# Physics307L F09:People/Andrego/Speed of Light

## SPEED OF LIGHT LAB SUMMARY

^{SJK 00:37, 16 November 2009 (EST)}

Please note that Anastasia Ierides was my lab partner for this lab. Her version of this lab can be found here. You can also find her lab summary by following this link.

### Brief Overview

The purpose of this lab was to measure the speed of light, [math]\displaystyle{ c\,\! }[/math], by using short pulses of an LED light with a high speed detector and a delay module in a *direct* time of flight measurement over distances of one to two meters. We were able to successfully complete this lab through the use of a photomultiplier tube (PMT), a TAC module, and an oscilloscope. By graphing the different voltage readings on the oscilloscope versus the distance between the PMT and our LED light, we were able to use our best-fit linear slope to calculate an experimental value for the speed of light.

### Data Results

^{SJK 00:33, 16 November 2009 (EST)}

- Our average measured value for the speed of light came out to be...
- [math]\displaystyle{ c_{measured, average}=\frac{150.0682128\times10^{-2}meters}{Volt}\times\frac{1 Volt}{5\times10^{-9}s}\simeq3.0014\times10^8 m/s\,\! }[/math]

- When we took our factors of uncertainty into account we were able to report that our experimentation observed the speed of light to be with in the range...
- [math]\displaystyle{ 2.9524\times10^8 m/s\lt c\lt 3.0520\times10^8 m/s\,\! }[/math]

### Error

For ALL RECORDED accounts of error in our experiment methods and procedures please see the Notes about Our Uncertainty section in our Speed of Light Lab Notebook.

**Calculated Error Percentage**

- The accepted value of the speed of light was taken from Prof. Gold's Lab Manual
^{SJK 00:34, 16 November 2009 (EST)}- [math]\displaystyle{ c_{accepted}=299,792,458 m/s \,\! }[/math]
- [math]\displaystyle{ \% error=\frac{c_{accepted}-c_{measured, average}}{c_{accepted}}\,\! }[/math]
- [math]\displaystyle{ \% error=\frac{(299,792,458-3.0014\times10^8) m/s}{299,792,458 m/s}\,\! }[/math]
- [math]\displaystyle{ \simeq0.116%\,\! }[/math]

- [math]\displaystyle{ c_{accepted}=299,792,458 m/s \,\! }[/math]

### Conclusions

- The hardest part about this lab was the careful setup procedure to insure that the data we were taking was legitimate. At first we struggled with the measurements between the LED and the PMT, we were not leaving enough space to take an adequate number of trials at different distances. The other hard part about this lab was over coming the concept of time-walk, which was nicely described in Tom Mahony's Lab Notebook. In order to get consistent data we had to manually rotate the PMT to align the polarizers in the set-up to adjust the intensity of the incoming light. With out this we could not have compared our data for each different distance reading. This lab could be improved in one of two ways, first, it would be phenomenal if we had better control over the alignment of the polarizers. We suffered from some error while manually twisting the PMT for every trial. Secondly, we realized that if our oscilloscope had a zoom function or a more finely tuned viewing function the manual process of adjusting the intensity could be done more accurately. All in all our measured values came out very reasonable, with a low percentage error and a range of values that does include the accepted value of the speed of light.
^{SJK 00:36, 16 November 2009 (EST)}