User:Tyler Wynkoop/Notebook/Junior Lab/SOL
Speed of Light
- Tektronix TDS 1002 Oscilloscope
- Time to Amplitude Converter (TAC)
In this lab, the goal is to measure the speed of light, simply enough, but this is not a simple experiment. As the most fundamental constant in physics, as well as the fastest, It is extremely difficult to measure. Since it is not possible to measure a phenomenon that occurs faster than measuring devices can send and receive signals using conventional means, we needed to use time delays and round-about methods to achieve our goal.
Set Up and Procedure
The lab consists of a long tube, ours was cardboard, 3 or so meters long. At one end of this tube is a photo-multiplier tub (PMT) with a polarizer in front. On the other end is a green LED on the end of a movable rod, also with a polarizer. The LED is powered by a pulsating DC power source, which pulses at around 10 kHz at 150-200V. Both the LED and the PMT are linked to a time-to-amplitude converter (TAC), which is, in turn, linked to an oscilloscope for analysis.
When the LED flashes at one end of the cardboard tube, it sends a signal to the TAC. When the PMT receives the light from the LED, it sends a signal to the TAC as well. The difference in time is then converted to voltage in the TAC, and sent to the oscilloscope, where it can be recorded. The difficulty is that the light in the cardboard tube, travels faster than the signal down the BNC cable to the TAC. The TAC has a time delay to compensate for this when it receives the signal from the PMT. Ours was set to 12 ns.
In order to measure the speed of light, the length between the LED and the PMT is carefully measured, and the time difference between the LED signal and the (time delayed) PMT signal is recorded. The distance is then carefully adjusted, in our case by 20 cm on the first day and 10 cm on the second day. There is one complication that needs addressed. When the distance between the PMT and the LED is decreased, the intensity of the light increases. By a phenomenon called "Time Walking," this results in a change in the amplitude of the voltage pulse, yielding erroneous data. To correct for this, the intensity of the light is also displayed directly on the oscilloscope. The PMT polarizer is rotated so that the intensity of the light pulse of a new measurement matches the intensity of previous measurements. In our case, since the polarizer was fixed directly on the PMT, I simply rotated the entire PMT in the cardboard tube. In the data collected, 1V = 1ns
Results I used matlab to analyze the data as follows, where L is in meters:
function SOL(L, V)
T = V.*(10^(-9));
c = L./T
c_av = (sum(c)./length(c)) int=(c-c_av).^2; StDev=(sum(int)./(length(int))).^(1/2)
c_acc= 299792458; Error = 100-(c_av/c_acc*100) StDevError = StDev/c_acc*100
0.4630 0.5288 0.5882 0.6500 0.7143 0.7813 0.8511 0.9239 0.9783 1.0556 1.1364 1.2209 1.3095
This gave us an average value of .86x10^8 ± .26x10^8, and an error of 71.3±8.7%. While this appears to be a significant error, the order of magnitude was correct. There is also enormous systematic error in this lab. The polarizer cannot be adjusted precisely, nor can the distance of between the two end points. Beyond this, the PMT is very easy to influence with outside light, and it is very difficult to keep the intensity the same as the distance changes. Finally, the voltage reading was very volatile, each voltage recorded varied as much as ±.75 volts at any given instant leading to very inaccurate data. I would like to note that the longer the distance between the PMT and the LED, the more accurate the readings became.