User:Randy Jay Lafler/Notebook/Physics 307L/2010/10/18

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=Speed of Light= The purpose through the setup as well as the Excel sheet and graphs are the same as in Emran's notebook

Purpose
To measure the speed of light by using a T-A converter and an oscilloscope.

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 supplys, the T-A converter, and the oscilloscope.
 * We studied the wires connecting the devices together and the display of the oscilloscope until we understood what everything meant. We also asked for an explanation for Professor Koch  and for Katie.
 * 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 diviation using linest, and calculated a Standard diviation 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 diviation is symmetric about our best value.
 * Emran insisted in doing a weighted mean calculation for C as well.

Data
Excel 2003 Data File



Analysis
The accepted value for the speed of light is 30cm/ns. We got a value of 31.5(1)cm/ns for the first trial, and we obtained a value of 32.1(19)cm/ns for the second trial. These values are both larger than the accepted value for the speed of light. The accepted value is a little more than one standard diviation smaller for both of our measurements. Even though our values for the speed of light are both larger than the accepted value, they seem to be consistent with each other. The range for our first data is 30.5cm/nm to 32.5 cm/nm, and the range for our second data set is 30.2cm/nm to 34cm/nm. So, the ranges for our data do overlap.

Error
The accepted value of C:
 * $$C=30cm/ns\,\!$$

Since both our data sets are larger than the accepted value by a similar amount, it is possible we had some systematic error in our measurements. Other possible error could be do to us not holding the intensity of the light completely constant. We had to turn the PMT within the tube to maintain the spike measured by the oscilloscope at the same level, and thereby keep the intensity the same. We had to do this by matching the side of the spike to the cursor line on the oscilloscope, and the spike was very sensitive at close distances to turning the PMT. I have more explanation for the error in my summary. Error in Summary

Acknowledgments/Citations
Emran for the picture's, Excel sheet and graphs.


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