Physics307L F09:People/Gooden/Formal Lab Report


 * MEASUREING THE SPEED OF LIGHT ELECTRONICALLY

Matthew E. Gooden, Zane Gibson

UNM Department of Physics

[mailto:mgooden@unm.edu mgooden@unm.edu]

[mailto:zgibson@unm.edu zgibson@unm.edu]

Abstract

 * The objective of this experiment was to determine the value of c, the speed of light. We have measured $$c=\left(2.83 \pm .23\right)\times10^8 m/s$$ in good agreement with the accepted value of $$2.99\times10^8 {m/s}$$.

Introduction

 * We investigated the Speed of Light during this experiment. The speed of light is just what it sounds,How fast light Travels! The speed of light historically have been very fascinating. It was once believed that light travels instantaneously between locations, that its speed was infinite. However, once physicists began investigating more and they discovered that light's speed is very very large, but FINITE! and specifically it is around 300 million meters per second by todays calculations. Physicists also believed that light followed Galilean relativity/motion and that its speed was always dependent upon how fast you were traveling. However, Albert Einstein showed in 1905 with Special Relativity that the speed of light is a constant, that it never changes for anyone/anything no matter how fast you move. The speed of light c, can also be found in dealing with the energy of photons, special relativity and the lorentz transformations and many other areas of physics. As one can tell this constant plays a very big role in physics.

Methods and Materials

 * This experiment requires the use of a lot of different equipment:

Time-Amplitude Converter (TAC)

LED

Photomultiplier Tube (PMT)

DC Power supply (150V-200V) - LED

DC Power supply (1800V-2000V) - PMT

Oscilloscope

Delay box

Several Meter Sticks

Long Tube

Procedure {{SJK comment|l=16:59, 12 November 2007 (CST)|c=This is actually a nice detailed "how to," but unfortunately isn't quite the correct style for a formal report. Even though the purpose is to allow people to reproduce your experiments, you don't write it in a "here's how you do it," but rather, "this is what we did". To make this easier, you should draw a schematic with all the connections, and then you can say, "we connected the instruments as in "figure ____". {{SJK comment|l=17:00, 12 November 2007 (CST)|c=Great pictures and good start on the captions. Probably more detail in the captions to make sure people know which piece of equipment they are supposed to look at.}}
 * 1) WARNING:Never expose the PMT to direct light while power source is on, this will destroy the PMT.
 * 2) To begin you must connect the power supplies to both the LED and the PMT that are at either ends of the tube; the low and high voltage supplies respectively.
 * 3) With the PMT in the left end of the tube near the equipment, attatch the meter sticks to the LED and insert it into the right end of the tube.You will want to tape or fasten the meter sticks together to be able to move the LED a sufficient distance.
 * 4) Then connect the LED to the TAC's start jack with a BNC cable, and also connect the PMT to the stop jack on the TAC with another BNC cable. Next you also want to run a cable from the PMT to the oscilloscope's Channel 1 and from the TAC to channel 2 on the oscilloscope.
 * The oscilloscope will measure the voltage output from the PMT on channel 1 and the signal from the TAC will respresent the time delay that you want to be measuring.
 * 5) You now want to adjust the oscilloscope to be able to see the signals from the PMT and LED. On channel 1 of the Oscilloscope you are wanting to see a level curve with a sudden drop in potential and then a rise back up. On channel 2 the signal from the TAC should look like a semi-square wave that is oscillating up and down rather rapidly.
 * 6) Once all set up, you want to pick a value of the voltage on Ch 1 and attempt to maintain that value for your measurments. This is accomplished by turning the PMT left/right to allign or unallign its polarizer with that of the LED.
 * 7) Next, using the aquire button on the oscilloscope you can choose to average over the values that the oscilloscope is recieving to allow you to take measurments. You want to choose the 128 setting under the average command, so the signal is more stable. Then use the measure function to allow you to see the values outputed to channels 1 and 2 to make your measurments. Looking for the minimum on channel 1 and maximum on channel 2.
 * 8) Now we can start making measurments! - to do this you must pick your desired value for channel 1 and then holding the PMT steady have your partner pull or push the meter stick connected to the LED in or out of the tube. Record how far the meter stick moved relative to the opening of the tube and then readjust the PMT so that channel 1 on the oscilloscope returns to your previously picked value.Then simply continue.
 * For this experiment, we are not concerned with the actual distance between the PMT and LED. Which can seem a little strange. Rather at any particular distance between the PMT and LED we make a measurment and then we are only concerned with the change in that distance for the next measurment, since we are measuring the time delay of the signal from the LED pulse and the PMT signal.

Results and Discussion

 * In the tables below we give our data, that was obtained from the experiment. Immediately afterwards we will detail our analysis and present our final results that were mentioned above.
 * In analyzing the data we used the equation :$$V = G*T$$ to relate the voltages to time, with G=1/10 volts/nanosecond


 * Once we collected the data above from the three different trials we began our data analysis using Microsoft Excell and Matlab to perform least-squares fits to the data, find our error and produce plots of the data.


 * Here are the plots of our data given above,where the slope of the least-squares line respresents the speed of light approximation by the data:




 * After performing the least-squares analysis on each data set we were able to come up with these values for the speed of light C for each set along with the suspected error.

$$c=\left(2.68 \pm 0.18\right)\times10^{8} m/s$$
 * Data Set 1

$$c=\left(2.94 \pm 0.42\right)\times10^{8} m/s$$
 * Data Set 2

$$c=\left(2.89 \pm 0.08\right)\times10^{8} m/s$$
 * Data Set 3


 * By averaging the three values above for the speed of light and taking this to be our final value for this experiment,we find that the speed of light is:


 * $$c=\left(2.83 \pm .23\right)\times10^8 m/s$$

Conclusions

 * With our value of the Speed of Light c, we are fairly happy with the result. Unlike most experiments however we do know the true value for c, and so we can look at the relative error between the accepted value and our reported value, which is given by:

$$Relative Error=\frac{\left|2.99\times10^{8}-c\right|}{\left|2.99\times10^{8}\right|}=0.0535=5.3%$$


 * With this result we are very pleased with the outcome of the experiment.
 * Given the 5% error in the measurment, we can see that there is error in our measurments and the experiment. If we had more time we would have liked to make several more sets of measurments to use in our analysis, and also to improve on how the distance measurments were done and the apparatus was set up. The LED fit into the tube very tighly and this caused the tube to be shifted and/or rotated when the LED was pulled or pushed out the tube to change the distance between it and the PMT. Also, the area that the experiment was set up on was not suitable or desirable to perform the experiment. The PMT end of the tube was set on an extra piece of equipment balanced on its power cord and set up in such a way that reaching out and holding the PMT still and also rotating it to align its polarizer with the LED was difficult. If we were to redo the experiment in the future we would attempt to fix the problems in how the experiment was set up,which would hopefully allow more accurate measurments to be taken and reduce the error.

Acknowledgments

 * We would like to acknowledge Dr. Koch for his help in explaining how equipment such as the TAC and PMT operated so that we could have a better understanding of what was happening. He also was able to explain the signals from the LED and PMT and why we dont care about the actual distance between the PMT and LED but only the change in that distance at each measurment. Dr. Koch was a very valuable asset in performing this experiment.

Koch comments
Overall, I think your data and analysis are good, which is a great thing, because that is the heart of a good report, of course. However, the report needs significant work in a lot of areas, as noted above throughout. Some sections had good starts, but needed more info (such as introduction) and in many other places, the style is not what it should be for a formal report. You should make significant revisions and then get more feedback from me before submitting the final version. Additionally, in order to get an outstanding grade, I will want you to take more measurements, trying to obtain even better data than you have already. Some notable things:
 * Need many more citations (as discussed in class)
 * Take a look at several published articles to get a feel for the formal writing. You need to emulate this (e.g., not written as bulleted lists, etc.)