Light at a Distance*

Teacher Version(.doc)

Student Version(.doc)

• Primary Focus: Math; NC Standard Course of Study Areas: 6th: 1.01, 1.04, 1.07, 5.02, 5.04; 7th: 1.02, 1.03, 2.01, 4.01, 5.01, 5.02, 5.03, 5.04; 8th: 1.02, 4.01, 4.02, 5.01b, 5.02, 5.04
  • (Key Concepts:  Linear, Quadratic, Exponential, Inverse and Inverse Square Functions and variables)
• Secondary Focus: Science; NC Standard Course of Study Areas: 6th: 1.04, 1.05, 1.06, 1.07, 1.09, 6.04, 6.05; 7th: 6.05
  • (Key Concepts:  Lumens, Lux, and data collection)
• Computer/Technology Skills: Calculators, Probeware, Data Visualization; NC Standard Course of Study Areas: 6th: 3.01; 7th: 3.01, 3.02, 8th: 3.01
• Essential Question: Why does the brightness of light change as you get closer to it? Can we use a math equation to predict how the brightness changes?
• Summary of Activity: Much of what we observe in our world can be modeled with mathematics.  For instance, have you ever observed while traveling in a car at night, the headlights of an oncoming vehicle?  The light starts as a dim glow in the distance, but as the vehicle gets closer, the brightness of the headlights increases rapidly. This is because the light becomes more focused as the surface it shines upon moves closer. As a result, light intensity increases as the distance from a typical light source decreases. What is the relationship between distance and intensity for a simple light bulb?
• Cognitive Teaching Strategies: In this lesson students explore the behavior of several mathematical functions using a spreadsheet.  Students investigate changing parameters of a particular kind of function to observe the behavior of those functions.  Then, using a light intensity probe they see how one of those functions relates to distance and intensity for a light bulb. The data can then be graphed and modeled mathematically.
• Materials:
  • TI-83 Plus or TI-84 Plus graphing calculator
  • EasyData application
  • EasyLink interface
  • Light Sensor
  • meter stick or tape measure
  • masking tape
  • dc-powered point light source
  • Computer with spreadsheet application
  • Internet connection
  • Electronic copies of tableIO.xls spreadsheet on each computer
  

Procedure:

1. You can motivate the lesson by having the students create and discuss examples of real-world phenomena that could possibly be modeled using mathematical equations.  This would likely require about 25 minutes of time.  If time is short you may just wish to supply several examples yourself.  Examples should probably include at least one linear and several non-linear examples such as time it takes to walk a particular distance (linear), time it takes for a rock to fall from a particular height (quadratic), population growth (exponential).
2. Show students the spreadsheet tableIO.xls.  The spreadsheet is password protected so students can only change the values of the green cells.  If you wish to edit the spreadsheet the password is: function.  Students working in groups of 2-3 per computer work well for this activity.
3. Demonstrate the first function showing students that the behavior is linear no matter which values you input for ‘m’and ‘b’.  Copy and paste the data into the Data Flyer graphing program to look at the data graphically.  Be sure to only copy the numerical values, not the labels of the columns.  When showing the Data Flyer activity be sure to have the “auto-scale” option checked.
4. Have students experiment with the other functions on the spreadsheet by changing values and graphing them.  Students should complete questions 1 and 2 on the Analysis sheet while using the spreadsheet.
5. Using the document camera you may wish to have the students come up and share their responses with the rest of the class.
6. In small groups of 3-4 have students discuss what it means to measure light.  See if each group can come up with how to measure light.  You may want to introduce such terms as Candela, Footcandle, Lumen, Luminance, and Lux.  If you wish to relate the lesson to energy you may also wish to discuss Watt, Kilowatt, and KilowattHour.  Pull the class back together and discuss their responses.  The General Electric website also has some good information o measuring light you may wish to you’re your students read: http://www.gelighting.com/na/home_lighting/gela/students/math_measuring_light.htm
7. Demonstrate the idea of the lumen as a unit of measure by drawing a large square on the board.  Turn off the lights and shine the flashlight in the center of the square.  Slowly walk away from the board while continuing to shine the flashlight in the square.  Have the students describe what they see.
8. Arrange the equipment: 
   1. Secure a meter stick or measuring tape on the table or floor in order to measure distance from the source to the sensor consistently.
   2. Remove any surfaces near the bulb, such as books, people, walls or tables. There should be no reflective surfaces behind, beside, or below the bulb. The filament and Light Sensor should be at the same vertical height.
   3. There must be no obstructions between the bulb and the Light Sensor during data collection. This makes the light bulb look more like a point source of light as seen by the Light Sensor. While you are taking intensity readings, the Light Sensor must be pointed directly at the light bulb. 
9. Set up the Light Sensor for data collection.  Discuss with the students how the light sensor works and what it actually measures.  The Light Sensor will measure from the filament.
10. Turn on the calculator.
11. Set the Light Sensor to 0–600 lux for a small light source, or 0–6000 lux for a larger light source.
12. Connect the Light Sensor and calculator with the EasyLink cable.
13. Set up EasyData for data collection.
    1. Start the EasyData application, if it is not already running.
    2. Reset the application by selecting file->new.
    3. Select Events with Entry from the setup menu.
14. Dim the lights to darken the room. A dark room is critical to obtain good results.
15. Hold the Light Sensor about 10 cm from the light bulb filament. Move the sensor away from the bulb and watch the displayed intensity values on the calculator screen.
16. Answer Question 1 on the Data Collection and Analysis sheet.
17. To account for the particular brightness of your light source, choose a starting distance that gives a reading less than the maximum reading for your sensor (600 or 6000 lux), but as large as possible. However, do not get any closer than 5 cm for small (<5 mm) bulbs, or 10 cm otherwise. Choose the starting distance, and enter it as XL in the Data Table on the Data Collection and Analysis sheet.
18. Again place the Light Sensor at your planned starting distance 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 tip on the Light Sensor.
19. Select  from the Main screen to prepare for data collection.
20. Wait for the value displayed on the calculator to stabilize. Select , and then enter the distance between the Light Sensor and the light source in meters on the calculator and store the data pair.
21. Move the Light Sensor 1 cm farther away from the light source and repeat Step 9.
22. Continue moving the sensor in 1-cm increments until the readings fall to less than 10% of the initial reading, collecting data as before.
23. Inspect the graph of light intensity versus distance. Trace to read the x and y values of the left-most point, round the values to three significant figures, and record them as XL and YL in the Data Table.
24. Return to the Main screen and exit EasyData be sure to make note of which lists your data is stored.

Analysis:

1. Display your data in list form and record several of your data points.  Display your graph outside of EasyData using the Stat Plot feature.  You may also wish to use the ZoomStat feature to automatically scale the window to the data. 
2. Inspect your graph of the light intensity versus distance.
   1. Answer Question 2 on the Data Collection and Analysis sheet.
   2. Another model can be used to compare to your data. The general power law of y = axb may provide a better fit than the inverse square function, especially if the light source is not small or if there are reflections from walls or other surfaces. The difference between this new model and the inverse square model is that the exponent is not fixed at –2. Instead, the exponent is now an adjustable parameter. The calculator can be used to automatically determine the parameters a and b in the general power law relation to the data.
   3. Press  and use the cursor keys to highlight CALC.
   4. Press  repeatedly to scroll down to PwrReg. When it is highlighted, press  to copy the command to the home screen.
   5. Press  [L1]   [L2]  to enter the lists containing the data.
   6. Press  and use the cursor keys to highlight Y-VARS.
   7. Select Function by pressing .
   8. Press  to copy Y1 to the home screen.
   9. On the home screen, you will now see the entry PwrReg L1, L2, Y1. This command will perform a power law regression with L1 as the x and L2 as the y values. The resulting regression curve will be stored in equation variable Y1. Press  to perform the regression. Use the parameters a and b, rounded to two significant figures, to write the power law model equation in the Data Table.
   10. Press  to see the graph of your data and the power regression function.
   11. Answer Questions 4 and 5 on the Data Collection and Analysis sheet.

Instructional Strategies:

1. It will probably be helpful to informally discuss the concept of light measurement before delving into the experiment.  The students should have an intuition on what it is they are measuring.

Additional Resources for this lesson:

• The “HowStuffWorks” website has some great information on light in general. http://www.howstuffworks.com/light.htm
• Energy Books has a reference guide that explains the terms mentioned in the lab referring to measuring light.  http://www.energybooks.com/pdf/D1150.pdf

Re-teaching and Enrichment Strategies:

For students who like mathematics you may wish to share with them one or both of the mathematical formulas used to predict light intensity and see if they can fit their data to the model. 
The first model holds that the intensity is proportional to the inverse square of the distance from a point light source; that is, a graph would be of the form .  The value, C, changes based on other conditions within the environment.  Students need to estimate a value for C by solving the given equation for C and solving the equation .  Then graph the equation and the data.  If the model is systematically high or low, you may want to adjust the value of C to improve the fit.
The second model of y = axb may provide a better fit than the inverse square function, especially if the light source is not small or if there are reflections from walls or other surfaces. The difference between this new model and the inverse square model is that the exponent is not fixed at –2. Instead, the exponent is now also an adjustable parameter. The calculator can be used to automatically determine the parameters a and b in the general power law relation to the data by following these steps:

1. Press  and use the cursor keys to highlight CALC.
2. Press  repeatedly to scroll down to PwrReg. When it is highlighted, press  to copy the command to the home screen.
3. Press  [L1]   [L2]  to enter the lists containing the data.
4. Press  and use the cursor keys to highlight Y-VARS.
5. Select Function by pressing .
6. Press  to copy Y1 to the home screen.
7. On the home screen, you will now see the entry PwrReg L1, L2, Y1. This command will perform a power law regression with L1 as the x and L2 as the y values. The resulting regression curve will be stored in equation variable Y1. Press  to perform the regression. Use the parameters a and b, rounded to two significant figures, to write the power law model equation in the Data Table.
8. Press  to see the graph of your data and the power regression function.

Data Collection and Analysis:

HYPOTHESIS:

DATA:

Distance (cm)	Intensity (lux)

QUESTIONS:

1. Based on the data collected from the light sensor, what do you observe about the relationship between distance and intensity? 
2. Is the graph of the light intensity versus distance consistent with your earlier prediction?  Explain.
3. How would using a brighter light bulb affect the light intensity?

DISCUSSION:

Why does the brightness of light change as you get closer to it? How do we use math equations to predict how the brightness changes?

*Adapted from: Brueningsen, C., Bower, B., Antinone, L., Kerner, E., Gastineau, J. E., & Cortez, W. (2005). Real World Math Made Easy: Explorations. Dallas, TX: Texas Instruments Inc.

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Schoolyard Study *

Teacher Version(.doc)

Student Version(.doc)

• Grade Level(s): 6th, 7th, and 8th
• Primary Focus: Science  NC Standard Course of Study Areas: 6th: 3.05, 6.01, 6.05, 7.02; 7th: 3.05; 8th, 4.06
• Secondary Focus: Math; NC Standard Course of Study Areas: 6th: 4.03, 4.06; 7th: 2.01, 3.01; 8th: 4.01
• Computer/Technology Skills: Calculators, Probeware, Data Visualization; NC Standard Course of Study Areas:
• Essential Question: How is the shaded area of the schoolyard different from the sunny area?  Do differences affect the living organisms in the area?
• Summary of Activity: Our environment is important to all of us. In this activity you will investigate your schoolyard as an environment. Scientists study large areas by looking at samples. One way to sample an environment is to look at data along a straight line called a transect. In this experiment, you will gather data along a transect in your schoolyard.
• Cognitive Teaching Strategies: It may be helpful to give the students examples of a good transect in the schoolyard so they know what to look for.  Students should be able to explain why they picked their transect and describe the differences they expect to find in the opposing areas. 
• Materials:
  • Stainless Steel Temperature Probe (1 per group)
  • Light Sensor
  • TI graphing calculator with EasyData application(1 per group)
  • EasyLink interface
  • 2 rubber bands
  • 10 meters of string
  • meter stick
  • ruler

Part I: Making a Transect

1.  Make your transect.
      a.   Stretch 10 meters of string in a straight line across an area of your schoolyard.  You will be collecting data along this line called a transect.  Choose a stretch with as many different conditions as possible (e.g., shade vs. sun, asphalt vs. grass).
      b.   In the Data table, write a description of each location you choose to study along the transect.
      c.   Record observations of any living things you see at the chosen locations.
      d.   Measure and record the distance (in m) from the beginning of your string to each location.
2.  In the space provided on Data Collection and Analysis page, make a sketch of your transect.  Label each location on the sketch.

Part II: Measuring Temperature

3. Connect the Temperature Probe to the EasyLink interface and the calculator.

4. Set up EasyData for data.
     a.  Start the EasyData application, if it is not already running.
     b.  Make sure the calculator displays Temperature (°C) in the top box.  No collection will take place, simply read the data from the screen and record it in the Data table.

5.   Measure the surface temperature at one end of the string.  Place the tip of the Temperature Probe in the ground.  Wait for the temperature reading on the calculator screen to stabilize before recording it.  Note: If there is direct sunlight on the probe tip during data collection, the readings will be too high. To prevent this, use your hand to shade the tip of the probe.

6.   Fasten the Temperature Probe to a ruler using two rubber bands as shown in Figure 1. The probe tip should be at the 5 cm mark on the ruler. Measure the temperature 5 cm above the surface at the same location. Wait for the temperature reading on the calculator screen to stabilize before recording it.

7.   Repeat Steps 5–6 for each location you chose in Step 1.

 

Part III  Measuring Reflected Light Intensity

8.   Connect the Light Sensor to the EasyLink interface and the calculator making sure that the switch is in the 0-150,000 lux position.
9 .  Set up EasyData for data.
     a.  Start the EasyData application, if it is not already running.
     b.  Make sure the calculator displays Light 150000(LX) in the top box.  No collection will take place, simply read the data from the screen and record it in the Data table.

10. Using two rubber bands, fasten the Light Sensor to the ruler as shown in Figure 2. The tip of the sensor should be at the 5 cm mark.
11.   Measure and record the intensity of the reflected light 5 cm above each location you chose in Step 1. Make sure that neither you nor the ruler shade the area below the Light Sensor.

 

 

 

Instructional Strategies:

1. This lab works best with students in groups of two or three.  Make sure students understand that they are measuring the light being reflected from the ground and that the temperature being measured is air temperature not ground or soil temperature.  Ground temperature may be added as outlined in the next two sections.  Discussing different types of environments and possible findings before conducting the experiment may allow students to pick better areas and reach better conclusions based on data. 

Additional resources for this lesson:

1. This is a lab that can be adapted to use with the Temperature probes.  It focuses on ground temperature at different depths in the soil as opposed to different environments. http://www.iscienceproject.com/labs/pdf_labs/6336_groundtemperature.pdf
2. Alliant Energy has information on their website discussing ground temperature in the context of a geothermal heating and cooling unit. http://www.alliantenergygeothermal.com/stellent2/groups/public/documents/pub/geo_how_001211.hcsp
3. HowStuffWorks.com has great information on both temperature and light.  http://science.howstuffworks.com/light.htm

Re-teaching and Enrichment Strategies:

• As mentioned above, ground temperature (particularly at different depths) could be added to this experiment.  This could lead to a discussion concerning different types of energy, especially those used to heat our homes.
• This lab can be used with the soil study lab to complete a thorough study on the environment on the transect.  The study may also be conducted over time showing changes along the transect during different months and seasons.
• Prepare a poster that presents your results.
• Prepare one or more bar graphs from your data.
• Do additional transects in different areas and compare results.

Data Collection and Analysis:

HYPOTHESIS:

 

SKETCH OF TRANSECT:

DATA:

Distance (m)	Description	Temperature (at surface) (°C)	Temperature (at 5 cm) (°C)	Temperature Difference	Light intensity (lux)

QUESTIONS:

1. In the space provided in the data table, subtract to find the difference between the temperature on the surface and the temperature 5 cm above the surface at each location.
2. Which location had the greatest difference between its two temperatures? The smallest difference?
3. Give possible reasons for the results in Question 2.
4. Which location had the highest reflectivity? The lowest?
5. Give possible reasons for the results in Question 4.
6. Look at your reflectivity and temperature data. Do your results follow a pattern? Explain.

*Adapted from: Volz, D., & Sapatka, S. (2000). Middle School Science with Calculators. Beaverton, OR: Vernier Software & Technology.