Physics307L:People/Gibson/Formal Lab Report 2

MEASURING THE SPEED OF LIGHT BY A TIME DELAYED SIGNAL BETWEEN A LIGHT EMITTING DIODE AND PHOTOMULTIPLIER TUBE

Author: Zane Gibson

Experimentalists: Zane Gibson Matthew Gooden,

Department of Physics and Astronomy

University of New Mexico

Albuquerque, NM

zgibson@unm.edu

Abstract

This experiment was done to determine the value of [math]\displaystyle{ c }[/math] or the value of the speed of light. To complete this experiment, a time amplitude converter (TAC) and an oscilloscope were used to measure the time between a light signal from an light emitting diode (LED) and a photo multiplier tube (PMT). By changing the distance between the PMT and the LED, we were able to record various voltages for various distances, then we converted the voltage to a time and constructed a trend line of our distances and times using a least squares fit analysis. The slope of this trend line was the constant we were originally looking for, the speed of light. For this experiment we found our constant to be [math]\displaystyle{ c=\left(2.892 \pm .077\right)\times10^8 m/s }[/math] which is very close to the theoretical approximation of [math]\displaystyle{ 2.99\times10^8 {m/s} }[/math].

Methods and Materials

Equipment List

---

1.Time-Amplitude Converter (TAC) - EG&G Ortec Model 567 TAC/SCA

2.Light Emitting Diode

3.Photomultiplier Tube (PMT) - Magnetic Shield Co., 22P50

4.DC Power supply (LED) - Harrison Laboratories, Model 6207A 0-160V,0-.2A

5.DC Power supply (PMT)- Bertan Associates,Inc. Model 315, DC Power Supply 0-5000V,0-5mA

6.Oscilloscope - Tektronix TDS 1002 2 Channel Digital Storage Oscill., 60MHz 1GS/s

7.BNC Connector Cables - 6

8.Delay box - Canberra NSEC Delay Box, Model 2058

9.Several Meter Sticks - 4

10.Long Tube (cardboard or other nontransparent material) - 4 meters long

Procedure

---

Set up - To begin the experiment we first collected all our equipment, then proceeded to first get power to the LED. We then did the same for the PMT (NOTE: Do not expose the PMT to massive quantities of light while operating, this can destroy the PMT) then placed them in the long cardboard tube. We then bolted the LED to one of the ends of a meter stick (so we could vary the distance) and taped the sticks end to end to allow us plenty of variable distances. Using a connector cable, we connected the PMT signal output into channel 1 of the oscilloscope and plugged the response from the LED (when it sent a signal) to the TAC. We then ran a cable from the TAC to the time delay box, and then to channel 2 of the oscilloscope. The distance of how far in or out the LED was is arbitrary. Taking whatever place as the zero works fine and recording the differences in the distances is what is important.

Running the Experiment-

Results and Discussion

^{SJK 13:49, 18 November 2007 (CST)}

13:49, 18 November 2007 (CST)
Your data are excellent! This section, though, is too informal. Again, take a look at some published papers to get a feel for what is typical. Some discussion you can include is what are the sources of your uncertainties, what (if any) are the differences in the data sets..

In discovering the times for each data set, we were required (since we didn't measure time) to use the equation V=G*T where V is voltage; T is the time we want, and G is a constant set before we began taking measurements = 1/10 volt/nanosecond.

Here we took down measurements as listed in the procedure and placed them below:

Data Set 1 Measurments	PMT Ch1 Voltage	TAC Time delay voltage	Distance (cm)	Time (ns)
1	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.24\pm.04 }[/math]	60	32.4
2	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.2 \pm.04 }[/math]	80	32
3	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.08 \pm.04 }[/math]	100	30.8
4	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.00 \pm.04 }[/math]	120	30
5	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.96\pm.04 }[/math]	140	29.6
6	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.00 \pm.04 }[/math]	130	30
7	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.12 \pm.04 }[/math]	90	31.2
8	[math]\displaystyle{ 600 \pm 8 {mV} }[/math]	[math]\displaystyle{ 3.2 \pm.04 }[/math]	70	32

Data Set 2 Measurments	PMT Ch1 Voltage	TAC Time delay voltage	Distance (cm)	Time (ns)
1	[math]\displaystyle{ 800 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.44\pm.04 }[/math]	70	24.4
2	[math]\displaystyle{ 800 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.4 \pm.04 }[/math]	80	24
3	[math]\displaystyle{ 800 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.36 \pm.04 }[/math]	90	23.6
4	[math]\displaystyle{ 800 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.32 \pm.04 }[/math]	100	23.2
5	[math]\displaystyle{ 800 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.32\pm.04 }[/math]	110	23.2

Data Set 3 Measurments	PMT Ch1 Voltage	TAC Time delay voltage	Distance (cm)	Time (ns)
1	[math]\displaystyle{ 720 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.8\pm.04 }[/math]	27.5	28
2	[math]\displaystyle{ 720 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.64 \pm.04 }[/math]	70	26.4
3	[math]\displaystyle{ 720 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.52 \pm.04 }[/math]	110	25.2
4	[math]\displaystyle{ 720 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.44 \pm.04 }[/math]	130	24.4
5	[math]\displaystyle{ 720 \pm 8 {mV} }[/math]	[math]\displaystyle{ 2.72\pm.04 }[/math]	50	27.2

• NOTE: See acknowledgments section

Once we completed calculating our times for each of the trials, we then proceeded to construct 3 least squares plots to determine what our value of the speed of light would be. To do this we simply took the distance recorded vs time which then gave us a very linear graph... the slope of this line is the constant we were looking for.

These are plot of data sets 1-3 along with least-squares fit lines

• The slopes for each data set are listed below:

Data Set 1

          [math]\displaystyle{ c=\left(2.68  \pm 0.18\right)\times10^{8} m/s }[/math]

Data Set 2

          [math]\displaystyle{ c=\left(2.94  \pm 0.42\right)\times10^{8} m/s }[/math]

Data Set 3

          [math]\displaystyle{ c=\left(2.89  \pm 0.08\right)\times10^{8} m/s }[/math]

Average of all three data sets:

          [math]\displaystyle{ c=\left(2.83 \pm .23\right)\times10^8 m/s }[/math]

From here we calculated our relative error to determine the amount off of the theoretical value:

[math]\displaystyle{ Relative Error=\frac{\left|2.83\times10^{8}-2.99\times^{8}\right|}{\left|2.99\times10^{8}\right|}=0.0535=5.3% }[/math]