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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. | |||
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Revision as of 10:20, 10 December 2010
The Time of Flight method to Calculate the Speed of Light
SJK 11:46, 3 December 2010 (EST)
Author: Randy Lafler
rlafler@unm.edu
University of New Mexico Physics Department
Undergraduate
Abstract
SJK 11:44, 3 December 2010 (EST)
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)
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)
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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 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
- [math]\displaystyle{ C=31.5(1)cm/ns\,\! }[/math]
Trial 2
- [math]\displaystyle{ C=32.1(19)cm/ns\,\! }[/math]
Accepted value
- [math]\displaystyle{ C=30cm/ns\,\! }[/math]
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 the general format of the formal report and for references. I must thank Emran for being my lab partner.
References
- 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
- Mahony's Formal Report Mahony's
http://www.speed-light.info/measurement.htm
http://ajp.aapt.org/resource/1/ajpias/v73/i3/p240_s1
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.