User:Anastasia A. Ierides/Notebook/Physics 307L/2009/10/12

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Speed Of Light
Partner: Alex Andrego

Equipment

 * Bertan Associates Inc. Power Supply Model 313B (0-3000V, 0-10mADC)
 * Harrison Laboratories Power Supply Model 6207A (0-160V, 0-0.2A)
 * Canberra 2058 Delay Module
 * Ortec 567 TAC/SCA Module
 * Harshaw NQ-75 NIM Bin
 * Photomultiplier Tube (PMT)
 * Tektronix TDS 1002 Oscilloscope
 * LED circuit
 * BNC Cables

Safety
Before we begin, some points of safety must be noted:
 * 1) First and foremost your safety comes first and then the equipments'
 * 2) Check the cords, cables, and machinery in use for any damage or possible electrocution points on fuses of machinery by making sure the power cords' protective grounding conductor must be connected to ground
 * 3) Be careful when handling the photomultiplier tube (PMT) (it can be ruined in ambient light when at operating voltages)
 * 4) Be careful when handling the Harrison Laboratories 6207A Power Supply when the capacitor plates are fully charged, even when unplugged wait for it to discharge for it may be a source of electrical shock
 * 5) Make sure the areas containing and around the experiment are clear of obstacles

Purpose
The purpose of this lab is to measure the speed of light, $$c\,\!$$ using short pulses of light and a high speed detector in a direct time of flight measurement over distances of one to two meters. Speed Of Light Introduction

Brief Description of Light
Light, in physics, is described as electromagnetic radiation of any wavelength consisting of photons (tiny packets of energy with both a wavelike and particle-like property, called wave-particle duality). The speed of light $$c\,\!$$ in vacuum is currently accepted as $$299,792,458 m/s \,\!$$. The speed of light is constant in every reference frame between particles. The speed of light appears to slow down through particles; the reason for this is the displacement of energy through which subatomic particles, such as electrons, are excited. Light can be measured by its intensity, frequency (or wavelength), polarization, and/or phase. Wiki on Light

Setup & Procedure
Note: Alex and I used the same set up and procedure. This is a direct copy of it. 
 * The procedure we followed was based on the descriptions given in | Professor Gold's manual and outlined with more detail in Tom Mahony's Speed of Light Lab Note Book.




 * We first connected all elements of our experiment with our BNC cables.
 * The "-HQ" connection of the photomultiplier tube (PMT) to the Bertan Power Supply (PSU).
 * The "A" connection of the photomultiplier tube (PMT) to the top input of the delay module.
 * The output of the delay module to a BNC T-splitter
 * One side connected to the channel 1 input on the oscilloscope
 * The other to the "Stop" input of the Time-Amplitude Converter (TAC).
 * The "Start" input of the TAC to the cable attached to the LED.
 * The power cable for the LED to the Harrison PSU.
 * The output of the TAC to the channel 2 input of the oscilloscope.


 * We then had to varify that all of our equipment was on the correct setting
 * For the Bertan power supply:
 * Top polarity switch on negative
 * 2000 volts
 * Voltage adjustment to 400


 * For the the delay module
 * Delay equal to 9 ns.


 * The Ortec Time-Amplitude Converter (TAC)
 * The range at 100 ns
 * The multiplier to 1
 * Start and stop switches to "anti"
 * The output switch to "out."


 * The Harrison PSU
 * 190 volts


 * We then turned our entire set up on and witnessed the delay between the LED circuit triggering and the PMT measuring the LED's pulse
 * We measured this delay using the TAC
 * We were then able to convert the measured voltage to be the response time.
 * By measuring this voltage at different points, we were able to calculate the difference and divide by the distance to find the speed of the incident light.

Calculations
The slope achieved by excel from our plot was:
 * $$0.006663636\frac{Volts}{centimeter}\,\!$$

The uncertainty in our slope was calculated using codes in excel and was:
 * $$0.000110554\frac{Volts}{centimeter}\,\!$$

The uncertainty is added and subtracted to the slope before it is inverted:
 * $$(0.006663636\pm0.000110554)\frac{Volts}{centimeter}\,\!$$

Then we invert it to get:
 * Minimum Range Inverse Slope:
 * $$\frac{1}{0.006663636+0.000110554}\simeq147.6191135\frac{centimeters}{Volt}\,\!$$
 * Maximum Range Inverse Slope:
 * $$\frac{1}{0.006663636-0.000110554}\simeq152.5999475\frac{centimeters}{Volt}\,\!$$
 * Average Inverse Slope:
 * $$\frac{1}{0.006663636}\simeq150.0682128\frac{centimeters}{Volt}\,\!$$

To attain a slope in "meters per second" we use the TAC conversion given for our settings which was $$5ns/Volt\,\!$$
 * $$c_{measured, average}=\frac{150.0682128\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq3.0014\times10^8 m/s\,\!$$
 * $$c_{measured, minimum}=\frac{147.6191135\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq2.9524\times10^8 m/s\,\!$$
 * $$c_{measured, maximum}=\frac{152.5999475\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq3.0520\times10^8 m/s\,\!$$

Here we've found our best guess as well as the maximum and minimum range of values for the measured speed of light.

The percentage error of our average measured value relative to the accepted value of the speed of light $$c_{accepted}=299,792,458 m/s \,\!$$ can be calculated as:
 * $$\% error=\frac{c_{accepted}-c_{measured, average}}{c_{accepted}}\,\!$$
 * $$\% error=\frac{(299,792,458-3.0014\times10^8) m/s}{299,792,458 m/s}\,\!$$
 * $$\simeq0.001159\,\!$$
 * $$\simeq0.116%\,\!$$

Notes About Uncertainty
Systematic Error:
 * The meter stick was placed in an odd way in which each distance measurement had originated from a value of $$+0.8 mm $$ more than a rounded measurement (i.e. instead of reading 60 cm off of the meter stick we had to read 60.8 cm)
 * The PMT had to be manually adjusted so that the polarizers would align; this was to decrease the intensity of light approaching the PMT in order to have consistent data with the time walk effect (time walk effect is due to differing voltage peaks on oscilloscope, therefore different trigger levels)
 * Note:For a better explanation of the time walk effect please refer to Tom Mahony's Lab Notebook which explains this in greater detail.

Other Error:
 * Due to the fact that zooming into the graphs of the oscilloscope was not possible, our data may vary due to the level of precision we were allowed for measuring the intensity of light coming through for each trial

Speed Of Light Lab Summary
This is the link to my Balmer Series Lab Summary: Speed Of Light Lab Summary

Acknowledgments
Please note that Alexandra S. Andrego was my lab partner for this lab. Her version of this lab can be found here
 * Prof. Gold's Lab Manual served as a loose guideline for our lab procedure and our calibration wave lengths
 * We used Google Docs to format and post our raw data and error analysis to our wiki notebook
 * We used Tom Mahony's Speed of Light Lab Note Book for more specific set up instructions, since his was so well done
 * This link Wiki on Light was used as the reference for the description of light


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