User:Randy Jay Lafler/FormalReport

The Time of Flight method to Calculate 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

University of New Mexico Physics Department

Undergraduate

Abstract

^{SJK 11:44, 3 December 2010 (EST)}

11:44, 3 December 2010 (EST)
This is a good start on the abstract. You should include your actual measurement +/- uncertainty in the abstract. You also could end with a concluding statement. You do a good job describing the methods, but there is probably too much for an abstract. The last four sentences (starting with "We used a Time-...") should probably be condensed into one or two less detailed sentences. Also, the "all kinds of formuals" is too informal...something better would be "many formulas and..."

The speed of light is a fundamental constant in physics influencing many 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 an oscilloscope to measure the time delay of an emmitted photon. We did not use the Time to Amplitude Converter (TAC) as the manual suggests in an attempt to avoid time walk. We determined the speed of light to be 26.8(7)cm/ns.

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 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).

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  Figure 1: This is the Photo Multiplier Tube from a side view.

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  Figure 2: TAC: The front of the TAC. We did not use this in this version of the experiment.

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  Figure 3: Oscilloscope: We plugged the cables from the LED and PMT directly into the oscilloscope in channel one.

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  Figure 4 Cardboard Tube: This is the opening of the cardboard tube from the LED side. The LED is attached to the meter sticks, and we changed the distance between the LED to the PMT by pulling our or pushing the meter stick in the cardboard tube.

We set up the cardboard tube with the PMT(Nano N-134 Photo Multiplier Tube) on one side and the LED (Photon Emitting Diode) attached to a meter stick in the other end. Using BNC cables we attacked the PMT and the LED to the oscilloscope in channel one. We set one of the cursors at a fixed location on the oscilloscope screen, and adjusted the other vertical cursor to the initial downward spike in the signal. In fifty 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 adjusted the second cursor of the oscilloscope to be exactly at the initial downward spike in the signal, and we recorded the reading given for the change in time. We followed this procedure for the first three trials. For the fourth trial we rotated the PMT inside the cardboard tube and tried to hold the first spike of the signal at the same vertical position on the oscilloscope screen for every fifty centimeter measurement. For our last trial we rotated the PMT so that the average, or middle, of the first several spikes in the signal would be at the same position for every measurment. Using Excel we plotted the change in distance of the LED verse the change in time. The slope of the linear fit line to these data points gave us the speed of light. We also used Excel to give us an average velocity by summing up the total distance and dividing by the sum of the times from each measurement.

Results and Discussion

We did five trials to measure the speed of light. The first three have similar results because we used the same method. The last two we did with a different method describe in the methods section. Here is a summary of the values we obtained for each trial. Trial 1

[math]\displaystyle{ C=24.1(1)cm/ns\,\! }[/math]

Trial 2

[math]\displaystyle{ C=23.2(7)cm/ns\,\! }[/math]

Trial 3

[math]\displaystyle{ C=23.6(11)cm/ns\,\! }[/math]

Trial 4

[math]\displaystyle{ C=26.8(7)cm/ns\,\! }[/math]

Trial 5

[math]\displaystyle{ C=34.8(1)cm/ns\,\! }[/math]

Accepted value

[math]\displaystyle{ C=30cm/ns\,\! }[/math]

Below is the link to the Excel sheet we used to calculate the speed of light.

Speed of Light 2 XL Doc

The plots we obtained for trials 4 and 5 are displayed below in Trial Run 4 and Trial Run 5. We choose only to display these two plots because the data from these two trials are more consistent with the accepted value for the speed of light. We also determined that the changes we made in our method for these last two trials better took into account the changing intensity of the signal at different distances of the LED fromm the PMT.

Conclusions

asd

Acknowledgments

I need to thank Tom Mahony for the general format of the formal report and for references. I must thank 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.speed-light.info/measurement.htm

http://ajp.aapt.org/resource/1/ajpias/v73/i3/p240_s1

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

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.