User:Emran M. Qassem/Notebook/Physics 307L/2010/10/18

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Speed of Light
 * style="background-color: #F2F2F2" align="center"|  |Main project page
 * style="background-color: #F2F2F2" align="center"|  |Main project page


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=Speed of Light=

Purpose
To measure the speed of light by means of distance and and time it takes a photon to travel.

Equipment



 * EG&G Ortec Model 567 Time-to-Amplitude Converter/Single channel Analyzer
 * Tektronix TDS 1002, 2 channel digital storage oscilloscope
 * Power Supply: Harrison Laboratories Model #6207A 0-160 Volts/ 0-0.2 Amps
 * Meter sticks taped together with a photon emitting diode on the end
 * Nano N-134 Photo Multiplier Tube
 * 5 Meter cardboard tube
 * Photon emitting diode

Safety

 * High voltage on the PMT and on the LED, make sure not to shock yourself.
 * PMT should not be exposed to room light while voltage is applied to it or it will be damaged.
 * Do not apply more than 200 Volts to the LED.
 * Do not apply more than -2000 volts to the PMT.

Setup

 * Connect Power supply to Start and to LED using BNC cables.
 * Connect Power on the back of the T-A Converter to the BNC port on the PMT labeled HV.
 * Connect the BNC port between A and D on the PMT to the NSEC Delay on the T-A Converter.
 * Connect the LED to the 200V power supply.
 * Connect the start on the T-A converter to the LED Power.
 * On the T-A Converter, connect the 'stop' connector to the bottom of the Nsec Delay connector with a T BNC connector and then connect to the *Channel 1 of the oscilloscope.
 * Connect the 'TAC' on the T-A converter to the channel 2 of the oscilloscope.
 * Set multiplier to 1.
 * Set Range to 100.
 * Set Tac inhibit to down position (out).
 * Set Voltage to 2000 Volts.
 * Set the counter to 400.
 * Set time delay to 56 nsec (32 + 16 + 8)

Procedure

 * We turned on the power supplies, the T-A converter, and the oscilloscope.
 * Made sure we understood how the wires were connected and to what.
 * We then pushed the LED at the end to the meter stick into the tube until it just touched the PMT, and then we pulled it out a little more than 150cm.
 * We pushed the meter stick in the tube in 10cm increments.
 * We also rotated the PMT in the tube after every change in distance until the dip in the side of the spike was at the same level that it was for the first measurement.
 * We matched the side of the spike to the horizontal cursor line on the oscilloscope that we set during our first measurement. This ensured that the intensity of the light was the same at each distance.  The LED and the PMT both have polarizers on them, so rotating the PMT's polarizer relative to the polarizer on the LED changes the intensity of light allowed to pass through the polarizers and cause a voltage.
 * After we pushed the meter stick in 150cm or until the LED was almost touching the PMT and measured the voltage, we began to pull the meter stick back out the tube in 20cm increments until the meter stick was 140cm away. This is our Data 2 in our Excel sheet.
 * Then we asked how to calculate the time from the voltage, and Professor Koch showed us the range and the voltage on the T-A converter. (Originally we misunderstood the conversion and our measurements we off by a factor of ten.)  The conversion is 1volt=10nm.
 * Then we plotted our data as time verse distance. This is because the almost all of the error in our measurements are due to calculating the voltage and therefore the time.
 * We did a linear fit to our data by using LINEST. We also obtained a standard deviation using LINEST, and calculated a Standard deviation in our final measurement for C by calculating a range in C and subtracting our best answer from the high or the low range value for C.  This is of course assuming the deviation is symmetric about our best value.
 * We did a weighted mean calculation for C as well.

Data
Excel 2003 Data File



Analysis
In our first trial we got a value of 31.5 (10) cm/ns, and in the second we got 32.1(19) cm/ns. These are both larger than the accepted value of 30 cm/ns and off by a little more than one sigma. Our values overlap each other, so this shows that our measurements are reasonable.

Error
As both our results were larger than the accepted value, it seems that our experiment must have had some systematic error. Being off by a little more than 1 sigma isn't that bad of a result, so the systematic error might be in our method of rotating the PMT to adjust the intensity.

Acknowledgments/Citations
Randy for the procedure.


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