Physics307L:People/Young/Young's Speed of light

Brief Summary of Experiment
The basic idea of this experiment was taken from the lab manual written by Dr. Gold.

notebook entry for Speed of Light lab

To find the speed of light we have an apparatus set up with a LED giving off short pulses of light at one end and at the other a photomultiplier tube. The photomultiplier tube takes electrons generated by the photoelectric effect from the LED and used a large potential difference to accelerate them giving a reading of Voltage out the other side proportional to the intensity of light received. The reading passes through a delay box and then a time-voltage converter and then into our oscilloscope. Our oscilloscope reads the voltage from the voltage time converter. The voltage converter has a connector that measures the start time of our pulse as well as our stop time.

The second channel of our oscilloscope is a pure reading of Voltage from the PMT (Photo Multiplier Tube). Throughout the experiment this channel will let us know what intensity the light is at. For consistent readings for light it will be important to maintain a constant intensity for all readings of time.

To take data we start the LED around the middle of our Apparatus and call that point position zero. Then we move the LED in increments taking readings for different distances at constant intensities. Using polarizers on the LED and the PMT we can turn either of these instruments to maintain our intensity. With data of time and distance we should be able to find the speed that light travels.

Error Analysis
One major concern of mine that arose during the experiment the the fickleness of the polarizers. The polarizers are set in place to solve the problem of known as a 'time walk'. However, a slight bump to the polarizer would cause the intensity to shoot up or down. Also, A small change in the intensity would cause a great change in our reading for time. KNowing that in order to get good data we should have higher times for higher distances. The difficulty with the intensity caused an uncertainty in the readings so great that our values span in a manner that look uncorrelated.

Also, the time it takes signals to travel through the wires can cause a change in our data for these measurement. When we move out the LED the light has to travel the extra distance x, however we did not account for the extra distance that the signal has to travel. The wire is stretched farther and when we are measure nanoseconds this can make a great difference.

Changes and Improvements
To improve this experiment I would take many more data points and spend more time getting our intensity to be exactly the same on every measurement. I would like to unplug the PMT and check out the Polarizers in the apparatus as well. The delay box also has a possibility of giving us better accuracy. The calibration for the box may not be linear for all distances we measured. I would have liked to take measurements at all points with delays to get a better idea as to how the signals change our data.

Data Analysis
Using a least squares fit in Matlab with the averaged values of time for all data points and our distances I found the speed of light to be

c=10.783e8 (Steve Koch:What are the units here?)

The error for this value would be three times larger than the excepted value for the speed of light. Using our time delay data I hope to calibrate the time lost in our circuits to find a value for signal speed. The correction made here will take us much closer to the true value since the error in our system will now be mostly accounted for.

Using known delays in our system we took data for delay vs. Voltage/time output. When this data is plotted it shows us how time is changed by our apparatus.

The y of the above equation give us our calibrated time. After applying our time data for the changing distance part of the experiment the data gives us ...

After using a least squares fit to find the best solution to this data I found that our speed of light constant was

5.4e9m/s ± 1.4261e-011


 * note: The value for the speed of light turned out to be negative simply because of the order I put my data in.  The magnitude of the value is what is truly important and the direction I choose to be positive has no impact on the data.

Compare to accepted speed of light
accepted speed of light= 2.99792e9m/s

percent error=79%

Matlab code for data analysis

Final thoughts
I found this experiment to have many interesting obstacles to overcome. When dealing with speeds of this magnitude every piece of instrument adds to the error since the event and the equipment measurement time are on the same magnitude of speed. I would say that this experiment was a great success. Given more time to do the experiment again I know with more attention paid to the polarizing system and intensity our value of c could get very close to the accepted value.