Measuring the Speed of Light (Foucault Method)

[ltetor]

Abstract

In this experiment, a beam of light from a laser was reflected off of a rotating mirror to a fixed mirror, and then reflected back to the rotating mirror. The returning light was focused to a point image in a microscope. Due to the continued rotation of the mirror while the light was in transit from the rotating mirror, to the fixed mirror, and back, the beam was reflected into the microscope at an altered angle, resulting in a displacement of the point image. Measurement of this displacement, along with distance parameters from our setup, known as the Foucault Method, allows for the speed of the light to be calculated. The mean speed of light calculated from this experiment was (2.9972 ± 0.0139) x 10⁸ m/s.

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[fluidistic]

Hi, I did not check the details but

A = 0.26 m ± 0.0005 m
B = 0.49 m ± 0.0005 m
D = 11.8237 m ± 0.0500 m

looks weird to me. I'd write A=(0.2600 ± 0.0005) m, etc.
In the table

2.838152
± 0.039977

I'd write 2.84 ± 0.04, etc.
Also in table 3 I get suspicious because the lesser is the calculated c value, the lesser the error you get. Using my intuition the opposite should happen.
Maybe I was not taught the right way though and keep in mind that I'm just an undergraduate student.

 

[Vanadium 50]

I am not sure what your question is. Looking at the attached document, though, and I conclude that you have underestimated your uncertainties by a rather large factor: perhaps two or three.

Also, Table 3 has a serious problem with significant figures.

 

[K^2]

The mean speed of light calculated from this experiment was (2.9972 ± 0.0139) x 10⁸ m/s.

If that is your estimate of the error, how do you explains statistical error being (2.9972 ± 0.1071) x 10⁸ m/s?

You should always check the statistical error on your data. It should never be higher than the error you claim. You have made a mistake somewhere by a whole order of magnitude. It doesn't affect your answer, but it affects how believable your answer is. If you claim an error of less than 0.5%, you need to show statistical variation of less than 0.5%. It's not. The fact that you didn't get 3.1 for an answer is entirely down to luck. Unless it's not even that. Did you keep all of the data points you took, or only the ten you liked?


Just to illustrate this a little better I've attached a plot of your data. Red dots are the data from the table. Pale blue band is the probability distribution according to 2.9972 ± 0.0139 you claim, with solid blue dashes marking off the area of the band that should contain 90% of your data points according to that error. Doesn't look good, for your claim, does it?

 

[sardar]

I find this experiment using the Foucault Method to measure the speed of light to be well-designed and executed. The use of a laser and mirrors to create a precise and controllable system for measuring the displacement of the point image is a clever approach. The calculated mean speed of light of (2.9972 ± 0.0139) x 108 m/s is very close to the accepted value of 299,792,458 m/s, which demonstrates the accuracy of this method.

One potential limitation of this experiment is that it relies on the assumption that the mirrors are rotating at a constant speed, which may not be entirely accurate. Variations in the speed of rotation could introduce errors in the measurement of the displacement and ultimately affect the calculated speed of light. Additionally, the experiment is dependent on the precision and calibration of the measuring equipment used, which could also introduce errors.

Overall, the Foucault Method is a reliable and effective way to measure the speed of light. It provides a clear and reproducible technique for obtaining accurate results. Further experiments and refinements of this method could potentially lead to even more precise measurements of the speed of light.