User:Richard T. Meyers/Notebook/Phys307l/Speed of Light Lab

The Speed of Light

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

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. It should be noted that we needed to divide the final slope by 0.1 because the Voltage to time conversion ratio is $$\frac{1}{0.1}\,\!$$. 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:

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

Error
In the data I used the LINEST function in Google Docs to propagate the error. I then averaged the SEM's together and divided by 0.1 as I did with the values for the speed of light to find my ultimate error.

Also with accepted value of the speed of light being:

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

Our value is off by this amount:

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

This is pretty good.

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.