Physics307L:People/Phillips/SpeedofLight

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Speed of Light Summary


Data & Summary

After collecting quite a bit of data and doing some analysis ( Data is here), we (Stephen and I) found decent results for the speed of light:

  • Accepted Value: C = 299,792,458 m/s = 30.0 cm/ns (centimeters per nanosecond)
  • Our Average Value: c = 23.2 cm/ns SJK 02:48, 22 October 2008 (EDT)
    02:48, 22 October 2008 (EDT)I really like that you're using cm / ns!  I didn't realize it until now, but I am sick of 3x10^8 m/s.  30 cm / ns seems more practical to me now.Also, you need an uncertainty on this value...perhaps that's what you're doing below, but I couldn't make sense of it, and it needs to be right next to the final value anyway.
    02:48, 22 October 2008 (EDT)
    I really like that you're using cm / ns! I didn't realize it until now, but I am sick of 3x10^8 m/s. 30 cm / ns seems more practical to me now.

    Also, you need an uncertainty on this value...perhaps that's what you're doing below, but I couldn't make sense of it, and it needs to be right next to the final value anyway.

What we realized while doing the analysis from all of our data is that there were very many sources for error. One huge source (huge meaning how effective it would be in corrupting all the rest of our data) is the calibration. If we were off even just a little bit during our calibration, it would be catastrophic, no matter how good our other data were, because we used this calibration to calculate everything else. Another really big source came in just obtaining decent values for our voltage coming from the TAC (time-to-amplitude converter). While we were rotating our PMT (photo-multiplier tube) to maximize the amount of light entering it, we were really just maximizing the PMT voltage seen on our oscilloscope. This is done by hand, carefully but still surely inaccurately, and by eye, in a similar fashion. These two together make for quite a high probability of error.


Error

SJK 02:39, 22 October 2008 (EDT)
02:39, 22 October 2008 (EDT)I haven't read your notebook yet, so maybe it will become clear.  But I thought I would point out that these 0.0004 and 0.5 and 0.9 "errors" mean nothing to me w/o units and out of context.  Just to give you an idea of the perspective of one of your readers.(Later) OK, now I see where it's from, and it's in cm/V units and needs conversion to cm / ns.  Actually, though, I think you inverted your LINEST formula, and so the error is wrong anyway.  From your data, I get something more like 5% uncertainty, about 1 cm / ns, which if you look at the graph seems more reasonable than the very precise number you're stating.
02:39, 22 October 2008 (EDT)
I haven't read your notebook yet, so maybe it will become clear. But I thought I would point out that these 0.0004 and 0.5 and 0.9 "errors" mean nothing to me w/o units and out of context. Just to give you an idea of the perspective of one of your readers.

(Later) OK, now I see where it's from, and it's in cm/V units and needs conversion to cm / ns. Actually, though, I think you inverted your LINEST formula, and so the error is wrong anyway. From your data, I get something more like 5% uncertainty, about 1 cm / ns, which if you look at the graph seems more reasonable than the very precise number you're stating.
From our excel analysis, each linear fitted plot (using LINEST) had between 0.0004 (which is the data that gave the speed of light provided above) and 0.004 for all of our good data. One thing to point out is that our "good" data is not simply the data that worked best (got us closest to the accepted value) but is the data that took the time walk effect into account SJK 02:40, 22 October 2008 (EDT)
02:40, 22 October 2008 (EDT)Yahoo!  That's a great description of "good" data.  Good for you for avoiding the trap of picking the data that gives you the "right" answer
02:40, 22 October 2008 (EDT)
Yahoo! That's a great description of "good" data. Good for you for avoiding the trap of picking the data that gives you the "right" answer
. Without taking this into account, our linear fits had between 0.5 and 0.9 errors. Clearly, this is much more significant than the other ones, and gave us a speed of light of about 5.7 cm/ns.


Conclusions

After working through all of our data and thinking about it, we decided that the discrepancy in our result from the accepted value is not due to our instrumentation or general procedure, but is mainly due to the cumulative errors created from all of the hands-on aspects of this lab. It gave us a valuable experience, I think, but rotating a polarizer by hand while trying to maximize a semi-steady amplitude square wave on an oscilloscope just by looking at it supplies us with significant error. In the end, however, we did come up with a decent value, "only" 22.3% away from the accepted value.

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