Physics307L:People/Long/Formal Report

Author: Ryan Long

Experimentalists: Ryan Long & Tom Mahony

The University of New Mexico

Department of Physics & Astronomy

email: rlong1@unm.edu

Abstract

The speed of light is a very large value, nevertheless, the speed of light can be measured using relatively simple time of flight methods. Experiments of this sort have been carried out since Isaac Beeckman and Galileo Galilei first tried in the early 1600s. [1] In Junior Lab at University of New Mexico, we measure the speed of light by measuring flight time of LED pulses over the course of a short distance. A major obstacle to overcome in this experiment is the occurence of "time walk", this can cause major systematic error, if not addressed properly. We obtain a value of 29.448 +/- .1424 cm/ns, which is inconsistent with the accepted value of 29.979 cm/ns, indicating some source of systematic error. We discuss possibilities for removing this systematic error in future work.

Introduction

Perhaps one of the most well known and frequently used constants of physics both classical and modern, is the speed of light, denoted by a lower case “c”. The speed of light constant is used for many purposes from calculating the distance to astronomical events, to understanding quantum mechanics. In 1972, the accepted value of the speed of light was c=299 792 500(100)m/sec [2]. Today the value for the speed of light is defined as 29.9792 cm/ns. we measured the speed of light using a relatively simple method which involves measuring time delay of an LED pulse using a photomultiplier tube and a Time amplitude converter or simply (TAC). The photomultiplier is a device sensitive enough to measure individual photons. When the cathode of the PMT receives incident photons, photoelectrons are ejected from an anode inside the PMT, [3] the resultant charge pulse intervals from the photoelectrons are then converted into amplitudes by the TAC and displayed on an oscilloscope. The voltage amplitudes can then be converted to time and divided by the distance to obtain the speed of light. This simple, yet effective experiment yielded some exciting results for my partner, Tom and I.

Methods, Materials and Procedure

Fig. 1: A sketch of our equipment setup.

Fig. 2: Sketch of the time-walk effect, varying amplitudes are shown, (a result of moving the LED to and from the PMT.

In order to measure the speed of light, we set up a long, opaque tube made of cardboard with a pulsating LED light source in one end and the photomultiplier tube on the other end of the tube. We connected the photomultiplier tube with BNC cables first to a Canberra 2058 delay module. We then connected the delay module to a Tektronix TDS 1002 digital oscilloscope in parallel with the “Stop” input on the Ortec 567 TAC/SCA Module. The Light source is also connected to the TAC in the “start” input. The delay module was set to 9 ns, to make certain that the stop signal from the PMT arrived after the start signal from the LED. This procedure is necessary due to a substantially longer BNC cable connecting the LED and the TAC. See Figure 1 for an illustration of our setup.

The light source is mounted on a meter stick so that we can measure various distances of light travel time, which ideally would lower our uncertainty. However this introduces a possible source of systematic error. As the LED is moved closer to the PMT, the PMT amplitude rises due to heightened intensity of photon bombardment. This issue is known as “time walk”. In order to reduce this time walk or fluctuation in voltage, a polarizer is mounted to the front of the PMT. As the LED is pushed down the tube toward the PMT, we rotate the PMT to keep the intensity as continuous as possible. Figure 2 shows the differences in amplitude as a result of "time walk".

Results and Analysis

Figure 3: Comparison of results from trials 1-6, calculated weighted mean, and the accepted value.

For my analysis, I performed a linear regression analysis of my data using the "LINEST" function of Excel (Microsoft Office 2008). To compute my final value for the speed of light, I computed a weighted average and corresponding weighted uncertainty. My excel sheet can be downloaded here.

My calculated value is: [math]\displaystyle{ 29.4480\pm .1424\frac{cm}{ns} }[/math]

The accepted value from NIST is: [math]\displaystyle{ 29.9792\frac{cm}{ns} }[/math]

Figure 3 shows each measurement from trials one through six, my calculated weighted mean, and the accepted value. The figure also demonstrates that my calculated value is inconsistent with the exact value from NIST. I speculate that this inconsistency is attributed to systematic error in our experiment.

Conclusions

Our data collection was very consistent, and seems to be mildly accurate if I have done my calculations correct, but there are inevitable systematic error set-backs. Time walk is a large part of it, perhaps the photomultiplier could be modified so that it is stationary with only a rotating polarizer, instead of rotating the entire PMT. Another possible source of error is varying the distance from the LED to the PMT, it is nearly impossible to make perfect increments of ten centimeters. This error would probably be reduced by simply taking more measurements, which perhaps we will try to do before the final report is finished.

My results and analysis are incomplete as of right now, (as I am baffled by the principle of maximum likelihood), but will be finished for the final report. I hope to also add a figure with a plot of the different measurements to show the best fit line from my formula attempt.

Acknowledgements

My partner Tom could not have done a better job, he is absolutely amazing to work with, so a big thanks to Tom. Also we could not have set up this experiment without the fantastic supervision and helpfulness of our professor Dr. Koch, and the teaching assistant, Pranav Rathi. Thanks gentleman.

References

[1] Boyer, CB (1941). "Early Estimates of the Velocity of Light". Isis 33 (1): 24. doi:10.1086/358523. (from wikipedia)

[2] K.M. Evenson et al “Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser” Physical Review Letters, Vol. 29, no. 19, (1972)

[3] R. Foord, R. Jones, C.J. Oliver, E.R. Pike “The Use of Photomultiplier Tubes for Photon Counting” Applied Optics, Vol. 8, No. 10, pg. 1 (1969)