# Physics307L:People/Josey/Speed of Light

## Speed of Light Summary

SJK 22:05, 3 October 2010 (EDT)
22:05, 3 October 2010 (EDT)
Excellent work on this lab! Good summary, excellent primary notebook. Keep it up!

For this lab, my partner, Kirstin, and I measured the speed of light. The speed of light is a fundamental physical constant and the highest speed at which anything can travel. To measure this quantity, we fired light from a light emitting diode (LED) to a photomultiplier tube (PMT). From the firing and detection signals from these two pieces of equipment, we were able to measure the flight time between the LED and the PMT at various distance. Plotting this travel time verses the distance traveled, and using linear regression, we were able to measure the speed of light as 31.0 ± 0.5 cm/ns. The accepted value is given as 29.98 cm/ns, which is outside of two standard deviations from our measured value. Because of this we believe there was some unaccounted systematic error in our data. My notebook entry for this experiment can be found here

## Procedure and Results

As described above, we measured the speed of light by measuring the time it took for the light to travel a fixed distance, and then plotting these two ranges against one another. In order to get the best possible value, we took five sets of data where we varied the distance between the PMT and LED from a 1 m to touching in 20 cm increments. We then measured the voltage of the time delayed signal at each point, and took the average for each distance. Then we converted the voltage in to an elapsed time and plotted them over the range of distances. This gave us the following plot:

By using linear regression on our original data points, we were able to determine that our measured value for the speed of light was 31.0 ± 0.5 cm/ns, while the accepted value is 29.98 cm/ns.

## Conclusions

SJK 20:27, 3 October 2010 (EDT)
20:27, 3 October 2010 (EDT)
I really like your discussion here and the way you present your measurement in comparison to the accepted value. I'm not convinced, though, about the long wires causing the systematic error. All wire lengths remain constant throughout your measurements, right? It would be good, though to see how your measurements change as you adjust the fixed delay. My guess is that time walk could still be a significant problem. Even though you adjust the PMT, you cannot ensure that the signal shape does not depend on proximity to LED. Another possibility is calibration of the TAC, which we don't have a good way of checking that I know of.

From the wide gap between our measured speed and the accepted speed, it is clear that our data has some systematic bias to it that has altered the value. The are multiple possible sources for this error. The first is time walk, which is a phenomena when our measured signal is displayed late due to it hitting some minimum voltage specified by the tools we used. To counter this, for each measurement, we rotated the PMT, which has a polarizer on it, so that an output signal from it was returned to the same point, and then measured the time traveled. Because of our care in these measurements, I am confident that time walk is not the source of the systematic error. Another possible source for systematic error is from the cables used to connect each of the components in the set up. A signal does not travel instantaneously down a wire, but travels at a speed comparable to the speed of light. Due to the long length between the PMT, LED, and oscilloscope used in this experiment, wires of different lengths, from about a dozen centimeters, to nearly five meters were used to connect all of the components. We used a delay module to specifically time the signals so that the signal from the PMT and LED reached the TAC at the appropriate times, but it is clear that we failed to do it precisely the right amount. If I was to repeat this experiment, I would spend much more time working with the cables and delay module to remove this possible source of systematic error.