User:Ginevra Cochran/Notebook/Physics 307L/Speed of Light lab

Purpose
This lab's purpose was to measure the speed of light and compare it to the accepted value.

Equipment

 * Tektronix Oscilloscope - TDS 1002
 * Bertan Power Supply - 215
 * Canberra Delay Module - 2058
 * Ortec TAC/SCA Module - 567
 * Harshaw NIM Bin - NQ-75
 * Harrison Laboratories Power Supply - 6207A
 * Photomultiplier Tube PMT
 * LED circuit
 * BNC Cables

Safety
The main personal risk in this lab was electrical - we checked all cords for fraying and made sure the power supply was grounded. We also were careful not to expose the photomultiplier tube to direct light.

Setup
I worked with Cristhian on this lab. We followed Professor Gold's manual and Alex Andrego's lab notebook. The PMT was already inside the tube and attached to the delay module, and the LED was connected to the TAC and the Harrison power supply, as well as the oscilloscope. We set the Bertan power supply to 2400 V, the Harrison power supply to 190 V,and the delay module to 32 ns. We set the TAC's range to 100 ns and its multiplier to 1. We set the output switch to out and the stop switch to anti.

Analysis
Our measurement of the speed of light was obtained from the delay between the signals from the LED and PMT, which was converted to voltage. We took measurements of the delay voltage every 10 cm from 260 to 140 cm. At 260 cm, we twisted the PMT to maximize the calibration spike on the oscilloscope. Using the measure function on the oscilloscope, we recorded the height of the second signal, which represented the time-of-flight. Our calibration spike was adjusted at each increment, but basically seemed to stay at the same voltage. We repeated this process 5 times, with Cristian recording trials 1 and 3 and me recording trials 2,4 and 5. The range setting on our TAC meant that our conversion factor was $$10 ns/V$$.

We averaged our voltages for each distance (column E) and converted these to time measurements using the TAC conversion factor given above. I then graphed these time measurements vs. distance and found a best-fit line using Excel - the slope of this line was $$.1061 ns/cm$$. This slope is also calculated in cell H2 of the Google document above. Inverting this value gives the speed of light as $$9.43 cm/ns$$ (cell I9). Using Google Docs, I calculated the standard deviation (J2) and standard error of the mean (K2) of the set of time measurements (F2:14). I inverted this standard error of the mean and obtained an estimate of uncertainty for our speed of light value: The accepted value for the speed of light, according to Wikipedia, is
 * 9.43 ± 0.87 cm/ns.
 * 29.98 cm/ns.

Error
Error in this lab could have stemmed from the oscilloscope - the voltage measurement was hard to obtain because it fluctuated so much, even when we maximized the number of averages we were taking. Another major source of error was due to the calibration spike - I was not sure whether it should be set to a specific value or constantly set to its lowest possible value. We tried to maintain a calibration level of 1.57 V. This varying spike represented a varying amplitude in the light pulse, which caused a "time walk" which we may not have corrected for properly. Cristhian and I took turns reading the scope, and that also may have been a source of inconsistency between our sets of measurements. I do not feel that any of these sources account for the vast systematic error in our results, but I am at a loss to explain where it did come from, unless the setting on the delay module were incorrect.