# Physics307L:People/Meyers/Speed of Light Lab Summary

Steve Koch 21:02, 21 December 2010 (EST):Very nice data ... and great result.
The Speed of Light

Delay Apparatus
Light Tube (Cardboard Tube)

## Purpose

Light Source Signal

The purpose of this lab is to measure the speed of light. To do this we are using a Photo-Multiplier Tube (PMT) and a light source combined with an oscilloscope and a delay system for the measurements. The general process for this lab is the light source emits the light and a start pulse simultaneously, then these travel down a darken tube and cable, respectively. Once the light in the tube hits the PMT, the PMT sends a cut off signal down a cable. This is where the delay system takes control. We use the delay system and the to insure the the turn-on signal is received before the turn off. We display this delay on an oscilloscope and through moving the light source back and forth through the tube and recording the change in the time delay. With this we believe we can calculate the speed of light.

## Procedure

Oscilloscope

A more complex version of the procedure, than what is listed above is posted here.

## Data

Measuring sticks attached to the light source

## Calculations

It is trivial to see from the graph in my second google doc spread sheet that the data follows a linear path. I took the regression slopes from trails 1, 2, 4, 5, 6, and 7 and averaged them together. I also averaged their SEM's.SJK 20:57, 21 December 2010 (EST)
20:57, 21 December 2010 (EST)
Averaging the SEMS, (if that's what you really did) is not correct. If you think measurements should be combined, then a weighted mean is appropriate. And the overall SEM will be lower than any individual SEM...adding measurements should only decrease the uncertainty.
It should be noted that we needed to divide the final slope by 0.1 because the Voltage to time conversion ratio is $\displaystyle \frac{1}{0.1}\,\!$ . Secondly, I disregarded the third trial because it seem evident that it was a bad set of data, as it is nowhere near linear.

I calculate the speed of light to be:

$\displaystyle c=30.6 \pm 1 \frac{cm}{ns}\,\!$

## Error

With accepted value of the speed of light being:

$\displaystyle c=29.97cm/ns\,\!$

Our value is off by this amount:

$\displaystyle % error=\frac{30.6-29.97}{29.97} x 100%=2.1%\,\!$

This is pretty good.

## Conclusion

With a percent error of 2.1% and an SEM that captures the accepted value of the speed of light within one SEM from our calculation I believe we've done a fairly good job at measuring the speed of light. It's interesting to think that the speed of light can be measured at such a small distance to such accuracy. (Steve Koch 20:59, 21 December 2010 (EST):Agree!)

## Acknowledgments

Thanks to Nathan and Peng for being great lab partners. Their help in this lab was much needed and appreciated.

## Citation

I got the accepted value of the speed of light from Wikipedia.