# Speed of Light Lab Summary

### Summary of Activities

SJK 21:37, 25 October 2010 (EDT)
21:37, 25 October 2010 (EDT)
This is a good summary. Very nice job with you and Joe taking lots of good data. See notes about uncertainty estimation.
During this lab we performed the speed of light lab, following the procedure outlined in my lab notebook User:Alex_G._Benedict/Notebook/Physics_307L:_Junior_Lab/Speed_of_Light_Lab. We took data for the speed of light using two different techniques, one where the distance of the LED from the PMT mattered, and one where that could be arbitrary. To measure the time it took light to traverse some distance we measured the peak to peak voltages of a waveform on the oscilloscope, and converted the voltages to nanoseconds using the values given by Joesy and Harriger of 1V=10ns. The units from the first day of data measurement are volts and meters. For the second day the units are 0.1 voltsSJK 21:35, 25 October 2010 (EDT)
21:35, 25 October 2010 (EDT)
Did you mean "millivolts" here?
and cm. For the first day of measurements we took data for 10 trials and averaged the voltages for each trial, and produced a least squares fit of the data. For the second day, we took 10 sets of data, then produced a least squares fit for each set of data and averaged the slopes of each fit.

### Results

For the first day:

The slope of the line in the picture is 0.20079999999999 +/- 0.1258206130436 which actually contains the speed of light(about 0.3 in those units) within the uncertainty. So we known with about 68% confidence that the speed of light is in the interval [7.4,32.59] cm/ns.

For the second day:

The average slope for the data was -3.26848484848484 +/- 0.24476146068253, where the uncertainty is taken to be the maximum of the the uncertainties of each fit. The minus sign is irrelevant and comes from the fact that the distance from the LED to the PMT was decreasing, so with 68% confidence we know the speed of light is within the interval [30.24,35.13] cm/ns.

A sample plot from this day is given below for trial 8(this was a particularly good trial):

The actual value of the speed of light is 29.9792458 cm/ns. Which lies within the range for the first day, but is outside of the range for the second day. The error could be due to time walk, human error, old equipment, or one of many other things. SJK 21:32, 25 October 2010 (EDT)
21:32, 25 October 2010 (EDT)
You should go further and say what you think is the most likely source(s) of uncertainty. How would old equipment do anything? Do you really think humans (you) made mistakes?