Author: John Quintanilla

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.

Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem

This was a nice write-up (with some entertaining interspersed snark) of the solution of the the Wasserman-Wolf problem concerning the construction of a perfect lens (like a camera lens). Some quotes:

[L]enses are made from spherical surfaces. The problem arises when light rays outside the center of the lens or hitting at an angle can’t be focused at the desired distance in a point because of differences in refraction.

Which makes the center of the image sharper than the corners…

In a 1949 article published in the Royal Society Proceedings, Wasserman and Wolf formulated the problem—how to design a lens without spherical aberration—in an analytical way, and it has since been known as the Wasserman-Wolf problem…

The problem was solved in 2018 by doctoral students in Mexico. For those fluent in Spanish, the university press release can be found here. As an added bonus, here’s the answer:

 

Significant Digits and Useless Digits

A pet peeve of mine is measuring things to far too many decimal places. For example, notice that the thickness of these trash bags is 0.0009 inches (0.9 mil) but is 22.8 microns in metric. There are two mistakes:

  • While the conversion factor is correct, there’s no way that the thickness is known within only 0.1 microns, or 100 nanometers. That’s significantly that a typical cell nucleus.
  • Less importantly, if they rounded correctly, it should be 22.9 microns, not 22.8.

My favorite example that I’ve personally witnessed — that I wish I had a picture of — is measuring student’s perceptions of a professor’s teaching effectiveness is 13 decimal places.

This webcomic from xkcd illustrates the point both cleverly and perfectly.

Source: https://xkcd.com/2170/