# User:Ryan P. Long/Notebook/Physics 307L/2009/09/14

Speed of Light Main project page
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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.
SJK 23:50, 4 October 2009 (EDT)
23:50, 4 October 2009 (EDT)

## 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

Our setup for this experiment was based on Professor Gold's manual, and the necessary manuals for the equipment listed above.

We connected the following setup using BNC cables. We connected the "-HQ" connection on the back of the PMT to the back of the Bertan 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 TCA. We connected the "Start" input of TCA going 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 TCA 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 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.

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.

Note: The PMT is a very sensitive instrument, and should not be removed from the tube while it is powered on, large amounts of ambient light will damage the PMT.

## 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). We then pushed the LED farther into the tube in 10 cm increments, and rotated the PMT to compensate for the increased intensity of the LED. 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).

For all trials but the first 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, 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. This is why we only took 0-90 cm measurements for trial 1.

For the first trial we just looked at the raw signals. For the rest of the trials, we used the averaging function on the oscilloscope to reduce the noise on the signals.

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.

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

The TAC converted a time delay to a voltage (up to 10 V). The time setting we used 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, taking the reciprocal (since we are looking for m/s and not s/m), and multiplying by a negative sign. The negative sign was included simply because we measured negative changes in distance. (see the Analysis sheet under the data table)

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

Our mean speed of light was $2.9461 \pm 0.0437\times 10^{8} m/s$. This can be compared to the accepted value of $2.9979\times 10^{8} m/s$. Our standard error of the mean was $1.7837\times 10^{6} m/s$.

## Discussion

This lab, like all labs, had error. One possible source of systematic error could have been from each of us having the same role during 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 to previous measurements. There is room for human error in judging when the signals were equal. 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.

Despite the error present in this lab, our measurement came very close to the accepted value, matching it up to the 3rd digit.

## Suggestions

Our measurements seemed to work out well for the most part. but we do 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 risk moving the PMT. Other improvements would include using more refined methods for moving the LED circuit, and measuring its changing position. 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.