Translation and discussion of the De Iride, a treatise on optics by Robert Grosseteste

Here I am proposing a translation and discussion of the De Iride, one of the short scientific treatise written by Robert Grosseteste. In the first part of his Latin text we find reflection and refraction of light, described in a geometrical optics. In the second part, Grosseteste is discussing the rainbow and how the colors are created.

that was a stimulus to thinkers in the Oxford of the fourteenth-century, who were developing the beginnings of a mathematical physics. In a recent paper [5], I have shortly discussed the role of the light in the creation of the world as seen by Grosseteste. Here I am translating and discussing one of the works of Grosseteste on optics, entitled De Iride, On Rainbow. In fact he is not only discussing the rainbow. In the first part of the text, he discusses reflection, refraction and optical instruments. In the second part he is proposing the rainbow as a phenomenon of refraction of light. He explains how the shape of the rainbow is originated and the formation of the colors. Here, I am subdividing the Latin text in several sections [6]. For each section, it is reported the original text and it is given translation, where who is writing, ACS, applied her knowledge of Latin. Some additional comments are given too. The Latin text is given in MS UI Gothic characters. I have translated "perspectivus" as "optical", like in Ref. 2. In [7], it is told that Perspective, in the sense of the "science of optics," came in English from Old French perspective and directly from Medieval Latin perspectiva ars "science of optics," from fem. of perspectivus "of sight, optical" from Latin perspectus "clearly perceived," pp. of perspicere "inspect, look through, look closely at," from per-"through" + specere "look at". In the sense of "art of drawing objects so as to give appearance of distance or depth" is first found 1590s, influenced by Italian prospettiva, an artists' term. The figurative meaning "mental outlook over time" is first recorded 1762. The "iris" is a flowering plant, also "prismatic rock crystal," from L. iris (pl. irides) "iris of the eye, iris plant, rainbow," from Greek iris (gen. iridos) "a rainbow; the lily; iris of the eye," originally "messenger of the gods," personified as the rainbow. The eye region was so called (early 15c. in English) for being the colored part.
It is of optics and physics to speculate about the rainbow. But, the same "what" the physics needs to know, is a "because of what" the optics needs. And in fact, Aristotle, in the book on the meteorology, did not show "because of what", in the sense of optics, but "what" is the rainbow, which is physics, in a quite short discussion. Hence in this paper, this "because of what", concerning optics, is started discussing and explaining, in our manner and time opportunity.
Here we have "quid" (interrogative pronoun [8]), "what", that is the effect, or the phenomenon, the physics needs to describe. The "propter quid", "because of what", is instead an answer given by the research, on the causes of the phenomenon. In the Latin text, we have also "modulo nostro". Modulus is a "small measure," dim. of modus "measure, manner". First of all [7], the noun "figure", is the "visible form or appearance of a person," from Old French figure (10 century) "shape, body, form, figure, symbol, allegory," from Latin figura "a shape, form, figure". Originally in English with meaning "numeral," but sense of "form, likeness" is almost as old (mid-13 century). And "species", that from 1550s, is a classification in logic, here is meaning "kind, sort," originally "appearance, sight, a seeing," related to specere "to look at, to see, behold". Therefore I translated as "object". 5. Perspectiva igitur veridica est in positione radiorum egredientium.
In optics, then, the true position concerning the rays is that of their emission.
Position (n.) [7], as a term in logic and philosophy, is coming in English from the Old French posicion, from Latin positionem (nom. positio) "act or fact of placing, position, affirmation" from posit-, pp. stem of ponere "put, place". Meaning "manner in which a body is arranged or posed" first recorded 1703. Meaning "official station, employment" is from 1890. We have that Grosseteste used "extramissionem" in section 4 and here "egredientium". So I have softened "out-emission" in "emission". It seems that Grosseteste agreed with the theory of out-emission, but in any case, I suppose that he believde simply in the emission of light from some sources. About the visual perception, there were two ancient Greek schools, providing a different explanation of vision. The first was proposing an "emission theory": vision occurs by means of rays emanated from the eyes and received by objects. We can see an object directly, or by means of refracted rays, which came out of the eyes, traversed a transparent medium and after refraction, arrive to the object. Among the others, Euclid and Ptolemy followed this theory. The second school proposed the "intro-mission" approach which sees vision as coming from something entering the eyes representative of the object. Aristotle and Galen followed this theory, which seems to have some contact with modern theories [9]. It seems that Grosseteste had mixed Aristotle's ideas with the out-emission theory, and therefore I used simply "emission". Transition means the passage from one place to another. Grosseteste is subdividing the propagations of rays in three cases, the first is the direct propagation, the second is the reflection on mirrors and the third the refraction. I rendered "spiritualis" using "virtual". Couplet (n.) [7], from the Latin copula "tie, connection". I supposed that Grosseteste was telling that the first part of optics is coupled with the direct propagation of rays. In this part of the treatise we find the description of some phenomena that we can obtain with lenses; he seems to describe, for instance, a magnifying glass useful to see the small things or read the small letters in a book. And then I am supposing that Grosseteste had some lenses in his "laboratory". Moreover, he tells that "we can made things at very long distance appear at very close distance, and large things closely situated appear very small, and small things at a certain we can see as large as we want". Had he a sort of telescope?
In any case, we can suppose that he had some reading stones. A reading stone was a more or less hemispherical lens, that was placed on a text to magnify the letters, so that people with presbyopia could read. Reading stones were among the earliest common uses of lenses. According to Wikipedia, [10] they were developed in the 8th century, by Abbas Ibn Firnas. The function of reading stones was replaced by the use of spectacles from the late 13th century onwards. Early reading stones were made from rock crystal (quartz) as well as glass.
The earliest written records of lenses date to Ancient Greece. In his play, The Clouds (424 BCE), Aristophanes is mentioning a burning-glass, a lens used to focus the sun's rays to produce fire. Pliny the Elder show that burning-glasses were known to Romans, [11] and mentions what was probably a corrective lens: Nero was said to watch the gladiatorial games using an emerald, probably concave to correct for myopia [12]. Pliny is also describing the magnifying effect of a glass globe filled with water. And here too, Grosseteste is describing a globe filled with water. What is interesting in the Grosseteste description is that he find the reason of these effects in the refractions of the rays. Here we find the Grosseteste's refraction law. Grosseteste's law is telling that the angle of refraction is one-half the angle of incidence i. Of course, it is quite different from the Snell's law that we use, containing the trigonometric functions of angles and the refractive index. Refraction was studied by the Greek science too. Ptolemy had found a relationship regarding the angles of refraction [13]. Ptolemy found in fact an empirical law, fitting figures with experimental data. He measure the refraction from air to water, and water to glass [14]. Ptolemy plotted r, the refractive angle, against i, the incident angle, at ten-degree intervals from i=0° to i=80°. The resulting values of r were in agreement with the sine-law. Alhazen, in his Book of Optics (1021), studied the refraction too. Refraction was accurately described by Ibn Sahl, of 9. Quod autem sic determinetur anguli quantitas in fractione radii, ostendunt nobis experimenta similia illis, quibus cognovimus, quod refractio radii super speculum fit in angulo aequali angulo incidentiae. Et idem manifestavit nobis hoc principium philosophiae naturalis, scilicet quod "omnis operatio naturae est modo finitissimo, ordinatissimo, brevissimo et optimo, quo ei possibile est".

So we have determined the amount of the refractive angle of the rays. We know that there are similar experiments giving the refraction of the rays on mirrors, fitting an angle equal to the angle of incidence. And the same tells us that principle of the philosophy of nature, namely, that "every action of the nature is well established, most ordinate, in the best and shortest manner, as it is possible."
Here we have Grosseteste's principle of "least action". I have translated "finitissimo" with "well established", as given by [8]. The English finite (adj.) is coming from L. finitus, pp. of finire "to limit, set bounds, end," from finis (see finish). But, in Latin, finitus has also the meaning of established, defined, determined [8]. In my opinion, this second meaning was that used by Grosseteste. It is interesting to note that the Grosseteste's principle is given after a sentence on the reflection of rays from mirrors, that he named refraction. It was in the 17th century, that Pierre de Fermat postulated that "light travels between two given points along the path of shortest time," which is known as the principle of least time or Fermat's principle [15].

Moreover, the object which is seen through a medium composed of several transparent materials, does not appear to be as it truly is, but it is appearing composed by the concurrence of the rays from the eye, continuous and direct, and by the lines starting from the viewed object and falling on the (second) surface, that is nearest to the eye, according to its normal (the line having equal angles from all the sides). This is clear to us from experiments and similar reasoning that we know, that an object seen in a mirror appears in the concurrence of the propagation of the lines of sight and the lines drawn directly upon the surface of the mirror, normal to this surface.
Here we can suppose that he had a method to create the images of objects reflected from mirrors and for objects passing through a transparent medium. In the last sentence, he is telling that we can create the image of an object reflected from a mirror, using the rays and the normal to the mirror, as we are used to do in geometric optics. It is remarkable that Grosseteste does not use in the De Iride a term such as "diopter" or "dioptron" (instrument to look through), which is coming from the Greek. From the Guglielmo Gemoll's dictionary, 1959, we have that διοπτευω, means to observe, consider all sides, explor); διοπτηρ, is the ranger; διοπτρον, the instrument to look through. The ancient dioptra were astronomical and surveying instrument, dating from the 3rd century BCE. The dioptra were a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. So, the ancient dioptra usually had not lenses. However, in Italian, we use "diottro", to define the interface between two different optical media. And "diottrica" is the science concerning the light refracted by diaphanous media. In English, the term diopter arrived from French, having the same meaning it has in Italian. Probably Grosseteste knew that the Greek term dioptra was used for surveying; the second sense, that of optical medium, was not yet arrived from French. It is evident, namely, the quantity of the angle according to which the ray is broken at the interface (contiguity) of the two transparent media, and where the image of an object appears arising from several transparent media; and let us add those principles of optics, which are given by the philosophers studying the natural phenomena, that is, that given the amount of the angle, under which an object is seen, it appears its position and size, according to the order and organization of the rays; and that it is not the great distance rendering a thing invisible, except by accident, but the smallness of the angle under which it is seen: it is clear that it is possible, using geometrical ratios, knowing the position and the distance of the transparent medium, and knowing the distance from the eye, to tell how an object appears, that is, given its distance and size, to know the position and the size of the image; and it is also clear, how to design the shape of the transparent medium, in order that this medium is able to receive the rays coming out from the eye, according to the angle we choose, collected in the eye, and focusing the rays as we like over the observed objects, whether they are large or small, or everywhere they are, at long or short distances; in such a way, all objects are visible, in the position and of the size given by the device; and large objects can appear short as we want, and those very short and at a far distance, on the other hand, appear quite large and very perceptible.
This is a quite interesting part of the treatise. Here we find that Grosseteste is proposing the geometrical optics, and applied to rays of light, we can give the position and magnitude of the images of objects. Moreover, he is telling that we can obtain some recipes to design the surface of lenses, and arrange some lenses to have a telescope. Again, we can ask ourselves, whether he had actually a telescope or he simply was arguing on its possibility, after studying the descriptions of optical devices in some Arabic manuscripts.
12. Et huic tertiae parti perspectivae subalternata est scientia de iride. Non enim possibile est iridem fieri radiis solaribus per incessum rectum a sole in concavitatem nubis incidentibus. And in the third part of optics we have the study of the rainbow. Undoubtedly, it is not possible the rainbow is given by a direct crossing of the solar rays in the cavities of the clouds. Because the continuous illumination of the cloud does not produce an arc-like image, but some openings towards the sun, through which the rays enter the cavity of the cloud. And it is not possible that the rainbow is produced by a reflection of the rays of the sun upon the surfaces of the raindrops falling down from the cloud, as reflected by a convex mirror, so that the cavity of the cloud receives in this manner the reflected rays, because, if it would be so, the rainbow would not be an arc-like object; moreover, it would happen that increasing the altitude of the sun, the rainbow would be greater and higher, and decreasing the sun altitude, the rainbow would be smaller; this is contrary to what is shown by the experience. It is therefore necessary that the rainbow is created by the refraction of the sun's rays by the humidity of the cloud. Let me tell, therefore, that outside the cloud is vaulted, and inside it is hollow. This is clear from the nature of "light matter" and "heavy matter". And that, what we see of a cloud is smaller than a hemisphere, even though it appears to us as a hemisphere, and when the humidity comes down from inside of the cloud, it is necessary that it assumes the volume of a convex pyramid at the top, descending to the ground, and therefore it is condensed in the proximity of the earth, more than in its upper part.
Convex [7] in English is coming from French convexe, from Latin convexus "vaulted, arched," pp. of convehere "to bring together". Possibly, it is coming from the idea of vaults carried together to meet at the point of a roof. "Convex lens" is from 1822. Concavity [7], in English from Old French concavité "hollow, concavity", or directly from Latin concavitatem (nom. concavitas), from Latin concavus "hollow". I have therefore considered the concavity of the cloud, as its hollow parts. The convex part as its arched part. Roratione in Latin in the drew drop falling. I translated with raindrops and humidity in the air. For a discussion on the Grosseteste's and Medieval theories on rainbow, see [16]. Then, in the universe there are four transparent media, through which the rays of the sun penetrate, that is, pure air containing the cloud, second the cloud itself, third the highest and most rarefied humidity coming from the cloud, and fourth, the lower and denser part of that humidity. From all the things discussed before on refraction and related angles at the interface between two media, it is necessary the rays of the sun are first refracted at the boundary of air and cloud, and then at the boundary of cloud and humidity, so that, after these refractions, the rays are conveyed in the bulk of humidity, and after, they are broken again though its pyramidal cone, however, not assuming the shape of a rounded pyramid, but in the form similar to the curved surface of a rounded pyramid, expanded opposite to the sun. Therefore its shape is that of a bow, and to us (in England), the rainbow never appears in the South, and, because the aforesaid cone is close to the earth, and it is expanding opposite the sun, it is necessary that more than a half of that cone falls on the surface of the earth, and the rest of it falls on the cloud, opposite the sun. Accordingly, on sunrise or sunset, a semicircular rainbow appears and is larger; when the sun is in other positions, the rainbow appears as a portion of the semicircle. And increasing the altitude of the sun, the portion of the rainbow decreases. And for this reason, in those places where the sun can reach the zenith, the rainbow never appears at noon. Aristotle tells that the "quantity" of the different arcs we can see on sunrise and sunset is small, but, Aristotle's small "quantity" is to be understood not concerning the "size" but the luminosity, which happens because the rays are passing, during these hours, through a large quantity of vapor, much larger than in other hours of the day. Aristotle himself suggests as a consequence, that there is a reduction of that which shines because of the rays of the sun in the clouds.
Here Grosseteste continues his discussion on the rainbow phenomenon. Let us note that Grosseteste uses the term "zenith", which is coming from Arabic. "Et propter hoc in locis multae accessionis solis ad zenith capitum non apparet omnino iris in hora meridiana". Zenith (n.): Reference 7 is telling that it is used in English from the late 14 century, from Middle Latin, cenit, senit, as a bungled scribal transliterations of Arabic samt "road, path," abbreviation of samt ar-ras, lit. "the way over the head." Letter -m-misread as -ni-. The Medieval Latin word could as well be influenced by a rough agreement of the Arabic term with classical Latin semita "sidetrack, side path". 14 However, the color is light mixed with a transparent medium; the medium is diversified according to the purity and impurity, but the light is fourfold divided; it is to be divided according to the brightness, and of course, to the obscurity, and according to intensity (richness) and tenuity (thinness), and according to the six different enumerations the variety of all the colors is generated, the variety of colors that appear in the different parts of a single rainbow, is mainly due to the intensity or tenuity of the rays of sun. Where there is a greater intensity of light, it appears that the colors are more luminous and bright: but where there is less intensity of light, it appears that the color turns to the dark color of Hyacinthus. And because the intensity of light and the decrease of intensity is not subjected to a rule, except in the case of light shining on a mirror, or passing through a transparent medium, which, by means of its own shape, can gathers the light in a certain place, and, in a certain place can disrupt the light, diminishing it, and the arrangement of receiving the light is not a fixed one, it is clear that that it is not in the skill of an artist to reproduce the rainbow, but it is possible to imitate accordingly to a certain arrangement.
It seems to me that Grosseteste is telling that we can have convergent or divergent lenses. Or that different images can observed, with respect to the focal planes. And therefore an artist can reproduce the effects created by a mirror, or convergent and divergent lenses; but, for the rainbow, this is too much difficult. Here is the end of the discussion on the rainbow, according to a Lincolnian.