User:Nathan Giannini/Notebook/Physics 307L/101117

My lab partner is Richard T. Meyers.

Equipment

 * In addition to the cardboard tube, LED light, and PMT, we had several pieces of equipment that we used in this experiment. They were:


 * Tektronix TDS 1012 Oscilloscope
 * Bertan Model 215 High voltage power supply
 * Ortec TAC/SCA Module (Model 567)
 * Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)
 * Canberra Delay Module (Model 2058)

Safety

 * Warning! There is a high risk of shock hazard with this type of equipment, as the voltage supplied by both power supplies is significant. There is also a risk of damaging the PMT, as even a brief exposure to the light supplied by normal fluorescent lights can ruin it.

Set Up

 * We found that the PMT and LED were already set-up before we had started, as well as the power supplies and the oscilloscope. After verifying that all the BNC cables connected to the correct slots we proceeded with adjustments. We checked to make sure that the main power supply was at 2000V and the offset to 400V. We set the delay to 16 ns. We then set our TAC such that 0.1 V = 1 ns.

Procedure

 * In order to measure the speed of light, we had two signals being fed into the TAC. We found that we had to introduce a delay of 16 ns, so that the TAC would not receive the "Stop Signal" before the "Start Signal".


 * To get the data we initially measured the voltage at the current distance we were at, which we designated as "0" in the spreadsheet in the Data section. We then pulled the LED out by 10cm and would then take another measurement. We repeated this until we got to 100cm from our initial starting point. At this point we extended the ruler out an extra centimeter and then pushed it back in to the same distance. We believed this to be necessary as to eliminate the chance of backlash, since the LED was attached to the meter stick by some means, and may have the ability to stay still for a little bit before it starts moving in the direction we were pushing. It is also important to note that, after each time we moved the LED, we rotated the PMT so that the signal we saw on the oscilloscope had the same value for each measurement. An example of this signal is given by the spike you see in Figure 4.



A more complex version of the procedure, than what is listed above is posted here.

Data
The charts can be viewed by clicking on "Chart 1", etc in the document below.


 * The "Blue Lines" are the fits. Red is data.

Analysis

 * It is important to note that I tried to fit our data two different ways and got different results. They are illustrated below.

Part 1: The LINEST Fit

 * The value given by our LINEST Fit is 30.5 +/- 0.3 cm/ns. The current accepted value for the speed of light in air is 29.97cm/ns as given by this Wiki Article. This means that we are within 2 SEM of the accepted value.

Part 2: The AVERAGE Fit

 * The value given by our AVERAGE Fit is 30.2 +/- 0.5 cm/ns. This means that we are within 1 SEM of the accepted value.

Part 3: The Analysis

 * Obviously LINEST must use some kind of weighting method and should, in general, be more trustworthy. However, the AVERAGE Fit gives us a raw value with an unbiased SEM and should, therefore, be considered in all results determined. However, in general it is best to go with the result that offers you a lower amount of error, as long as the method to determine that result is free of serious error (being that there are no wrong assumptions for the case that is given). A Description of how LINEST works can be found here. The method found in the previous link shows that LINEST actually is better representative of this case and, therefore, is likely to be more accurate. It is interesting to note that the LINEST Fit is within exactly 1 SEM of the AVERAGE Fit's mean value.

Acknowledgements

 * Brian Josey for the pictures and equipment list and a cross-reference for the error that was present in my results.