User:Randy Jay Lafler/Notebook/Physics 307L/Speed of Light Summary

Purpose
The purpose for this lab was to measure the speed of light by using an LED to send photons across a tube to a PMT. We had to incrementally change the distance between the LED and the PMT, the distance the photon traveled, in order to generate a graph of travel time verse distance traveled. From this graph we calculated C as the inverse of the slope of the linear fit line. Link to my notebook

Data overview
Data 1
 * We calculated C for two different data sets.
 * $$C=31.5(1)cm/ns\,\!$$

Data 2
 * This value we obtained from 16 measurements of the voltage as we decreased the distance by 10cm.
 * $$C=32.1(19)cm/ns\,\!$$

We obtained these values in the following way:
 * This value we obtained for 8 measurements of the voltage, half as many as in data set 1, as we increased the distance back over the same distances by 20cm.
 * At each distance we measured a voltage, and we converted the voltage to ns by the conversion: 1v=10ns.
 * We then plotted time verse distance for each data point, and used the linest function in Excel to produre a linear fit to our graph.
 * We calculated our best answer for C by inverting the slope, and we calculated our standard diviation by using the diviation in the slope given by Excel to calculate a range in C and subtracting the best answer from the high range. This assumes symmetric diviation, but it appears to be a good approximation.

Error
The accepted value:
 * $$C=30cm/ns\,\!$$

Our measurements are larger than the accepted value. This could potentially be do to some systematic error. The largest place for error was probably in our ability to hold the intensity of the light constant. Making small rotations of the PMT would make the spike on the oscilloscope change quite a bit for closer distances. So, perhaps we did not hold the intensity constant. We also neglected what the manual calls time walk. Sinse, the TAC in our experiment activates at a fixed voltage it will trigger at different times based on the amplitude of the light pulse. The signal from the PMT increases in amplitude as the LED is moved closer. This might be why small rotations of the PMT at shorter distances cause large changes to the signal for the PMT. Because of this I think the travel times we obtained for short distances might be shorter than they should be. This might explain why our measurements were larger than the accepted value. A shorter time at the same distance means a faster velocity. When we did a linear fit to our curve, perhaps the data we obtained at short distances shifted the linear fit toward a shallower slope, and therefore a large value of C.

Acknowledgements
Thanks to Professor Koch and Katie for helping us understand the equipment and what we wanted to do, as well as explaining to us how to get time from our voltages. Emram for the pictures, graphs, and Excel sheet.