# User:Thomas S. Mahony/Notebook/Physics 307L/2009/09/14

Speed of Light Main project page
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## Lab Summary

SJK 23:49, 4 October 2009 (EDT)
23:49, 4 October 2009 (EDT)
You guys kicked some serious ass on this lab! Your primary lab notebook (this page) is terrific. The only thing I really noticed is the lack of graphs--but that's not a big deal since the raw data are there for anyone to see. I am really impressed at how well you mastered this lab, pretty much just by working together and developing your own technique. One thing about the data: I wonder whether the fact that your last digit of precision on voltage isn't quite precise enough makes a big systematic difference in your lab? I can explain better in person if you decide to pursue this lab further.

## Equipment

• Tektronix TDS 1002 Oscilloscope
• Bertran 313B Power Supply
• Canberra 2058 Delay Module
• Ortec 567 TAC/SCA Module
• Harshaw NQ-75 NIM Bin
• Harrison Laboratories 6207A Power Supply
• Photomultiplier Tube (PMT)
• LED circuit
• BNC Cables

## Setup

SJK 23:05, 4 October 2009 (EDT)
23:05, 4 October 2009 (EDT)
EXCELLENT Equipment and setup! The panorama is sweet and together all the photos convey a ton of information, including the intensity of the experimenters :)

Our lab followed the same general procedure outlined in Professor Gold's manual.

We connected the following setup using BNC cables. We connected the "-HQ" connection on the back of the photomultiplier tube (PMT) to the back of the Bertan Power Supply Unit (PSU). The "A" connection on PMT to top input of the delay module. We connected the output of the delay module to a BNC T-splitter, with one side connected to channel 1 on the oscilloscope, and the other going to "Stop" input of the Time-Amplitude Converter (TAC). We connected the "Start" input of the TAC to the cable attached to the LED. We connected the power cable for the LED to the Harrison PSU. Finally, we connected the output of the TAC to channel 2 of the oscilloscope.

The setup also included specifying the various settings of the equipment we were using: On the Bertran, we switched the top polarity switch to negative, switched the Voltage to 2000 volts, and turned the voltage adjustment knob to 400.

On the delay module, we set the delay to 9 ns.

On the Ortec Time-Amplitude Converter (TAC), we set the range to 100 ns, the multiplier to 1, start and stop switches to "anti", and set the output switch to "out."

On the Harrison PSU, we set the voltage to 190V.

The principle of the lab is that there will be a delay between the LED circuit triggering and the PMT measuring the LED's pulse. This delay is measured by the TAC and in knowing its parameters, we can convert this voltage to a time. By measuring this voltage at different points, we can find the difference between them and divide by the distance to find the speed.

## Data

Amazing sketch of the time-walk effect

We started our data acquisition process by pushing the LED to the start position. We then maximized the signal coming out of the PMT by rotating the PMT (since a polarizer was attached to it). The reason we maximized the intensity was that this corresponded to the position furthest from the PMT. We then pushed the LED down the tube in 10 cm increments, and rotated the PMT to compensate for the increased intensity of the LED. By reducing the intensity, we could make keep the amplitude of the pulse coming from the PMT the same. The purpose of this was to reduce the error due to the time walk effect. The time walk effect is a problem that arises when trying to trigger a pulse using peaks of different amplitude (see the amazing sketch). (Steve Koch 23:19, 4 October 2009 (EDT):Sketch is very effective!)

Except for the first trial, the 0 cm mark corresponds to the second 50 cm mark from the end. On our first trial, we started at the 60 cm mark instead of 50, but as we approached the last 60 cm mark (1 m from the start) the LED apparatus started to push the PMT out of the tube. For this reason, we only took 0-90 cm measurements for trial 1.

On our first trial, we just looked at the raw signals on the oscilloscope screen. For the rest of the trials, we used the averaging function on the oscilloscope to reduce the noise on the signals (this may have caused systematic error). (Steve Koch 23:21, 4 October 2009 (EDT): How many averages? Did you also notice that the trigger level can change your answers?)

Finally, all the trials but the last one were done with lab partners each doing 1 role in the data acquisition process. For the last trial, these roles were switched (the purpose was to see if our data would change by switching what each person was doing).

Oscilloscope sample screen

Note: The uncertainty in our voltage measurements is not the standard 68% confidence, but rather is the fluctuation of the signal from our reported value as measured on the oscilloscope screen. You could say it was our 99% confidence, since it included all possible values.

## Analysis

SJK 23:46, 4 October 2009 (EDT)
23:46, 4 October 2009 (EDT)
Some graphs in your spreadsheets would be really nice. This would allow the user to quickly judge your data for possible systematic problems. It's easy enough for me to cut and paste into Excel, but some readers won't realize that. Having the raw data there (which you do) is the essential part--a graph would just be very helpful.

We used google docs to do our data analysis. There are no explicit formulas listed here, but the details of our calculations can be seen on the "Analysis" tab on our data sheet. Our data consisted of the various voltages generated by the TAC from its measurements of the time delay between the 2 pulses. The maximum voltage for the signal generated by the TAC is 10 V. The time setting we used on the TAC was 100 ns, so this meant a 10 ns to 1 V conversion. We did a linear fit on our data to find the slope or change in voltage per cm. We then took this value and converted from V/cm to m/s by changing units, took the reciprocal (since we are looking for m/s and not s/m), and multiplied by a negative sign. The negative sign was included simply because we measured negative changes in distance. This conversion gave us a speed of light for each trial. We then took the mean of these measurements to arrive at our final value. We also found the standard deviation of these values to get our uncertainty as well as the standard error of the mean.

SJK 23:31, 4 October 2009 (EDT)
23:31, 4 October 2009 (EDT)
Good description here, definitely understand your method. I couldn't figure out how to see your formulae on the google spreadsheet (since I don't have edit privileges. That's definitely a deficiency of Google docs. Can't think of a workaround, besides either giving the world edit privileges, or exporting the spreadsheet and uploading it manually.

Despite the first trial having different absolute voltages from the other trials. Nevertheless, we decided this data was still relevant, since the relative changes in voltage with respect to distance in trial 1 matched the rest of the data. This is why we included it into our calculation of the mean value.

Our mean speed of light was:

• $2.9461 \pm 0.0437\times 10^{8} m/s$

This value can be compared to the accepted value of:

• $2.9979\times 10^{8} m/s$

Our standard error of the mean was:

• $1.7837\times 10^{6} m/s$.

Note: the uncertainty here actually is the standard deviation, and does correspond to the 68% confidence value.

## Error

Like all labs, this one did have error. One possible source of systematic error could have been from Ryan and I each having the same role in the data acquisition process. We switched roles in the last trial to see if this would affect our data at all. Despite having taken only 1 set of data with our roles reversed, the data seemed to deviate very little from the previous trials. Another source of systematic error was time-walk. This had to be reduced by rotating the polarizers and by looking at the voltage to match the amplitude with previous measurements. There is room here for human error in judging when the signals matched in amplitude. Since the polarizer was attached to the PMT, the entire assembly had to be rotated each time, and this could have caused more error in our measurements because the PMT could then change position with respect to the LED. Of course other sources of systematic error could include a miscalibrated the meter stick or TAC. We tried to reduce random error by using the averaging function on the oscilloscope, which may or may not have contributed to the systematic error.

## Conclusions and suggestions

I was quite pleased with the outcome of this lab. Our measurement came very close to the accepted value, agreeing to the 2 most significant digits before differing at the third.

We have a few suggestions for how to improve this lab. We think finding a way to detach the polarizer from the PMT would be a good idea, so it can be rotated without having to move the PMT. Other improvements would include using more refined methods for moving the LED circuit, and measuring its changing position. Also, it might be worth considering coating the inside of the cardboard tube with black aluminum foil to reduce reflections off the side, as this might result in shorter pulses and possibly less severe time-walk. Finally, this experiment could be done in a vacuum, since the speed of light is marginally slower in air.SJK 23:39, 4 October 2009 (EDT)
23:39, 4 October 2009 (EDT)
All good suggestions. Probably a pulsed laser would work pretty well compared with the LED? It would get quite elaborate building this thing in vacuum, with moving parts and everything.

## Acknowledgments

I'd like to thank my lab partner Ryan for his help with running the lab, taking data, and finishing up the lab notebook with me. I'd also like to thank Dr. Koch for his helpful explanations of various parts of the setup. (Steve Koch 23:40, 4 October 2009 (EDT): Did you get help from any previous students? I wasn't sure. If you did, definitely worth giving them credit.)