# Speed of Light Notes

SJK Incomplete Feedback Notice
Incomplete Feedback Notice
My feedback is incomplete on this page for two reasons. First, the value of the feedback to the students is low, given that the course is over. Second, I'm running out of time to finish grading!
SJK 18:31, 16 December 2009 (EST)
18:31, 16 December 2009 (EST)
Very good primary lab notebook, and looks like good data and analysis. Missing is a comparison of discrepancy from accepted value relative to your uncertainty. Also, on summary page, too many digits on uncertainty, and not quite written in traditional style.

In this lab we will try to determine the speed of light by means of a light pulse and a light detector by measuring the TOF(Time Of Flight) of the light when it leaves the source and gets detected by the photomultiplier.

## Equipment

The equipment is as follows:

• Tektronix Oscilloscope (Model TDS 1002)
• Bertan Power Supply (Model 215, 3000V, 5mADC)
• Canberra Delay Module (Model 2058)
• Ortec TAC/SCA Module (Model 567)
• Harshaw NIM Bin (Model NQ-75)
• Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)
• Photomultiplier Tube (PMT)
• LED circuit
• BNC Cables

## Safety

The major safety concerns are as follows:

• Human Safety the main concern is for the electricity due to the electrical equipment we are using the Harrison Power supply for example has enough volts and amps to cause serious electrical shock to an individual which could potentially ruin your day, in addition there are quite a few things that plug into the wall and draw power and current which could cause problems so be careful when using electricity
• Be careful about damaging the equipment. The photomultiplier for example can be damaged quite easily especially when plugged in never expose it to sunlight while operating it this can potentially ruin it due to the fact that it is very sensitive to light and is designed to detect very low intensity light and when exposed to light that has intensity grater that it is designed to operate with it will burn out and destroy the equipment. Also make sure you are operating at the electrical equipment with in its operating specifications as not to cause any harm to each individual piece of equipment.

## Set Up

• I followed the following set up procedure outlined in Dr Golds Lab Manual and took also from Tom Mahoney's Lab Notebook thanks Tom
• 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.

## Notes

### Day 1

• Worked with Elizabeth Allen during this lab
• First we had the safety brief with Dr. Koch witch involved a good amount of electrical safety as well as what danger we pose to the equipment specifically the photomultiplier.
• After the brief we plugged in and set up all the equipment and started to figure out what we need to find and measure
• We did not take any data this day but mostly figured out how to set the triggering and what to look for on the oscilloscope and at what dime delay to put on the delay module

### Day 2

• Worked with Elizabeth Allen
• We came into the lab again and set up the equipment again and set the lab up with a 9 nanosecond delay on the delay module
• We ended up doing 3 trials with the equipment. We first had the led at a distance of 0 cm away from the photomultiplier according to the ruler on the end of the led and took an initial reading with the voltage at 7 volts and then bringing the led a distance of 10 cm closer to the photomultiplier and adjusting the filter to compensate for the additional amount of light that was hitting the photomultiplier by rotating the photomultiplier in its holder until we got the voltage back to 7 volts again. We repeated this process every 10 cm until we reached a distance of 100 cm at witch point we would start again. The data we collected was on the voltage that was read on the oscilloscope after we adjusted for the time walk that we compensated for these readings were taken from a averaging function on the oscilloscope with was 16 averages. We used the same process as above for the next two trials but the voltages we were adjusting for changed due to the fact that we would have trouble getting to the same voltage and in addition we also changed the averaging function on the oscilloscope. For the second trial the averaging function was changed from 16 to 64 averages and the voltage for the time walk was changed from 7 to 6.8 volts. On the third and last experiment the averaging function was again changed this time to 128 averages and the voltage was at 7 volts again. This was recorded on the data chart.
• We did another 3 experiments with the same set up again but this time we took data every 25cm instead of every 10 cm and went to a distance of 150 cm instead of 100 cm. We also varied the voltage and the averaging functions of the oscilloscope. For the first trial we used 16 averages and a voltage of 6 volts. On the second we used an averaging function of 64 averages and a voltage of 6.6 volts. For the last run we used an averaging function of 128 and a voltage of 7 volts.

## Data

Graph of first 3 trials
Graph of the second 3 trials

## Calculations and Data Analysis

• To find the speed of light first I needed to graph the voltage vs the distance the light would travel and find a linear fit.
• My slope was $6.068(.38)\times 10^{-3\frac{volts}{cm}}$ for the first set of experiments when I was going on 10 cm increments and when I was going on 25 cm increments the slope was $6.95(.32)\times 10^{-3\frac{volts}{cm}}$
• Then I took the inverse of each slope to give me $164.26\frac{cm}{volt}$ for the first experiment and a slope of $143.83\frac{cm}{volt}$ for the second experiment. Then for the errors I just took the inverse of the slope plus the error and minus the error and subtracted the two
• So the values I obtained were first experiment $164.26(1.28)\frac{cm}{volt}$ ,and for the second experiment $143.83(.63)\frac{cm}{volt}$
• To obtain a figure that you can see what the speed of light actually looks like in the form that most of us are used to we need to convert from cm/volts to meters/second. We can do this by the following $\frac{meter}{volt}\times \frac{volt}{5\times 10^{-9}sec}$
• so doing this to my equation produces
Experiment 1 $3.285(.025)\times 10^8\frac{meters}{sec}$ which is my speed o'light
Experiment 2 $2.8767(.0127)\times 10^8\frac{meters}{sec}$ which is my speed o'light
• Based on the value of the speed of light given from Wikipedia witch is 299,792,458$\frac{meters}{sec}$ my error can be given by $\frac{actual-predicted}{predicted}=$%Error
• So for the value I obtained from experiment 1 I got 9.58% error with 68% confidence interval
• For experiment 2 I obtained an error of 4.04% with a 68% with confidence interval

## Errors in the process

• Some possible sources for error in this lab is the amount of random noise that was being detected by the oscilloscope when we were trying to collect our data. There was too much error to get correct reading while correcting for the time walk so we also had to use the function average on the oscilloscope which also may have introduced a significant amount of error into our experiment but not too much because the data was not to far from the average value we used to find the slope. This error from the averaging function is most likely systematic error due to the nature of averaging data instead of just taking raw data points. Random error was rampant in this lab due to the fact that we had to use the average function just to be able to view the data with out having too much deviation in the data and not being able to tell what the hell was going on. Other sources of error could come from not being absolutely perfect in reading the ruler that was used to determine distance that was reached but what can you do but your best. other sources could come from the fact that when you are compensating for the time walk you need to rotate the photomultiplier and you could end up moving the photomultiplier an additional distance away from the led that could not be taken account for but like I said you do the best you can.