Building Bridges, Connecting Arcs

A post by Joshua Harvey, D.Phil. student, Department of Engineering Science and Pembroke College, University of Oxford, funded by the Andrew W. Mellon Foundation as part of ‘The Mental and Material Laboratories of Medieval Science’ project, under the aegis of the Ordered Universe.

The latest research article from the Ordered Universe project: “Bow-shaped caustics from conical prisms: a 13^th Century account of rainbow formation from Robert Grosseteste’s De iride” is available to read now, open access at the Optical Society of America’s journal Applied Optics. Grosseteste’s treatise De iride [On Rainbows], which may be familiar to long-term followers of the Ordered Universe project, explores theoretical optics, colour theory, and meteorology to give one of the most comprehensive pre-renaissance scientific writings on the rainbow. With this most recent article, we explore his pioneering model of rainbow formation – the first to use refraction (and not just reflection) in medieval Europe. Through an interdisciplinary combination of historical review, geometric optics, and both practical and simulated experiment, we give a thorough overview of the historical significance of the De iride, and look at what lessons we can learn from it today.

This fruitful exploration has not been done before. Although Grosseteste provides a detailed description of what he believes are the geometric underpinnings of a rainbow, he has previously been disregarded in this area. David Lindberg even went so far as to say that ‘his theory of the rainbow could not account for even the most basic phenomena and has remained largely unintelligible to the modern day.’ Well, we thought there might have been more to Grosseteste’s thought than that, being familiar with his mathematical mind and keen curiosity about the natural world. As a research team with a diverse expertise, we together arrived at an interpretation of Grosseteste’s optical mechanism that was intelligible, elegant and, most excitingly, perfectly testable. To our surprise, the caustics – patterns of gathered light – produced by a transparent cone are just as Grosseteste describes.

Remarkably, we have already been contacted by researchers investigating atmospheric optics, who have found some striking correspondences between their own work and our interpretation of Grosseteste’s De iride. Markus and Sarah Selmke’s recent paper, “Artificial circumzenithal and circumhorizontal arcs” published in American Journal of Physics, explores to great depths the kinds of refractive optical interactions between transparent cones, as modelled by glassware filled with water, and incident light. The authors have shown that Parry arcs, a type of halo, are analogous to the caustics produced by shining light through a wine glass of water. Although not as frequently observed as rainbows, Parry arcs are similarly beautiful displays of dispersive colour seen in the heavens, providing certain atmospheric conditions are met. The paper features a combination of practical and mathematical experimentation, similar to our own approach in the Applied Optics paper, and states that “light entering through the top air-water interface and leaving through the lateral cone surface results in an analogy to Parry’s halo”. This is identical to Grosseteste’s geometric scheme, as we interpreted it. Although, to his detractors, his likening of a rainbow to that of light going through a transparent cone might sound crude, or even ridiculous, it appears this simple model does indeed capture the optical principles behind a dispersive atmospheric phenomenon.

Grosseteste was wrong about rainbows. Not long after him, rainbows were correctly understood to be produced by light interacting with near-spherical raindrops, by both Kamal al-Din al-Farisi and Theodoric of Freiburg in the fourteenth century. But Grosseteste was not wrong about the optical qualities of transparent cones, and although the optical scene he describes in De iride does not relate to rainbows, it is analogous to another kind of dispersive optical event seen in the heavens.

Of course, it would be incorrect to claim that Grosseteste had solved the mystery of Parry’s arc back in the thirteenth century. He had probably never seen or heard of one, as they are rare outside the Arctic circles, and it wasn’t until 1820 that William Parry observed and drew one. Was this mere coincidence, could Grosseteste have happened upon an atmospheric optical mechanism by chance? Perhaps. But it is worth bearing in mind that his theory was likely grounded in observation, and formulated to be as parsimonious as possible. I think that rather than chance, it is instead even clearer we are reading the work of someone with a scientific mind, curiosity about nature, and a belief in a profoundly ordered universe.

Joshua Harvey