Team Members
I received this data set from Elizabeth Jones .
Materials
This lab requires the CBL with the light intensity probe, a flashlight, and a ruler.
Procedure
Turn on the flashlight and place it on a table. Use the light intensity probe with the CBL to collect data at several increasing distances from the face of the flashlight. We used 10 cm increments up to 90 cm.
Data Set
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Scatter Plot
Analysis of Data
Let x equal the distance in cm of the probe from flashlight. Let y = f(x) equal the light intensity in lumens measured at a distance of x cm from the flashlight. The possible domain is the nonnegative rational numbers, but it is most practical to use relatively small integer multiples. We used multiples of 10 from 0 to 90. The range is contained in the nonnegative rational numbers less than 1. The y-value zero would probably not appear in the range, unless the measurement was taken at great distance from the flashlight in a totally dark room.
It seems that light intensity as a function of distance from the source would be a power function or a rational function reflecting some sort of inverse variation.
However, the power function is an extremely poor fit, as the low strength of correlation reveals.
The best fitting regression curve I could find is the following quartic function.
The quartic does not seem to be the best model of the data either. Because of the low number of data points and the high degree of the polynomial, the quartic regression curve is able to artificially mimic the odd , irregular behavior of our function.
The last two data points do not seem to fit with the rest of the data. It might be a good idea to remove these points from the data and determine if the resulting pattern is easier to fit to a regression curve. However, the power function still fails to reflect the behavior of the even the reduced data set.
Conclusion
Dr. Olive pointed out that our data for this experiment did not at all resemble the usual model for light intensity as a function of distance from the source when we used a flashlight. He reported that another class used a desk lamp instead and found the typical pattern in the data that they collected.
I thought of one possible explanation for this difference. I thought about the concentric circles of varying brightness that appear when you shine a flashlight on a wall. I assume that this behavior is a result of the position of the small bulb inside the narrow opening of the flashlight that directs the path of the light produced. Perhaps this concentric pattern reveals a pattern of light intensity that varies irregularly compared to the typical behavior of light produced by a lamp bulb and more loosely directed by a large shade.