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Theodoric of Freiberg: Optics of the Rainbow

Theodoric of Freiberg wrote a treatise on the rainbow, De iride, around 1310. This is about the same time as when Kamal al-Din similarly explained the colors of the rainbow. Because Theodoric worked far from the centers of Islamic science, he makes an interesting case study of the experimental methodologies in mathematical optics in Latin Europe in the 14th century.

Theodoric was a Dominican monk from Germany who studied in Paris for several years. Around 1304 the Master-General of the Dominican order suggested that he begin writing a treatise on the rainbow, which he completed in manuscript form around 1310. This comprehensive work built upon a long series of optical investigations of the rainbow stretching back to Aristotle, including medieval predecessors such as Ibn al-Haytham (Alhazen), Qutb al-din al-Shirazi, Robert Grosseteste, Roger Bacon, and Witelo. Theodoric's innovations derived also from his own extensive experimental investigations in which he used prisms, screens, and spherical flasks filled with water. Theodoric regarded a spherical flask as a model of a raindrop in a cloud. He observed that different colors appeared as he would raise the flask higher or lower. By covering certain portions of the flask at a time, one after another, to see where the light would come out, Theodoric determined the path that light follows from the Sun through the drop to the human eye to create a rainbow. Moreover, Theodoric also worked out the path light follows in creating the secondary rainbow. (From Aristotle's Meteorology it was known that the secondary rainbow may often be seen outside of the regular rainbow, fainter than the primary rainbow, and that rainbows always appear in the sky around a center that lies opposite the Sun.)

In the diagram on the right from Theodoric's manuscript, the Sun is located at the lower left corner. The eye of the observer is in the center at the bottom, where the colors of the rainbow are signified by different vertical bands or columns. The four circles on the right side represent four flasks signifying raindrops in a cloud. For a secondary rainbow, each ray of light from the Sun travels to the observer in four steps of refraction or reflection:

1. First refraction, as light enters the raindrop.
2. First reflection, as light bounces off the far side of the raindrop, remaining within the raindrop.
3. Second reflection, as light bounces off the far side of the raindrop, again remaining within the raindrop but moving down and toward the left.
4. Second refraction, as light leaves the raindrop and travels to the eye of the observer in the center.

The primary and secondary rainbows differ because the second reflection is omitted in the case of the primary rainbow, where light only has a single reflection in a three-step process. (Theodoric's diagram of the three-step process for the primary rainbow is not shown here.)

Note on terms:

• Reflection occurs when light changes its direction in a single medium. Example: In a mirror, light bounces or reflects off the mirror, but the ray of light is traveling through the air both before and after the reflection. In the raindrop, the light is traveling through water, as it reflects within the raindrop, as if the far side of the raindrop were a mirror.
• Refraction occurs when light changes its direction as it passes from one medium to another. Example: In a magnifying glass, light passes from the air into the lens (first refraction) and then from the lens back into the air (second refraction). In the raindrop, the ray of light is refracted when it enters the drop (air to water) and when it leaves the drop (water to air).

Theodoric therefore concluded that, as a result of the three or four step process of refraction and reflection, one drop of water would send only one color of light to the eye of the observer. The rainbow results from a combination of many drops of water in a cloud at different positions from a center, where the drops at each distance from the center send a particular color of the rainbow.

While incomplete in several respects we need not explore here, Theodoric's explanation of the primary and secondary rainbows as a result of these three and four-step processes of refraction and reflection is still regarded as correct; that is, the paths traced by the rays of light through raindrops to produce both the primary and secondary rainbows was confirmed by Descartes in the 17th century. For this reason, Theodoric of Freiberg's discovery of the optics of the rainbow is often regarded as a triumph of experimental methodology in the late middle ages.

Dive Deeper

• A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (Oxford: Clarendon Press, 1953), pp. 233-259.
• Carl Boyer, The Rainbow: From Myth to Mathematics (Princeton University Press 1959), pp. 110-124.
• Wikipedia explains the optics of the rainbow with a diagram resembling that of Theodoric.
• This page from The National Center for Atmospheric Research explains Descartes' theory of the rainbow, which as you will see is identical in many respects to Theodoric's theory.

Source Quiz study questions

1. T or F? Theodoric of Freiberg experimented with a spherical flask filled with water to model the optics of a single raindrop.
2. T or F? Theodoric of Freiberg explained the optics of the primary rainbow.
3. T or F? Theodoric of Freiberg explained the optics of the secondary rainbow.
4. T or F? Refraction occurs when light is bounced off the far side of a drop of water, remaining within the drop.
5. T or F? In the 17th century, Descartes confirmed Theodoric's explanation of the paths traced by rays of light within drops of water.
6. T or F? Theodoric of Freiberg, a medieval natural philosopher with a university education and a member of a monastic order, rejected the experimental method.

	HSCI 3013. History of Science to 17th century Kerry Magruder, Instructor, 2004-14 Brent Purkaple, TA Report typos or broken links	Go to this course at Janux spellcheck.net | wordcounter.net Many thanks to the pedagogical model developed in Mythology and Folklore and other online courses by Laura Gibbs, which have been an inspiration for this course.	Academic Calendar
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