Ptolemy's 2nd Refraction Experiment

  While reviewing some of the history of optics over the weekend I came across Ptolemy's experiments to measure the amount of refraction that light undergoes when going from one media to another. The first experiment was for light passing from air into water. His second experiment was for light passing from air into pure glass. Ptolemy did not publish a law governing refraction. That came later when Snell determined that the ratio of the sine of the angle of incidence, i, to the sine of the angle of refraction, r, was a constant, n, known as the index of refraction. We can use this law to see how good Ptolemy's measurements were. The plot for the second experiment is shown below. The angle of incidence ranged from 10° to 80° in steps of 10° measured from the vertical.

The fit indicates that for the glass that Ptolemy used the index of refraction was n=1.519 which is typical of crown glass. The Roman glass of Ptolemy's time was made from sand with soda (sodium carbonate) or natron to reduce the melting point of sand. Pliny's description of  glass making confirms this. For more on the history of Roman glass see Dillon, Glass.