Yuletide seems to be a good period for producing my favourite scientists, on Christmas Day we had Isaac Newton and St. Stephens Day gave us Charles Babbage. The series continues today the 27^{th} with the birthday of one of my all time favourites Johannes Kepler. Now for most people Kepler is just the three laws of planetary motion but as I have had occasion to remark in the past his range of scientific achievements was considerably larger. Today I wish to sketch his contributions to the founding of modern optics.

Optics plays a major role in observational astronomy and it was from the context of observing a solar eclipse that Kepler developed his own interest in optics and the need to improve it. His investigations threw up a whole series of optical questions to which, in his own words, he could not find answers in the existing literature and so he set about investigating the questions for himself. The results of these investigations were published in 1604 in a book with the following title *Ad vitellionem paralipomena quibus astronomiae pars optica traditor*, which basically translates as, an appendix to Witelo on the optical part of astronomy. Witelo refers to the *Perspectiva* published by this German-Polish mathematician in 1270, which was the most advanced treatise on optics available before Kepler published his own work. Normally one thinks of an appendix as something relatively short in comparison to a main work but Kepler’s so-called appendix runs to 459 large format pages in its English translation. In this book Kepler covers almost all aspects of optics and produces some very significant results in the process. Firstly he solves the so-called pinhole problem, which was one of his main reasons for starting his investigations. This problem is that the moon when projected through a small aperture such as that of a camera obscura during a solar eclipse appears smaller than at other times. This problem was known to both the Islamic and European optical experts in the Middle Ages but as Kepler had discovered none of them could explain why. This work also presented his inverse square law of the propagation of light, which is the first mathematical law of nature published in the early modern period. This law also inspired Ismael Boulliau to suggest, as the first scientist to do so, the inverse square law of gravity. Possibly Kepler’s greatest achievement in the Pars optica was to give the correct description of how the eye functions, namely as a form of camera obscura (a name invented by Kepler and the origin of the name of our photographic camera) in which the lens projects the image onto the retina which actually perceives the image. The major objection to this theory is that the projected image is inverted but we see the world the correct way up. Kepler countered this objection in a surprisingly modern way. He said that the brain is aware of what is up and what is down in the real world and corrects the inverted image delivered by the eye. At the end of his book Kepler makes some basic investigations of the optical properties of lenses and how they function together with the eye to correct defects in vision. This is historically interesting because convex lenses had been used in spectacles since about 1260 and concave ones since at least 1450 but Kepler’s optical analysis was the first ever published scientific investigation of how lenses function, something he would pick up on again eight years later in his second book on optics.

1608 saw the invention of the telescope and 1609 its first use in astronomy by various European scientists. The results of these early telescopic astronomical observations were called into doubt for various very good reasons. One of those reasons was the fact that there existed no scientific theory of how a telescope actually worked. In empirical science, if one uses an instrument to obtain empirical data then one requires a theory of that instrument in order to justify the validity of that data. In 1610 when Galileo published the first empirical astronomical observations made with the telescope no such theory existed for the telescope. The man who supplied the missing theory was Kepler. Going back to his initial investigations on lenses in his *Pars optica* he produced a mathematical description of how each type of lens functions both singularly and in conjunction with the eye. He then moves on to combinations of lenses giving a complete mathematical description of the Dutch or Galilean telescope. Following this he then proceeds to describe the as yet non-existent astronomical or Keplerian telescope and the three lens terrestrial telescope. To top off his achievement he describes the telephoto lens more than 200 years before it came into existence. The book published in 1611 is his *Dioptrice* a remarkable achievement because it is the first textbook for a branch of physics that he literally created whilst writing the book. Dioptrics the science of the refraction of light takes its name from Kepler’s book. It should be pointed out that Galileo was anything but impressed by Kepler’s efforts saying that the book was unreadable and unintelligible, a not wholly inaccurate assessment. The whole treatise is written in Euclidian geometry, and not as one would today in trigonometry, and Kepler’s proofs are incredibly complex and very, very hard to follow although mathematically completely correct.

Kepler’s two books on optics revolutionised this branch of physics and heavenly influenced the investigations carried out by Snel, Descartes, Gregory, Newton and other lesser lights in the course of the 17^{th} century. In the history of optics one could say that Johannes Kepler shed more than a little light on the subject!

I’ve got to get my trackbacks working. Until I do, I thought I’d simply leave a comment here with a link to the post where I’ve cited this post:

http://www.pachs.net/about/comments/kepler_on_supernova_theology_and_astrology/

Pingback: THe Darkened Room « The Renaissance Mathematicus

Pingback: Monday blast from the past #9: The posts of Christmas past. | The Renaissance Mathematicus

Pingback: The Renaissance Mathematicus Christmas Trilogy: An Explanation. | The Renaissance Mathematicus

Pingback: Discovery is a process not an act. | The Renaissance Mathematicus

Pingback: Christmas Trilogies! | The Renaissance Mathematicus

Pingback: An important 13th-century book on optics | The Renaissance Mathematicus