# Speed of Light: Measuring the Speed of Light

SJK 11:46, 3 December 2010 (EST)
11:46, 3 December 2010 (EST)
The title could use some work. You could delete the first phrase, and add a clause saying how you measured the speed (time of flight). Also, add your institutional affiliation to the autho area.

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

SJK 11:53, 3 December 2010 (EST)
11:53, 3 December 2010 (EST)
I like what you have here. See if you can find citations for the information. Probably you won't find any peer-reviewed research reports for what you have. But you can continue by talking about how the speed of light was measured in more modern times, and you can find some citations for that (try NIST CODATA). You will need to cite several peer-reviewed reports in your paper, and in the introduction is probably the easiest place to do so.

Then, finish your introduction by describing what you did and what you will show in this paper. E.g., "In this report, I describe our attempts to measure the speed of light using a time of flight method. We will describe our method and show how our measurements compare with the accepted value." Something along those lines.

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

SJK 12:39, 9 December 2010 (EST)
12:39, 9 December 2010 (EST)
For historical reasons, methods sections do not have a list of equipment. Instead, use sentences to describe the setup and when you first mention an item, put company / model in parentheses. Like this: "...was connected to a time-to-amplitude converter (Model 567, EG&G Ortec, _cityname_). Aside from typos (namosecond) what you have is good. Just more detail needed, and for sure need to mention how you dealt with time walk.
SJK 11:57, 3 December 2010 (EST)
11:57, 3 December 2010 (EST)
I like these photos. Make sure to number them and give them each a title, and add a bit more description for a reader to understand what the image is without referring to your text (as we discussed in class).
Photo Multiplier Tube side view
Photo Multiplier Tube back view
Time to amplitude converter
Oscilloscope
Light distance Measuring tube from LED opening
• 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

SJK 22:00, 9 December 2010 (EST)
22:00, 9 December 2010 (EST)
For sure you'll want to have text in this section. Number your figures, give them titles and description. And refer to the figures in the text.

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.

• But based on the previous data

Trial 1

$C=31.5(1)cm/ns\,\!$

Trial 2

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

Accepted value

$C=30cm/ns\,\!$

## Conclusions

SJK 22:06, 9 December 2010 (EST)
22:06, 9 December 2010 (EST)
I think you'll be able to expand on this after your measurements you took this week.

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

SJK 22:07, 9 December 2010 (EST)
22:07, 9 December 2010 (EST)
Turn the bullets into full sentences
• I need to thank Tom Mahony for general format of the formal report and for references.
• Emran for being my lab partner.

## References

1. Gal Boyer, Carl B. "Early Estimates of the Velocity of Light." Isis Vol. 33, No. 1 (Mar., 1941), pp. 24-40 http://www.jstor.org/stable/330649
2. Mahony's Formal Report Mahony's

http://www.gutenberg.org/files/11753/11753-h/11753-h.htm