The Speed of Light

A rapidly rotating mirror is used to time the transit of light along a path within B260. The answer is 2.99792458 x 1010 cm/s, what is the question?

Important Information Concerning the Speed of Light Experiment

For this experiment only, the equipment will be set up in advance, everyone will do this experiment during the same week in one hour slots, and groups can include up to 4 students. This experiment is required even if you have done it before in Physics 231A. If you are unable to be in lab this week contact Prof. Rothberg.

You will need to write all your reports following the posted lab practice and report writing procedure: http://courses.washington.edu/phys331/lab_practice_and_report.pdf

For the speed of light experiment, there will be two independent sets of measurements of the spot position versus frequency (by two different microscope observers).

For each set of measurements, one of the directions of mirror rotation should be plotted as positive frequencies and the other direction as negative frequencies and put on one graph.

The frequency counter measures the number of rotations per second; please plot your data versus this number and then determine the slope of each of the two sets of data from a least squares fit. You will need to estimate the uncertainty in your slope. (Several methods are described on the course website.)

You can then combine the two values for the slopes from your data and calculate the speed of light, converting the units of your slope to angular frequency for your final calculation.

A careful, well documented estimation of the uncertainty in your measurement is essential for every every analysis and report, especially this week's experiment. You may want to study some of the information on uncertainty analysis on the class website. The tutorial "Notes on data analysis and experimental uncertainty" is a good place to start.

For simplification of the analysis it is OK to treat D+B as independent of D2. This will overestimate the uncertainties. If you have time to be fancy you might decide whether it is important to improve on that. You need to realize that the relative error in D2 is twice that of D (see examples in postings or links on course website).

Then you have four terms whose relative errors add as the square root of the sum of the squares of the individual relative errors of 4 terms:

  1. the slope of displacement vs. frequency (plot CW and CCW as + and - frequencies so you fit all measurements from one set with one line);
  2. the D2 term;
  3. the A term;
  4. the D+B term.

You might also ask yourself if you mis-estimated the position of the rotating mirror whether it affects D and B is a similar way. Note also: the lens centers are displaced from the mark on their mounting on the scale on the track.

Experiment Information

  • Write-up
  • Professor Rothberg's simplified diagrams of the speed-of-light apparatus.
  • How to read the micrometer (Picture by Glenn McKechnie, from Wikimedia Commons):
    1. Take the reading from the sleeve (5.5).
    2. Add to it the reading from the thimble (5.5+0.28=5.78).
    3. Read the vernier scale by finding the line that most closely lines up with a line on the thimble (0.003).
    4. Add the reading from the vernier scale (5.78+0.003=5.783).

    Note: our micrometer differs from the one shown in that we do not have the last, smallest digit scale. This scale is called a "Vernier" scale and allows you to get values smaler than the finest scale gradation. It is common on other scales in the lab. Please click on the image to get a larger view.