User:Garrett E. McMath/Notebook/Junior Lab/2008/11/10
 Speed of Light
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SJK 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 17:09, 17 December 2008 (EST) See also Paul's notebook for more comments. Speed of LightThe speed of light is an important fundamental constant in nature. The constant forms the framework of special relativity, and plays a huge role in electrodynamics. Proper measurement of the constant is clearly an important goal in physics, and so in this lab we will attempt to do so. In this lab, we will be emitting light from a light emitting diode (LED), and then absorbing this light shortly after with a photomultiplier tube (PMT). Both of these components will be placed in a cardboard tube so as to remove the possibility of errors due to ambient light. To measure the speed of light, we will have to measure the time of photon emission and also the time of photon absorption. Both tasks will be accomplished with the help of an oscilloscope, and a time amplitude converter (TAC). In general, a time amplitude converter converts times to voltages, with a conversion factor of your choice. The time which we will be converting to a voltage will be the time delay between emission and reception. The output voltage will be intercepted by an oscilloscope. Equipment
Procedure
DataDay 1Dx measured relative to the point where the diode and PMT are touching. Min on channel 1 to max on channel 2 Conversion factor for the TAC: V=GT, G=1/10 Volts per nanosecond Channel 1: Min -618±8mV Dx=60cm Max=1.64 Time=16.4ns Dx=70cm Max=1.66 Time=16.6ns Dx=90cm Max=1.72 Time=17.2ns Dx=100cm Max=1.75 Time=17.5ns Dx=110cm
Trial 1 Day 2Channel 1 Min: -488mV Dx=.60m V=2.35V Dx=.70m V=2.60 Dx=.80 V=2.68 Dx=.90 V=2.82 Dx=1.00 V=2.76 Dx=1.10 V=2.74 Dx=1.20 V=2.84 Dx=1.30 V=2.92 Dx=1.40 V=2.98 Dx=1.50 V=2.92 Dx=1.60 V=2.96 Dx=1.70 V=3.04 Dx=1.80 V=3.08 Dx=1.90 V=3.14 Dx=2.00 V=3.18 Dx=2.10 V=3.18 Dx=2.20 V=3.24 Dx=2.30 V=3.26 Dx=2.40 V=3.30 Trial 2 Day 2Dx=2.40 V=3.30 Dx=2.30 V=3.26 Dx=2.20 V=3.22 Dx=2.10 V=3.16 Dx=2.00 V=3.06 Dx=1.90 V=3.12 Dx=1.80 V=3.06 Dx=1.70 V=2.94 Dx=1.60 V=3.00 Dx=1.50 V=2.94 Dx=1.40 V=2.84 Dx=1.30 V=2.80 Dx=1.20 V=2.72 Dx=1.10 V=2.80 Dx=1.00 V=2.78 Dx=.90 V=2.72 Dx=.80 V=2.72 Dx=.70 V=2.62 Dx=.60 V=2.64 Trial 3 Day 2Moving LED away from PMT 10ns Time Delay In effect Channel 1 Min: -488mV Points marked with asterisk were obtained without run-stop (first 3 points). Dx=.60m V=3.80* Dx=.70m V=3.90* Dx=.80 V=3.85* Dx=.90 V=3.90 Dx=1.00 V=3.92 Dx=1.10 V=3.96 Dx=1.20 V=3.98 Dx=1.30 V=4.06 Dx=1.40 V=4.06 Dx=1.50 V=4.14 Dx=1.60 V=4.10 Dx=1.70 V=4.12 Dx=1.80 V=4.18 Dx=1.90 V=4.22 Dx=2.00 V=4.32 Dx=2.10 V=4.28 Dx=2.20 V=4.32 Dx=2.30 V=4.36 Dx=2.40 V=4.42 Possible Sources of Error
I dont' see anywhere where you discuss the problems with the first two data sets, and you don't mention (as far as I can see) that your final value only comes from the 3rd data set. Post Experimental Data AnalysisAnalysis performed in Excel, please open attached file to view data analysis
Error PropagationWe had uncertainty in our measurement of the voltage, due to reading fluctuations in the oscilloscope. Because we converted this voltage to a time reading, we must propagate this error. Because the relationship between conversion is completely linear, propagation will be completely straight forward. The conversion ratio is given by the letter eta. [math]\displaystyle{ t=\eta V \Rightarrow \delta t = \eta \delta V }[/math] Least Squares LineThe most convenient way to determine the speed of light from the data obtained is to make a least squares line of the traveled distances versus the time elapsed. The speed of light will simply be the slope of the line, which can be easily obtained: [math]\displaystyle{ v(t)=c t \Rightarrow Slope = c }[/math] While the above relationship suggests that the line must travel through the origin, this is in fact not the case. The reason that we must not pass through the origin here is that we will be dealing with changes in distances. Therefore, the data points will be plotted in arbitrary space where the origin has no physical analog. AnalysisAfter doing several quick checks of the data it was clear that similar to our predictions the last set of data taken with the stop function on the oscilloscope was the best. The data anaylsis was performed in Excel.
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