User:Michael R Phillips/Notebook/Physics 307L/2008/10/01

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 * style="background-color: #339999"|[[Image:Green_laser.jpg|145px]] Speed of Light
 * style="background-color: #669999" align="center"|  |Main project page
 * style="background-color: #669999" align="center"|  |Main project page


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Set up & preliminary data
After taking our safety quiz, we started fiddling around with all our equipment, including our oscilloscope (Tektronix TDS 1002), photomultiplier tube (PMT) and the associated power supply (Bertan model 315) and NSEC Delay (Canberra model 2058), our LED light with a periodic voltage supplied to it by a 200V power supply (Harrison model 6706A), and the Time-to-Amplitude Converter (aka TAC, EG&G Ortec model 567).

We fired everything up, using these values:
 * Voltage to PMT: 1820V
 * Voltage to LED: 190V
 * TAC multiplier: 1
 * TAC range: 50
 * Delay: 0

We initially collected a lot of terrible data at first, using some error voltage created by the output of our TAC. Following is some actual preliminary Data (meaning on day 1 ).

These are all measured with our initial (farthest) data at x=0, slowly moving the LED closer to the PMT. They are the voltages of our output square wave (aka our TAC).
 * Reference Voltage = -432mV
 * At x=0: 5.2±0.2 V
 * At x=5: 5.0±0.4 V
 * At x=15: 5.8±0.4 V
 * At x=20: 5.4±0.4 V
 * At x=30: 3.6±0.4 V
 * At x=40: 4.0±0.4 V
 * At x=50: 5.0±0.4 V
 * At x=60: 4.6±0.2 V
 * At x=70: 4.0±0.2 V
 * At x=80: 6.2±0.2 V

Day 2


On the beginning of the second day, aside from deciding that our first day led to terrible data, we set up everything as we remembered from the previous week. Within just a couple of minutes, we powered everything up and got a square wave result for us to measure. As soon as we moved the light source back for a starting position, however, we lost our square wave and had to start fiddling with the O-scope and other equipent to recover it. After some time, we managed to regain a decent square wave by rotating our photomultiplier tube to get a maximum readable voltage. We even managed to measure the threshold of the TAC to be 400mV (this is the voltage that we do not want to allow below) with some minor assistance from Koch.

We started by setting our TAC voltage very high, at 1950V, so that we could get large outputs. This is our calibration data for a few different time delays.

We will use this data to do a linear fit. The slope should be very near 10V/50ns.

Data Acquisition
Here is the data we took initially, correcting for the amplitudes by rotating the photomultiplier tube (and polarizer).

x(cm) V(V) 0     4.8 10     4.8 20     4.8 30     4.8

We decided this was not the way for us to go about the experiment, so we changed our tactics:

Now we start taking actual (good) data. Following are the data points we took. The 'x' values are how much we moved the light source closer to the photomultiplier tube, and the 'V' values correspond to the output from the TAC. This is all taken without any rotation of the photomultiplier tube (thus no rotation of the polarizer) and using the measure function of our oscilloscope.

x(cm)    V(V) 0        5.0 10        4.6 20        4.0          30        3.7±0.1         40        3.4 50        3.2 60        2.8 70        2.6 80        2.2 90        2.0 100       1.6 110       1.2 120       1.0 130       0.4 140       0.2 150       0.0

As soon as we finished taking this data set, we thought it may have been a good idea to also show what our PMT voltage was doing as we changed the distance between the light source and the photomultiplier tube, but it was a little too late for that. Perhaps later...

Next, we decided to retry taking data with the corrections to polarizer rotation, keeping our PMT voltage constant. Again, 'x' represents our distance moved inward from our initial position, while 'V' represents our TAC output voltage

Constant PMT (using measure pk-pk): V=568mV

x(cm)  V(V) 0      4.96 10      4.88 20      4.80 30      4.72 40      4.64 50      4.56 60      4.48 70      4.40 All of these voltages have a ±0.08V error in them.

Now we return to what we did before, but with a more accurate measure and also while keeping track of the PMT voltage (denoted as 'P').

x(cm)   V(V)         P(mV) 0       4.88±0.08      576±8 10       4.32±0.08      616±8 20       3.96±0.04      672±8 30       3.64±0.04      720±8 40       3.40±0.04      760±8 50       3.08±0.08      848±8 60       2.42±0.04      992±8 70       2.20±0.04      1110±10      80       1.88±0.04      1230±10 90       1.56±0.04      1380±10 100      1.24±0.04      1550±10

After this, we did another run using correcting rotation so that we get very good values. Constant PMT voltage: 592mV

x(cm)    V(V) 0       4.84±0.03 10       4.57±0.03 20       4.55±0.03 30       4.51±0.03 40       4.40±0.04 50       4.35±0.03 60       4.24±0.04 70       4.02±0.04 80       4.14±0.04 90       3.92±0.06 100      3.97±0.03

Data Analysis
Now that we have decent data, we can use it all to calculate the speed of light. After we use linear fits to our calibration and true data, we will use the slopes to find a speed of light.

From change in position versus voltage plot: m=(cm/V)  [from actual data] From voltage versus delay time: n=(V/ns)   [from calibration data] So to find the speed of light: m·n=b (in cm/ns) Then converting to m/s (SI units): c=b·(109 ns/s)/(100 cm/m)

Here are our excel files: [[Media:SpeedOfLight1.xls | Speed of Light 1]], [[Media:SpeedOfLight2.xls | Speed of Light 2]]

Make sure to look in all sheets (tabs at the bottom) to see all of the data.


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