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A Middle Age interpretation of the Rainbow: Robert Grosseteste’s De Iride et Speculo

Here we present the English translation by A.C. Sparavigna of Grosseteste’s De iride seu de iride et speculo (on the Rainbow). Robert of Grosseteste’s (1175-1253) was one of the most accomplished masters of the University of Oxford, then Bishop of Lincoln. He maintained the need to apply mathematics to the study of the natural phenomena. Influenced by Neoplatonism and Arabic treatises on optics, in the first part of this work Grosseteste discusses the epistemology of optics. He explicitly distinguishes optics from Aristotelian physics, dividing it into the three traditional disciplines (optical, retroreflective and diopter). In the second part, Grosseteste presents a quantitative law for the refraction of light, while in the third part of the essay he discusses the phenomenon of the rainbow. Grosseteste’s explanation is quite interesting, having in mind the time he lived. He discusses the refraction of sun rays into four different bodies: ether or atmosphere, clouds, the highest and most rarefied part of dew (originated from the cloud), and its lower and denser 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.

First then, let us say that optics is a science, which is based on the figures of the visual perceptions, and it is subaltern to the science, which is based upon figures and schemes, which contain lines and radiating surfaces, being them cast by the radiating sun, or by stars, or by any other radiant body. And it has not to be thought that the going out of visual rays from eyes is only a virtual argument, without any reality, as people who consider “the part and not the whole” are arguing. But let us note that visible objects are of a nature similar to the nature of the shining and sparkling sun, the radiation of which, combined with the radiation of the external surface of a body, completes the total perspective of vision.

Therefore, some philosophers handling these natural things, are considering the natural visual perception as passive, that is, as an “intro-mission”. However, mathematicians and physicists, concerning the nature of visual perception, consider that it occurs according an “out-emission”. Now, this part of the sight, which is effected by an out-emission, Aristotle plainly discussed in the last chapter of his book on the animals, that “the back of the eye sees far away; from its emission it is not divided, nor consumed, but its ability of sight goes forward from him and right to the things we are seeing.” And again, in the same: “Three are our conscious senses, namely, sight, hearing, smell, they come out from the organs, just as it emerges from the water in canals, and therefore a long nose has a good smelling. In optics, then, the true position concerning the rays is that of their emission.

Of which (optics), there are three main parts, according to the three ways of transition the rays have to the objects of vision. Either the path of the rays to the visible object is straight through a transparent medium having a specific feature, interposed between who is looking and the object. Or, it is ruled by a path directed to a body having a virtual nature, that is, a mirror, reflected by it, back to the object we are seeing. Or it is the passage of the rays through more transparent media of different kinds, where, at the interfaces, the ray is broken and makes an angle, and the ray comes to the object not with a straight path, but by means of several straight lines, having a number of angles at the related interfaces.

The first part of this science is named “de visu”, the second “about mirrors”. The third part is coming in our possession unknown and untouched. We know, however, that Aristotle had discussed this third part, which is the much more difficult, and the subtlety of which was by far the more remarkable, emerging from the depths of the nature. This part of optics, if fully understood, shows us the way in which we can made objects at very long distance appear at very close distance, and large things, closely situated, appear very small, and small things at a certain distance we can see as large as we want, so that, it is possible for us to read the smallest letters at incredible distance, or count the sand, or grain, or grass, or anything else so minute. In what way, however, it is necessary to understand how this wonderful happens, so it will become clear to everybody. Visual rays penetrating through several transparent different materials, are broken at interfaces; and the parts of these rays, in the different existing transparent materials, at the interface of those are angularly connected. This, however, is clear by means of an experience, the principle of it is set down in the book on the mirrors: if we cast an object into a vessel, and the distance is assumed that it may not be seen, and some water poured into, it will be seen what is inside. The same is displayed by a body having a continuous nature too; therefore, the visual ray, at the interface of two transparent media with different features, is subjected to a contiguity law. When one total ray is generated from a source, the continuity of it cannot be broken, unless its generation is broken, and at the interface of two transparent media, the ray is not discontinuous; at the interface, we cannot have a full continuity and a complete discontinuity and therefore, at each point of the interface the two parts are, not directly, but angularly connected.

But how large is the angular deviation from the straight path associated to a ray? Let us consider the ray from the eye through the air medium, incident on a second transparent medium, as a straight line to the point, where it is incident on the transparent medium; then let us make the line deep in the transparent medium, line that makes equal angles with the surface of transparent medium, that is, normal to the interface. I say, therefore, that the prolongation of the ray in the second transparent medium is following a line, separating of a certain angle, which is one half of the angle i obtained as follow. i is the angle given by the line which is the prolongation of the ray, without interruption and direct, drawn away from the point of incidence deep in the medium, equal to the angle i, drawn above the surface of the second transparent medium.

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.”

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.

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.

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.

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.

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.

On the other hand, the difference of the colors of a rainbow from those of other rainbows is due to the purity and impurity of the transparent medium supporting it, as well as from the brightness and obscurity of the light impressing it. If we have a pure transparent medium and bright light, the color is whitish. If the recipient medium is a mixture of vapors and mist and the light is hazy, as occurs near the East and West, the colors are less splendid and their brightness reduced. In the same manner, according to the enumeration of brightness and obscurity of light and of purity and impurity of the medium, all the arcs of various colors can be seen.

This translation is part of Amelia C. Sparavigna (Department of Applied Science and Technology, Politecnico di Torino, Italy), Translation and discussion of the De Iride, a treatise on optics by Robert Grosseteste, from This translation has been also published as On the Rainbow, a Grosseteste’s Treatise on Optics, in International Journal of Sciences, Volume 2, September 2013 (9), pp. 108-113.