User:Randy Jay Lafler/FormalRoughDraft

= Speed of Light: Measuring the Speed of Light =

Author: Randy Lafler rlafler@unm.edu 

Abstract
The speed of light is a fundamental constant in physics influencing all kinds of formulas and physical phenomena. Because of relativity we now assert that it is invariant in any reference frame. In this experiment we measured the speed of light in a direct time-of-flight measurement. We used a Time-Amplitude converter to measure the time delay between the emission of a photon by the LED and the arrival of the photon at the photomultiplier tube (PMT). We had to apply a delay to the start signal with the (TAC)from the LED so that the stop signal from the PMT would not occur before the start signal from the LED. We then varied the distance between the PMT and the LED to have different delay voltages. Using the conversion on the TAC, we determined the delay times for each distance and plotted the results to determine the speed of the light. 

Introduction
Long ago, scientists debated whether light traveled instantaneously or at a finite speed. Scientists tried to estimate at least a lower bound on the speed of light by attempting to measure the start and stop of light signals over very large distances. It was found, however, that light traveled faster than any distance over which they could reasonable try to measure it on earth's surface. Descartes tried to utilized the larger distance between the moon and the earth, but even this distance was not great enough to measure the speed of light. So, he wrongly decided that light travels instantaneously. But, in 1671 Roemer determined by looking at the satillites of Jupiter that the speed of light must be finite. In 1862, Leon Foucault accurately measured the speed of light by sending a light signal from a rotating mirror toward a mirror fixed a large distance away. He then calculated the speed of light by using the angle through which the mirror rotated from the start to the reflection back of the light. 

Methods and materials



 * EG&G Ortec Model 567 Time-to-Amplitude Converter/Single channel Analyzer (TAC)
 * Tektronix TDS 1002, 2 channel digital storage oscilloscope
 * Power Supply: Harrison Laboratories Model #6207A 0-160 Volts/ 0-0.2 Amps
 * Meter sticks taped together with a photon emitting diode on the end
 * Nano N-134 Photo Multiplier Tube (PMT)
 * 5 Meter cardboard tube
 * Photon emitting diode (LED)

We set up the cardboard tube with the PMT on one side and the LED attached to a meter stick in the other end. Using BNC cables we attacked the PMT and the LED to the TAC and the oscilloscope. We also applied a time delay at the TAC to prevent the stop signal from the PMT from occurring before the start signal from the LED that the photon was emitted. In ten centimeter increments we moved the LED closer to the PMT, thus decreasing the distance for the photon to travel and the time. At each distance we recorded the voltage displayed by the oscilloscope, and converted each voltage to a time in namoseconds using the convertion factor on the TAC (one volt to 10 namoseconds). Using Excel we plotted the time verse the change in the distance of the LED. The inverse of the slope of the linear fit line to these data points gave us the speed of light. 

Results and Discussion
We are planning on running the experiment again, and determining the speed of light from the slope of the linear fit line to our data points as we did the first time. Trial 1
 * But based on the previous data
 * $$C=31.5(1)cm/ns\,\!$$

Trial 2
 * $$C=32.1(19)cm/ns\,\!$$

Accepted value
 * $$C=30cm/ns\,\!$$



Conclusions
Because our measurements are both larger than the accepted value perhaps there was some systematic error. I believe better measurements can only consistently be obtained if we take into account what the manual calls time walk, which is where the TAC measures a different time based on the imput amplitude of the signal. 

Acknowledgments

 * I need to thank Tom Mahony for general format of the formal report and for references.
 * Emran for being my lab partner.

General Steve Comments
Steve Koch 13:03, 6 December 2010 (EST):Obviously I haven't finished grading this. But since today is "extra data day" I need to give you some comments about that. I like your measurements so far. So, basically I'd like you to use what you know to see if you can reduce systematic error further. One really fun idea (to me at least) would be to try to use the oscilloscope with the higher bandwidth to see if you can measure the time delay without using the TAC. We can talk about this in the lab.