User:Garrett E. McMath/Notebook/Junior Lab/2008/11/10
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SJK 17:09, 17 December 2008 (EST)
Speed of Light
The 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.
Dx 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
Trial 1 Day 2
Channel 1 Min: -488mV
Trial 2 Day 2
Trial 3 Day 2
Moving 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).
Possible Sources of Error
Post Experimental Data Analysis
Analysis performed in Excel, please open attached file to view data analysis
We 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.
Least Squares Line
The 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:
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.
After 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.