STA110A Final Computing Assignment

Newcomb's measurements of the speed of light

Background Material

Verification of the fact that light travels at a finite velocity, and is not transmitted instantaneously as early scientists ( including Kepler and Descartes ) had thought, is generally credited to Ole Romer, who in 1676 made comparative measurements of the time of eclipses of Jupiter's satellites from two different relative positions of Earth and Jupiter. But another two centuries passed before the experiments of Michelson and Newcomb in 1879-1882 provided what are considered the first accurate determination of the velocity of light in vacuum.

In 1849 and 1850, the French physicists Fizeau and Foucault had separately devised methods of measuring the velocity of light. Foucault's method, as refined and improved by Newcomb and Michelson, was the source of the more accurate subsequent determinations. Foucault's method consists in essence of passing light from a source off a rapidly rotating mirror to a distant fixed mirror, and back to the rotating mirror. The velocity of light is then determined by measuring the distance involved, the speed of the rotating mirror and the angular displacement of the received image from its source.

Below is a table showing Newcomb's measurements of the passage time it took light to travel from his lab, to a mirror on the Washington Monument, and back to his lab. The distance of the path traveled is 7.44373 km. The primary goal of this experiment is to determine the speed of light, and to quantify the uncertainty of the measurement.

Data Set

Newcomb's 3rd Series of measurements of the passage time of light, made July24, 1882 to Sep.5, 1882. The given values *0.001+24.8 are Newcomb's measurements, reading down the columns, recorded in millionths of a second. The entire table constitutes three data sets, each collected on different days. The Excell datafile is obtainable here.

Data Set 1 (n=20)						Data Set 2 (n=20)						Data Set 3 (n=26)
28	-44	29	30			24	28	37	32			36	27	26	28	29
26	27	22	23			20	25	25	36			23	31	32	24	27
33	16	24	29			36	21	28	26			27	27	32	25	28
24	40	21	31			32	28	26	30			27	26	24	32	29
34	-2	25	19			36	29	30	22			28	33	39	25	16
																23

Data analysis assignment

In no more than two pages give a write-up that includes the following:

Confidence intervals for all three data sets (in km/sec).
An overall confidence interval for the speed of light in km/sec.
A plot showing the data and the confidence intervals.
In addition, the write-up should address the following questions:

How does your analysis treat the outlier(s) in data set 1?
Could there be sources of bias?
The distance measurement of 7.44373 km is accurate to 2 millimeters (0.00002 km). Does this have a substantial effect on the confidence intervals you computed?
Remember that you are allowed to work in groups (no more than 3) for this assignment. The TA's and I will be happy to answer questions. The assignment is due on 27 April at the end of class.