# User:Alexandra S. Andrego/Notebook/Physics 307L/2009/10/12

Speed of Light Main project page
Previous entry

Please note that the procedure, set up, brief description, and raw data were shared between Anastasia's Lab Notebook and mine. (Steve Koch 00:23, 16 November 2009 (EST):Thank you for the note! I'll put most of the comments on this page.)

## 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. You can see a more detailed purpose in Professor Gold's 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

## Materials

SJK 00:26, 16 November 2009 (EST)
00:26, 16 November 2009 (EST)
Outstanding job with setup, etc. I LOVE all the photos and detailed descriptions. Excellent.
• Tektronix Oscilloscope (Model TDS 1002)
• Bertan Power Supply (Model 215, 3000V, 5mADC)
• Canberra Delay Module (Model 2058)
• Ortec TAC/SCA Module (Model 567)
• Harshaw NIM Bin (Model NQ-75)
• Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)
• Photomultiplier Tube (PMT)
• LED circuit
• BNC Cables

## Safety

Before we begin some points of safety must be noted:
-First and foremost self safety comes first
-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
-Be careful when handling the photomultiplier tube (PMT) (it can be ruined by ambient light when at operating voltages)
-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
- Make sure the areas containing and around the experiment are clear of obstacles

## Set Up

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
• For the the delay module
• Delay equal to 32 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.

## Measurements and Data

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## Calculations and Analysis

From our raw data chart we were able to use the following excel spreadsheet to draw a linear fit line to the slope of our data and to convert our values to find our measured value of the speed of light!
When we graph our distances versus our average measured voltage from the PMT and TAC set-up our slope gives us the speed we are looking for! However just calculating the slope is not enough we had to refer to the manual for our TAC to find the correct conversions ( which in our case due to our settings on the TAC was $5 ns/1 Volt\,\!$
Here is our excel sheet with our calculations...

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}}

SJK 00:31, 16 November 2009 (EST)
00:31, 16 November 2009 (EST)
Very clear spreadsheet and explanation of analysis! I agree with your analysis, and very cool how precise and accurate you are! One comment: I notice how you fit time (well, voltage) versus distance, and then invert to get the speed. I agree with you doing this, since your dominant uncertainties are on your voltages, not your distances. I also agree with the exact way you convert to confidence interval on inverted slopes. Good work!
The slope of our linearfit plot is...
$0.006663636\frac{Volts}{centimeter}\,\!$
We calculated the uncertainty in our slope to be...
$0.000110554\frac{Volts}{centimeter}\,\!$
We used our uncertainty to find a reasonable range for our slope data...
$(0.006663636\pm0.000110554)\frac{Volts}{centimeter}\,\!$
We then had to invert our slope to get a value for velocity...
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 convert our velocity to "meters per second", in order to compare with the accepted value for the speed of light,we use the TAC conversion given for our settings which was $5ns/Volt\,\!$
Then we calculated our best guess, maximum, and minimum values for our measured speed of light.
$c_{measured, average}=\frac{150.0682128\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq3.0014\times10^8 \frac{meters}{second}\,\!$
$c_{measured, minimum}=\frac{147.6191135\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq2.9524\times10^8 \frac{meters}{second}\,\!$
$c_{measured, maximum}=\frac{152.5999475\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq3.0520\times10^8 \frac{meters}{second}\,\!$

-We had to manually turn the photo multiplier tube to align the polarizers to decrease the intensity of the light hitting the PMT to have consistent data due to the time walk effect caused by differing peaks of our voltage and hence different triggering levels. For a better explanation of the time walk effect please refer to Tom Mahony's Lab Notebook which explains this in greater detail.
-We were not able to zoom in close enough to the peaks of our graphs on the oscilloscope, and therefore some of our data may be varrying because we could not be very precise with the intensity of light coming through on each trial.
- Because we used a meter stick to determine the distances between our LED and the PTM there may be some systematic error.

## Summary

If you wish to see my informal summary of this lab follow this link

## Acknowledgments

Please note that Anastasia Ierides 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
Tom Mahony's Lab Notebook served as a better guideline for our procedure and set up for this lab
The manual for the TAC where we got our conversions from!
Professor Koch and Pranav for being patient with us!