10 feet out.
6. Tape the measuring tape to the floor with packaging tape.
7. Put the music stand close to the lamp (you'll set it at an exact position for testing later).
8. Raise up the music stand until the sensor is at the same level as the lightbulb.
9. Lock the music stand so that the music stand stays at the same height as the lightbulb, and so that the sensor is vertical to the floor. Your experimental setup should now look similar to Figure 3.

Figure 3. This photo shows an example of the experimental setup. Note that the sensor is vertical to the floor (makes a 90-degree angle to the floor) and is at the same height as the point source of light. Also note that one of the legs on the tripod of the music stand is on top of the measuring tape to help with the alignment of the sensor and the point source of light.

Testing How Light Intensity Changes with Distance

1. Create a data table in your lab notebook, like the one below.

2. Turn on the lightbulb.
3. Position the music stand at the 8-inch mark on the measuring tape.
1. Make sure that the vertical rod on the music stand (right below the sensor) is directly over the mark on the measuring tape.
2. Place the leg on the music stand tripod that is farthest away from the light source directly on the measuring tape, as shown in Figure 3.
3. Feel free to start at a closer initial starting point if you are able to physically get closer to the light source.
4. Take a measurement from the light meter and record your measurement in your lab notebook.
1. Be sure you, and any other people around, are standing behind the music stand when you take your measurement. You don't want any people or shadows between the light source and the sensor that might affect your measurement. See Figure 4.
2. Wait about 10 seconds (sec.) for the light meter to settle down to a final value.
3. If it is oscillating between one or two values, then choose the higher one.

Figure 4. This photo shows from where you should take measurements with the light meter, staying well behind the music stand.

5. Move the music stand back 4 inches.
6. Take a measurement from the light meter.
7. Repeat steps 5–6 until the music stand is at the 3-ft. mark.
8. Repeat steps 3–7 two more times for a total of three trials. By running a few trials, you will ensure your results are repeatable and accurate.

Analyzing Your Data Table

1. Calculate the average light intensity for each distance from the three trials and record your calculations in the data table.
2. Make a line graph that plots the distance (in feet) on the x-axis and the average light intensity (in lux) on the y-axis.
3. Look at your graph.
1. Is it linear? Or, does it look like a curve?
2. If it looks like a curve, does the average light intensity increase or decrease with distance?
3. If it looks like a curve, is the average light intensity equal to a constant divided by the distance? Does it follow an inverse relationship? Or, is the average light intensity equal to a constant divided by the distance squared? Do you think light intensity follows an inverse-square law?
4. What happens when you get very far away from the light source? Does the law still hold, or are reflections creating a background light that creates a non-zero baseline intensity? Can you think of ways to reduce reflections in your setup?

Variations

• What happens with a light source that is not a point source, but is directed, like a flashlight? Redo the project using a flashlight. Note: An LED flashlight is not recommended, due to variations in the source light as the flashlight comes to thermal equilibrium. Also, there is a risk of eye damage from looking into an LED flashlight.

• For more science project ideas in this area of science, see Astronomy Project Ideas.

Credits

Kristin Strong, Science Buddies

Last edit date: 2011-11-10 08:00:00