# User:Johnny Joe Gonzalez/Notebook/Physics 307L/2009/12/02

Speed of Light Main project page
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## Speed of Light

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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 15:21, 19 December 2009 (EST)
15:21, 19 December 2009 (EST)
Excellent lab notebook! Also, appears that you and John did a really great job in minimizing the systematic error from time walk. Such that your measurements were consistent with the accepted value.

### Safety

Electric shock is a primary concern, especially since this equipment and experiment has a history of shocking people, the photomultiplier tube requires a negative voltage anywhere from 1800V to 2400V. Sharp corners on the equipment can also be dangerous, and special care should be taken when dealing with the photomultiplier tube (PMT)since it can very easily be damaged with ambient light, it is important to always keep the PMT inside the cardboard tube in order to insure that none of the ambient light can reach it. The cable were checked for fraying or damaged areas.

### Materials

This is a list of the materials used for this lab, the list is actually provided by David Weiss, I used his lab notebook to get the model numbers for the equipment in order to save time in writing in the notes, I am confident that this is the same equipment he used for his lab. David's lab notes, used for gaining model numbers on equipment.

Figure 1, A picture of the Tektronix Oscilloscope(left), the Canberra Delay module, and the Ortec TAC/SCA Module, both fitted in the Harshaw NIM Bin(right), To the back, inside the cardboard tube is the PMT, the BNC cables are shown connected to all of the apparatus.
Figure 2. This is a long view of the experiment, at the bottom right of the figure you can see the Harrison Laboratories Power supply.

Tektronix Oscilloscope (Model TDS 1002)(figure. 1)
Bertan Power Supply (Model 215, 3000V, 5mADC)
Canberra Delay Module (Model 2058)(figure. 1)
Ortec TAC/SCA Module (Model 567)(figure. 1)
Harshaw NIM Bin (Model NQ-75)(figure. 1)
Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)(Seen in figure 2).
Photomultiplier Tube (PMT)(Shown in the back of figure 1)
LED circuit
BNC Cables(figure 1)

### Procedure

The procedure we followed was based on the descriptions given in Professor Gold's manual, the experiment was mostly setup when John and I arrived so we simply double checked all of the connections, we cross-referenced this with other lab notebooks to insure that there was minimal error in our setup. The two notebooks that were used primarily were Tom Mahony's lab notebook, and Alexandra S. Andrego's lab notebook.

Alex's lab notes were amazing and incredibly easy to read, so I simply followed her procedure and setup. The procedure below is copy and pasted from her lab book. We double checked our connections according to this.

This is a schematic of the experiment, this photo of the schematic found in Dr. Gold's lab manual, it was taken from Alaxandra's lab notebook.
• We first connected all elements of our experiment with our BNC cables.
• The "-HQ" connection of the photomultiplier tube (PMT) to the Bertan Power Supply (PSU).
• The "A" connection of the photomultiplier tube (PMT) to the top input of the delay module.
• The output of the delay module to a BNC T-splitter
• One side connected to the channel 1 input on the oscilloscope
• The other to the "Stop" input of the Time-Amplitude Converter (TAC).
• The "Start" input of the TAC to the cable attached to the LED.
• The power cable for the LED to the Harrison PSU.
• The output of the TAC to the channel 2 input of the oscilloscope.
• We then had to varify that all of our equipment was on the correct setting
• For the Bertan power supply:
• Top polarity switch on negative
• 2000 volts
Figure 3. The oscilloscope readings after Dr. Koch helped us through our confusion. Note that to the bottom right of the screen the measured potential can be made out, this is just an arbitrary reading, the distance the LED was from the PMT is still not established. After each change in distance the PMT is twisted, either clockwise or counter-clockwise until this exact graphical reading can be seen again.
• For the the delay module
• Delay equal to 32 ns.
• The Ortec Time-Amplitude Converter (TAC)
• The range at 100 ns
• The multiplier to 1
• Start and stop switches to "anti"
• The output switch to "out."
• The Harrison PSU
• 190 volts
• We then turned our entire set up on and witnessed the delay between the LED circuit triggering and the PMT measuring the LED's pulse. (It was in this part that John and I ran into some problems with the oscilloscope, fortunately Dr. Koch showed us how to fix the problem) After which we were able to get measurements for our light pulses, a picture of what the oscilloscope readings can be seen in figure 3.
• We measured this delay using the TAC
• We were then able to convert the measured voltage to be the response time.
• By measuring this voltage at different points, we were able to calculate the difference and divide by the distance to find the speed of the incident light.
• Four separate trials each ranging from 30cm to 120cm were taken at this time. The data from our trials is shown in Google docs below.

### Data

The data shown is the time of flight measurements with the distances measuring between 30cm to 120cm, the reason for using these boundaries was mostly due to space issues in the lab more than anything else. when a light pulse was sent from the LED to the PMT the TAC would generate an output voltage, the amplitude of the voltage was proportional to the start-stop time difference of the light pulse.

Across the top of the data is the measured range using a meter stick that was attached to the LED (we trust that it's distance from the PMT is calibrated correctly), on the far left are the trials, and inside the grid is the measured potentials that came from reading the oscilloscope. The potentials fluctuated at about 0.08V when we took these measurements, we simply used the median of the fluctuations and wrote that in as our measured potential.

After taking several measurements, linest on Google docs was used to find the slope of the measurements, both the slope of each individual trial was found and then the average of these slopes was taken.

Following is the same data as before, only this time using Microsoft excel, with excel I made two different plots, one with distance vs voltage and then it's inverse. I also fitted a trend line with both plots which was something I was unable to do with Google Docs.

#### Data Analysis

SJK 15:19, 19 December 2009 (EST)
15:19, 19 December 2009 (EST)
A bit confused because the 148.902 number doesn't match the 149.48 number in your excel sheet, and also the above graph looks a bit too linear? I see another graph in your excel sheet that looks different.

From the above we can then take the slope of the plots to gain the measurement for the speed of light.

The slope of my line turns out to be $148.902\frac{centimeters}{Volts}$

This value, however, is still not in the proper units, so we next have to convert this over to something we can actually understand(I have no idea how fast a cm/Volt is), we can do this by referring to the manual and finding our factor for the TAC, from this we can then calculate the true speed of light. For our measured data and configurations the TAC conversion is 5ns / Volt, once this is figured in we get the following:

$148.9\frac{centimeter}{Volts}X\frac{Volts}{5*10^{-9}seconds}=2.978*10^{8}m/s$

Unfortunately some of my measurements were very different, and because of this my standard deviation is quite high, when error is propagated our answer becomes far less precise:

$148(8)\frac{centimeters}{Volt}X\frac{Volt}{5*10^{-9}seconds}=2.96*10^{8}m/s$
with a minimum value of:
$140\frac{centimeters}{Volt}X\frac{Volt}{5*10^{-9}seconds}=2.80*10^{8}m/s$
and a maximum value of:
$156\frac{centimeters}{Volt}X\frac{Volt}{5*10^{-9}seconds}=3.12*10^{8}m/s$

This gives an overall result of: $2.9(2)*10^{8}\frac{meters}{second}$

When I use the inverted linest my result changes to the following:

$1/(0.00664\frac{Volts}{cm}*\frac{1}{5*10^{9}V/s})=3.01*10^{8}\frac{meters}{second}$

My Lab Summary
My lab Partner John Callow

SJK 15:20, 19 December 2009 (EST)
15:20, 19 December 2009 (EST)
The inverted method is probably better, since most of your random error is on your voltage measurements, not the distance values.