User:Joseph Frye/Notebook/Physics Junior Lab 307L/SpeedOfLight
Speed of Light
SJK 21:25, 25 October 2010 (EDT)
This is a good primary lab notebook. Very nice data & spreadsheet--great that you were able to complete ten independent trials! Your description of setup and procedure with photos is good. Your description of your analysis is a bit lacking, and I wouldn't have been able to understand where you got without benefit of Alex's notebook.
This lab was performed in the senior laboratory in the UNM physics building on September 27th and October 4th with Alex Benedict
Links
Equipment
- Photomultiplier tube
- Time-to-Amplitude-Converter (TAC)
- Ortec TAC/SCA Module (Model 567)
- Delay Module (Canberra Model 2058)
- High voltage power supply (Bertan Model 215, 3000V, 5mADC)
- LED pulser
- Power supply for the LED pulser (Harrison Laboratories Model 6207A, 160V, 0.2A)
- Oscilloscope (Tektronix Model TDS 1002)
Set up
we followed the procedure of lab number 10 in Dr. Gold's lab manual for this experiment.
- the anode signal from the PMT is connected to the 'STOP' on the TAC
- the signal from the LED is connected to the 'Start' on the TAC
- power supply is connected to the LED inside the tube. Ours was set to 190V
- The High voltage power supply connected to the PMT. Our voltage was 2400V
- The signal from the PMT is connected into channel 1 of the oscilloscope
- The signal from the TAC is connected into channel 2 of the oscilloscope
The equipment for this lab was already set up when we started. Thanks to Brian Josey and Kirstin Harriger for helping us to confirm that everything was still connected properly. Kirstin Harriger's notebook for this lab
Procedure
SJK 21:23, 25 October 2010 (EDT)
This photo and discussion is really important for future readers (me, you) to understand what you did. Only thing missing is description of which part of the PMT signal you tried to keep constant.
The top signal here in the photo is channel 1 and is the signal from the PMT. Each time we moved the LED closer to the PMT we rotated the PMT until we had the same amplitude on this signal as before so that the signal from the PMT was consistent in our measurements. The lower signal is the signal from the TAC. The TAC puts out a voltage that is proportional to the time delay from when the LED emits light and the PMT receives it. The idea is that we can measure the change in voltage from the TAC as we change the distance. We then use this to calculate the speed of light.
We started with the LED at some distance from the PMT. We then measured the voltage from the TAC, recorded it in our google docs spreadsheet then moved the LED closer and repeated.
On September 27, we moved the LED by 25cm each measurement and did 6 trials. We were still getting familiar with the technique on the first day so we did more runs the next week and changed the distance by less each measurement. On October 4, we moved the LED 10cm closer each time and did this 10 times to cover 1.0m each trial. We did 10 trials. We then did a linear fit of each trial to obtain the slope of the line. The we averaged the slopes from all 10 trials to obtain our final result.
Data and Calculations
Here is our spreadsheet where we recorded all of our data
{{#widget:Google Spreadsheet |key=0AsLE8iWrtjlSdG55d1hPNVp1c20waXMtLXhEX3F5U0E |width=1200 |height=600 }}
Results
We did a linear fit in google docs for each of our 10 trials on October 4th to find the slope for each trial. Then averaged the slopes for to find the result. Our measured speed of light is 32.685 cm/ns +/- (2.448 cm/ns). SJK 21:21, 25 October 2010 (EDT)
I don't see you saying anywhere in your analysis section how you obtain the uncertainty. I know from reading Alex's notebook that you guys chose the highest individual slope uncertainty, which is not correct, as I'm sure you know now. Here's my comment I put on his page: "As you probably realize now, saying the final uncertainty is equal to the most uncertain result does not correctly provide a 68% confidence interval. There are a couple routes you can go. One is to compute the mean of the slopes (as you do now) and the standard error of that mean. I think this gives you an uncertainty of .13 cm / ns. You could also compute a weighted mean and propagate the uncertainty using the formula we saw in class (total uncertainty = sqrt(1/sum(1/sig^2)). This gives a final uncertainy of .05 cm / ns and the weighted mean is slightly different at 3.25 cm/ns. However, at this point, you'd be presented with a puzzle: The individual measurements differ from each other by more than is expected from the uncertainty of the slopes. I don't know why, but it could be because the slopes seem more precise than they are, due to granularity of the voltage reading. Just a guess. At this point, I'd be inclined to use the SEM of the slopes and not do a weighted mean. So I'd report (3.27 +/- 0.13) cm/ns.
There's room for other arguments, but using the biggest individual uncertainty is not correct. Suppose you took that measurement first. Taking more data, you would only expect the overall uncertainty to decrease, not stay the same or increase."
The accepted value of the speed of light is 29.979 cm/ns
