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

Speed of Light Main project page
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### Set up & preliminary data

SJK 03:23, 22 October 2008 (EDT)
03:23, 22 October 2008 (EDT)
Good materials section. Also, at some point you could have included a picture of what the scope looks like when it's working, especially since one of you thought that would help future students.

It's very good how you keep all the "bad" data in here, along with comments on why you think it's bad. That's very good practice.

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 ). SJK 02:43, 22 October 2008 (EDT)
02:43, 22 October 2008 (EDT)
I presume you recorded this on paper. Yes, it's probably garbage. Probably too annoying to type in by hand. But you could scan in a PDF or take a photo.

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.

SJK 01:40, 23 October 2008 (EDT)
01:40, 23 October 2008 (EDT)
your calibration will also suffer from time walk, and that's why your number (about 0.18 V / ns) was below the expected 0.2 V / ns
Delay (ns) First Run(V) Second Run(V)
0 5.0±0.2 4.8
.5 5.0 4.9±0.1
1 5.0 5.0
2 5.2 5.2
4 5.6 5.6
6 6.0 6.0
8 6.4 6.4
10 6.8 6.8
12 7.2 7.1±0.1
14 7.6 7.6
16 8.0 8.0
18 8.4 8.4
20 8.6±0.2 8.5±0.1

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

#### Data Acquisition

SJK 01:42, 23 October 2008 (EDT)
01:42, 23 October 2008 (EDT)
One really good thing you did with your data was to adjust the oscilloscope sensitivity to a high enough level so you can get enough precision on the voltage measurements. Good work on that!

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

SJK 03:10, 22 October 2008 (EDT)
03:10, 22 October 2008 (EDT)
Well, it turns out we did not get to talk about a big issue: do you trust your calibration more than the manufacturer's? There is time walk when you calibrate, too, because the amplitude of the PMT signal changes from the delay!

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: Speed of Light 1, Speed of Light 2

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

SJK 03:09, 22 October 2008 (EDT)
03:09, 22 October 2008 (EDT)
I think I am following everything, after looking at all of the sheets. I don't understand, though, your motivation for using cell A14 and A16 (on the second sheet) as your final value? That effectively discards all of your data except for two points.???
SJK 03:16, 22 October 2008 (EDT)
03:16, 22 October 2008 (EDT)
Also, graphs are an essential way of presenting data...so, you should upload your graphs that you use for your final values and embed them in the notebook and / or summary. Buried in excel, it's tough to find them, and also, you can't easily refer to them in your writing.