The Cauchy Formula for the Dependence of

Index of Refraction on Wavelength

The Cauchy formula takes the form n = , where A, B, C,... are constants (see Blum and Roller, Physics, Volume Two, p. 1491, Holden Day 1982, ISBN 0-8162-7285-9). Taking, for example, the first two terms of the expression, it's an interesting data analysis problem to determine the constants A and B. Some of the data presented in chapter 43 of the above-mentioned text are reproduced below. Let's analyze that for crown glass using a graphing calculator and Graphical Analysis Version 2.0.6.


 
Since graphing calculators do not have as a regression option y = A + B/l2, let x = 1/l2 and do a linear regression on 

y = A + Bx. The results are shown below at left. l is in L1, n in L2, and 1/l2 in L3. A linear regression using L3, L2 yields the result n = 1.50367 + 4672.00/l2, which is shown to match the data quite well in the fourth figure.

 l (nm)             656.3       589.0       486.1       434.0

Water             1.3312     1.3330     1.3372     1.3404

Crown Glass   1.51458   1.51714   1.52326   1.52859

Flint Glass(light) 1.57638   1.58038   1.59029   1.59931

Flint Glass(dense) 1.65007   1.65548   1.66911   1.68181
In Graphical Analysis 2.0.6 the data can be analyzed directly by choosing the Automatic Curve Fit option under Analyze, selecting Other, and typing in f(x) = A + Bx-2. The result is n = 1.50355 + 4697.27/l2. I am not familiar with the algorithms used and cannot explain the slight differences, but both regressions match the data very well. In GA it is interesting the watch the curve being fit as the program iterates to a solution.

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The Computer Era Spawns a Paperless Paper-buried Society

-from The Hartford Courant, January 30, 1999

As we all can attest, the paperless society forecast when PC's began to proliferate has been, at best, a farce. The article in the Courant is quite interesting, and attributes the increase to the fact that much more information is now available and that it is easier to put it on paper. The data at right lists megatons of shipped white paper. Try a regression analysis- at least the growth is not exponential! And let's recycle more (and print LESS)! Year White Paper (Mtons)

1982             1.7

1987             2.7

1992             3.5

1997             4.6