Determination of the Mathematical Relationship
Between Illumination and Distance from a Light Source
Procedure
1. Plug Light sensor into Ch. 1 (make sure the switch is set to 0 – 6000 lux).
2. Open LoggerPro
3. Open the file entitled, “Exp 32 light brightness distance” It is found in the “Physics with Computers” folder inside the “Experiments” folder.
4. At “Change Sensor Setting” click “Use Sensor Setting.”
5. On the horizontal (distance) axis of the graph, click on the number “10” and change it to “60.”
6. Click on the “Collect” button.
7. Hold the light sensor exactly 10 cm away from the middle of the bulb. When the number on the screen for “Illumination” stabilizes, click on the “Keep” button.
8. Type in your distance (in this case 10) when prompted and click “OK.”
9. Continue the process for distances 20, 30, 40, and 50 cm.
10. When finished, click on the “Stop” button.
11. Record your “actual illumination” in the data table below for each of the distances 10, 20, 30, 40, and 50 cm (this information is in a table on your screen).
12. Use the “Analyze” menu’s “Curve Fit” function to find an equation (inverse-square) that fits your data. Once you have chosen it, slide this equation box on your graph out of your way.
13. From the “Analyze” menu choose “Interpolate.”
14. Move the mouse until you are at x (distance) = 10 (values are shown in a new information box). Record the corresponding y (“theoretical illumination”) value in the “theoretical illumination” column of the table below. These values correspond to points on the curve fit you chose.
15. Continue this process of finding “theoretical illuminations” for distances of 20, 30, 40, and 50 cm.
16. Fill out the “distance ratio” column by calculating how many times farther each subsequent distance is compared to the original distance of 10 cm.
17. Fill out the “theoretical illumination ratio” column by calculating how many times dimmer each subsequent theoretical illumination is compared to the theoretical illumination magnitude at a distance of 10 cm.
Data and Analysis
Distance (cm) / Actual Illumination (lux) / Theoretical Illumination (lux) / Distance Ratio / Theoretical Illumination Ratio10 / 1 / 1
20
30
40
50
Make a sketch of your graph shape that includes labeled axes.
Questions
1. Name the proportion.
2. Use the numbers that you found in steps 16 and 17 to state what happens to the illumination when distance is doubled, tripled, quadrupled, and quintupled.
3. How does this relationship apply to gravity?
3220.NWT1.inverse_square