# Purpose

SJK 18:07, 28 October 2010 (EDT)
18:07, 28 October 2010 (EDT)
Good summary, excellent work overall. I can't tell from your writing whether you found the entire experience frustrating, or whether, in retrospect, you appreciate your good measurements and that you learned some things. Well, I hope it was a bit rewarding! Another excellent lab by you and Matthew, thanks!

The purpose of this lab was to measure the speed of light. The specifics on how we managed to actually measure the speed of light can be found in my primary lab notebook (here), under the procedure section.

# Equipment

• PMT
• LED
• Oscilloscope TDS Tektronix 1002
• Bertan Power Supply Model 313B
• Canberra Delay Module NSEC 2058
• Ortec TAC/SCA Model 567
• Harrison Laboratories Power Supply (for LED) model 6207A
• Multiple BNC Cables
• Long Carboard Tube (which served as the housing for the PMT and LED)

# Lab Summary

This Lab turned out to be a very frustrating experience for my lab partner and me (more about the issues we experienced can be found under the 'Issues' section of my primary lab notebook). In order to measure the speed of light, we needed to shoot pulses of light from an LED at one end of the long cardboard tube to the Photomultiplier tube at the other end of the cardboard tube. A signal from both the LED (start signal) and the PMT (stop signal), which is generated when the light from the LED hits it, are sent to the TAC (time to amplitude converter). The TAC then generates an output voltage, which according to the lab manual, is "proportional to the start-stop time difference." We had to use a time delay on the TAC in order to ensure that the signals were being analyzed by the TAC simultaneously.SJK 17:38, 28 October 2010 (EDT)
17:38, 28 October 2010 (EDT)
not simultaneously--just need to ensure that STOP signal arrives after START signal
This output from the TAC, as well as the voltage from the PMT (which corresponds to the intensity of the light hitting the PMT)are displayed on the oscilloscope as CH2 and CH1 respectively. This is where the data is taken for this lab. By adjusting the position of the PMT (rotating it to keep the intensity the same which should correct for time walk), we can record the output voltages on CH2 for different positions of the LED. So the actual data that was recorded was volatges, but we want to measure the speed of light in cm/ns, so using a conversion in the data analysis part of this lab, we were able to calculate an average value for "c", the speed of light.

# Calculations and Results

$S_{time VS dist}=(3.2 +/- 0.03)\times10^{-2} \frac{ns}{cm}$
$C_{S} = \frac{1}{S}$, $C_{S_{i}} = \frac{1}{S +/- \delta_{S}}$
$C_S = 31.3 \frac{cm}{ns}$
$C_{S_{high}}=30.9 \frac{cm}{ns}$
$C_{S_{low}}=31.6 \frac{cm}{ns}$

## Accepted Value

$C_{accepted}=29.98 \frac{cm}{ns}$ which can be found here. This is the value for the speed of light in a vacuum, but I could not find a credible value for the speed of light in air.SJK 17:43, 28 October 2010 (EDT)
17:43, 28 October 2010 (EDT)
you can compute it from the index of refraction. It's a much smaller effect than you could detect and will be wavelength dependent as well--so there's no one speed of light in air. Here's a decent reference: hypertextbook

## Comparison

• Although the accepted value does not fall within our range (68% confidence interval), I am fairly satisfied that we were in the ball park with our measurements considering we experienced problems throughout the lab. In comparison to the accepted value, we had the following percent error:
%Error = 4.3%

# Conclusions

Overall I think that this lab taught my partner and I about some common mistakes that could be made in the lab. We were able to get usable data after struggling through some problems with Katie and Prof. Koch. This data allowed us to make a calculation for the speed of light that was about 4.3% off from the accepted value. This is not considering the equipment we were using and the very jumpy signal on the oscilloscope. Even with the Average Function turned on (on the oscilloscope), we were still doing a fair amount of estimation when we took our data. The fluctuations in this signal could account for some of our error as well as the other topics mentioned in the error part of my primary lab notebook.