# Speed of Light

SJK 12:28, 22 October 2010 (EDT)
12:28, 22 October 2010 (EDT)
Up until analysis section, this is a good primary notebook. Future analysis sections, though, need a lot of improvement. See comments below. Please see Ginny's page for more comments.
• Please note that I worked with Ginny for this lab.

## Purpose

The purpose of this lab is to measure the speed of light constant c and to compare it to the current accepted value.

## Equipment

SJK 12:25, 14 October 2010 (EDT)
12:25, 14 October 2010 (EDT)
Good equipment list and photos. You should also include some information on how the connections were made, because these would be tough to see from the photos. E.g., "PMT connector "A" was connected to the delay module and then to the TAC "stop" signal, using a T connector."
• 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

• Check the cords, cables, and electronic equipment in use for any possible electrocution points. Also check to see that the power cords protective grounding conductor is connected to ground.
• Do not expose the PMT to ambient light because the light can ruin it.

## Setup

I worked with Ginny for this lab. We followed Professor Gold's manual and also Alex Andrego's Speed of Light lab notebook for some extra help with the setup. Alex's setup worked well for us and so we decided to follow it step by step along with some extra help with Professor Gold's manual.

LED setup
Harrison power supply
TAC setup
best fit line

## Calculations and Analysis

• Using our raw data, we were able to make a best fit line to find the best fit linear graph of our slope. We then converted the values to find our measured value of the speed of light.
• We took measurements of delay voltages every 10cm. We went from 260cm to 140cm
• Recorded the time of flight from the second signal using the measure function from the o-scope.
• We repeated the process 5 times.

Due to the settings on our TAC, our conversion was $10 ns/1 Volt\,\!$.

The slope of our linearfit plot is...
$0.1061\frac{ns}{cm}\,\!$
We calculated the uncertainty in our slope to be...
$0.87\frac{ns}{cm}\,\!$SJK 12:21, 22 October 2010 (EDT)
12:21, 22 October 2010 (EDT)
This is clearly a typo, since it is 9 times higher than your slope! In the future, make sure to see if the numbers are sensible!
We used our uncertainty to find a reasonable range for our slope data...
$(0.1061\pm0.87)\frac{ns}{cm}\,\!$
We then had to invert our slope to get a value for velocity...
Minimum Range Inverse Slope:
$\frac{1}{0.1061+0.87}\simeq10.29507069\frac{cm}{ns}\,\!$
Maximum Range Inverse Slope:
$\frac{1}{0.1061-0.87}\simeq13.09071868\frac{cm}{ns}\,\!$
Average Inverse Slope:
$11.69289469\frac{cm}{ns}\,\!$
SJK 12:25, 22 October 2010 (EDT)
12:25, 22 October 2010 (EDT)
I'm guessing you're just not putting enough zeros in front of your uncertainty? These numbers don't make a lot of sense and I can't reconcile them with your spreadsheet. For future labs, you DEFINITELY need to be more careful than this and make sure things are making sense.

We looked up the accepted speed of light value, and according to Wikipedia, it is

• $29.98\frac{cm}{ns}\,\!$

## Error

A few reasons for our error could be...

• Wrong calibration
• Ginny and I took turns calibrating the o-scope, therefore we were not consistent with our measurements (ie. one of us might have been calibrating properly and the other one was not).
• Did not clearly understand the concept of time-walk.
• Measuring the distances with the meter stick might have given us an error

## Acknowledgements

Please note that Ginny was my lab partner for this lab. I would like to thank professor Koch and Katie for the help with our lab. I would also like to thank Professor Gold's manual, Alex Andrego and Anastasia Ierides for their detailed setup for the lab.