Physics307L F09:People/Barron/labsum~speedoflight
From OpenWetWare
Speed of Light Lab Summary
Here is the lab manual page.
Here are my lab notes.
Partner: Justin Muehlmeyer
Introduction
This lab is fairly straight forward  we basically measure the time of flight of flashes from an LED pulse generator with a TimetoAmplitude Converter (TAC). We take the voltage amplitude from the TAC for different distance measurements, then glean the value of c in air from the slope of a leastsquares fit of x vs. t. The TAC is fed time pulses resulting from LED flash detection from a PMT. In order to vanquish the effects of changing light intensity due to changing distance between the pulse generator and the detector (known as "time walk"), we adjust the orientation of two polarizers between the two and attempt to retain constant output from the PMT.
Approach
We took four data trials:
1) large and increasing individual Δx over large total Δx,
2) small, constant individual Δx over small total Δx,
3) large, constant individual Δx over large total Δx, and
4) medium Δx with no time walk correction.
Final Results
NOTE: AXES ARE SET TO "TIGHT," SO SOME DATA POINTS ARE ON GRAPH EDGES
Trial  Graphic Representation  Trial  Graphic Representation  
Trial 1:
Upper Error Bound:
Lower Error Bound:


Trial 2:
Upper Error Bound:
Lower Error Bound:

 
Trial 3:
Upper Error Bound:
Lower Error Bound:


Trial 4: (no time walk correction)
Upper Error Bound:
Lower Error Bound:


I notice that error range decreases with more measurements, but not necessarily accuracy. Here is a plot of all values with error compared to the accepted speed of light in air:
It appears that measurements taken over a large individual & total Δx, as in trials 1 & 3, yield the best results for c. Unfortunately, this experimental setup limits how much data can be taken this way, so the error is large. Small individual and total Δx yields an awful result, even though more data points narrowed the error range. The result of trial 4 illustrates how important adjusting for time walk is  c "walked" an entire order of magnitude! I wonder if taking data with small individual Δx over large total Δx would allow for the linear fit to filter out the "noise" from each small measurement in order to find the real trend of c. I believe the large amount of noise, from small xstepping, combined with the small data range forced the trial 2 result far from its actual value.
This experiment and result illustrates the mechanics of accuracy of precision rather well, I think. Trial 2 is not accurate at all, but is much more precise than our more accurate measurements. I believe the lesson to take away from this is that narrowing error isn't the entire battle  what good does small error do when the physical value isn't inside error bounds?^{SJK 01:32, 1 November 2008 (EDT)}