RAINBOW

, Iris, or simply the Bow, is a meteor in form of a party-coloured arch, or semicircle, exhibited in a rainy sky, opposite to the sun, by the refraction and reflection of his rays in the drops of falling rain. There is also a secondary, or fainter bow, usually seen investing the former at some distance. Among naturalists, we also read of lunar Rainbows, marine Rainbows, &c.

The Rainbow, Sir Isaac Newton observes, never appears but where it rains in the sunshine; and it may be represented artificially, by contriving water to fall | in small drops, like rain, through which the sun shining, exhibits a bow to a spectator placed between the sun and the drops, especially if there be disposed beyond the drops some dark body, as a black cloth, or such like.

Some of the ancients, as appears by Aristotle's tract on Meteors, knew that the Rainbow was caused by the refraction of the sun's light in drops of falling rain. Long afterwards, one Fletcher of Breslaw, in a treatise which he published in 1571, endeavoured more particularly to account for the colours of the Rainbow by means of a double refraction, and one reflection. But he imagined that a ray of light, after entering a drop of rain, and suffering a refraction, both at its entrance and exit, was afterwards reflected from another drop, before it reached the eye of the spectator. It seems he overlooked the reflection at the farther side of the drop, or else he imagined that all the bendings of the light within the drop would not make a sufficient curvature, to bring the ray of the sun to the eye of the spectator. But Antonio de Dominis, bishop of Spalato, about the year 1590, whose treatise De Radiis Visûs et Lucis was published in 1611 by J. Bartolus, first advanced, that the double refraction of Fletcher, with an intervening reflection, was sufficient to produce the colours of the Rainbow, and also to bring the rays that formed them to the eye of the spectator, without any subsequent reflection. He distinctly describes the progress of a ray of light entering the upper part of the drop, where it suffers one refraction, and after being by that thrown upon the back part of the inner surface, is from thence reflected to the lower part of the drop; at which place undergoing a second refraction, it is thereby bent so as to come directly to the eye. To verify this hypothesis, he procured a small globe of solid glass, and viewing it when it was exposed to the rays of the sun, in the same manner in which he had supposed the drops of rain were situated with respect to them, he actually observed the same colours which he had seen in the true Rainbow, and in the same order. Thus this author shewed how the interior bow is formed in round drops of rain, viz, by two refractions of the sun's rays and one reflection between them; and he likewise shewed that the exterior bow is formed by two refractions and two sorts of reflections between them in each drop of water.

The theory of A. de Dominis was adopted, and in some degree improved with respect to the exterior bow, by Des Cartes, in his treatise on Meteors; and indeed he was the first who, by applying mathematics to the investigation of this surprising appearance, ever gave a tolerable theory of the Rainbow. Philosophers were however still at a loss when they endeavoured to assign reasons for all the particular colours, and for the order of them. Indeed nothing but the doctrine of the different refrangibility of the rays of light, a discovery which was reserved for the great Newton, could furnish a complete solution of this difficulty.

Dr. Barrow, in his Lectiones Opticæ, at Lect. 12, n. 14, says, that a friend of his (by whom we are to understand Mr. Newton) communicated to him a way of determining the angle of the Rainbow, which was hinted to Newton by Slusius, without making a table of the refractions, as Des Cartes did. The doctor shews the method; as also several other matters, at n. 14, 15, 16, relating to the Rainbow, worthy the genius of those two eminent men. But the subject was given more perfectly by Newton afterwards, viz, in his Optics, prop. 9; where he makes the breadth of the interior bow to be nearly 2° 15′, that of the exterior 3° 40′, their distance 8° 25′, the greatest semidiameter of the interior bow 42° 17′, and the least of the exterior 50° 42′, when their colours appear strong and perfect.

The doctrine of the Rainbow may be illustrated and confirmed by experiment in several different ways. Thus, by hanging up a glass globe, full of water, in the sun-shine, and viewing it in such a posture that the rays which come from the globe to the eye, may include an angle either of 42° or 50° with the sun's rays; for ex. if the angle be about 42°, the spectator will see a full red colour in that side of the globe opposite to the sun. And by varying the position so as to make that angle gradually less, the other colours, yellow, green, and blue, will appear successively, in the same side of the globe, and that very bright. But if the angle be made about 50°, suppose by raising the globe, there will appear a red colour in that side of the globe toward the sun, though somewhat faint; and if the angle be made greater, as by raising the globe still higher, this red will change successively to the other colours, yellow, green, and blue. And the same changes are observed by raising or depressing the eye, while the globe is at rest. Newton's Optics, pt. 2, prop. 9, prob. 4.

Again, a similar bow is often observed among the waves of the sea (called the marine Rainbow), the upper parts of the waves being blown about by the wind, and so falling in drops. This appearance is also seen by moon light (called the lunar Rainbow), though seldom vivid enough to render the colours distinguishable. Also it is sometimes seen on the ground, when the sun shines on a very thick dew. Cascades and fountains too, whose waters are in their fall divided into drops, exhibit Rainbows to a spectator, if properly situated during the time of the sun's shining; and even water blown violently out of the mouth of an observer, standing with his back to the sun, never fails to produce the same phenomenon. The artificial Rainbow may even be produced by candle light on the water which is ejected by a small fountain or jet d'eau. All these are of the same nature, and they depend upon the same causes; some account of which is as follows. |

Let the circle WQGB represent a drop of water, or a globe, upon which a beam of parallel light falls, of which let TB represent a ray falling perpendicularly at B, and which consequently either passes through without refraction, or is reflected directly back from Q. Suppose another ray IK, incident at K, at a distance from B, and it will be refracted according to a certain ratio of the sines of incidence and refraction to each other, which in rain water is as 529 to 396, to a point L, whence it will be in part transmitted in the direction LZ, and in part reflected to M, where it will again in part be reflected, and in part transmitted in the direction MP, being inclined to the line described by the incident ray in the angle IOP. Another ray AN, still farther from B, and consequently incident under a greater angle, will be refracted to a point F, still farther from Q, whence it will be in part reflected to G, from which place it will in part emerge, forming an angle AXR with the incident AN, greater than that which was formed between the ray MP and its incident ray. And thus, while the angle of incidence, or distance of the point of incidence from B, increases, the distance between the point of reflection and Q, and the angle formed between the incident and emergent reflected rays, will also increase; that is, as far as it depends on the distance from B: but as the refraction of the ray tends to carry the point of reflection towards Q, and to diminish the angle formed between the incident and emergent reflected ray, and that the more the greater the distance of the point of incidence from B, there will be a certain point of incidence between B and W, with which the greatest possible distance between the point of reflection and Q, and the greatest possible angle between the incident and emergent reflected ray, will correspond. So that a ray incident nearer to B shall, at its emergence after reflection, form a less angle with the incident, by reason of its more direct reflection from a point nearer to Q; and a ray incident nearer to W, shall at its emergence form a less angle with the incident, by reason of the greater quantity of the angles of refraction at its incidence and emergence. The rays which fall for a considerable space in the vicinity of that point of incidence with which the greatest angle of emergence corresponds, will, after emerging, form an angle with the incident rays differing insensibly from that greatest angle, and consequently will proceed nearly parallel to each other; and those rays which fall at a distance from that point will emerge at various angles, and consequently will diverge. Now, to a spectator, whose back is turned towards the radiant body, and whose eye is at a considerable distance from the globe or drop, the divergent light will be scarcely, if at all, perceptible; but if the globe be so situated, that those rays that emerge parallel to each other, or at the greatest possible angle with the incident, may arrive at the eye of the spectator, he will, by means of those rays, behold it nearly with the same splendour at any distance.

In like manner, those rays which fall parallel on a globe, and are emitted after two reflections, suppose at the points F and G, will emerge at H parallel to each other, when the angle they make with the incident AN is the least possible; and the globe must be seen very resplendent when its position is such, that those parallel rays fall on the eye of the spectator.

The quantities of these angles are determined by calculation, the proportion of the sines of incidence and refraction to each other being known. And this proportion being different in rays which produce different colours, the angles must vary in each. Thus it is found, that the greatest angle in rain water for the least refrangible, or red rays, emitted parallel after one reflection, is 42° 2′, and for the most refrangible or violet rays, emitted parallel after one reflection, 40° 17′; likewise, after two reflections, the least refrangible, or red rays, will be emitted nearly parallel under an angle of 50° 57′, and the most refrangible, or violet, under an angle of 54° 7′; and the intermediate colours will be emitted nearly parallel at intermediate angles.

Suppose now, that O is the spectator's eye, and OP a line drawn parallel to the sun's rays, SE, SF, SG, and SH; and let POE, POF, POG, POH be angles of 40° 17′, 42° 2′, 50° 57′, and 54° 7′ respectively; then these angles turned about their common side OP, will with their other sides OE, OF, OG, OH describe the verges of the two Rainbows, as in the figure. For, if E, F, G, H be drops placed any where in the conical superficies described by OE, OF, OG, OH, and be illuminated by the sun's rays SE, SF, SG, SH; the angle SEO being equal to the angle POE, or 40° 17′, will be the greatest angle in which the most refrangible rays can, after one reflection, be refracted to the eye, and therefore all the drops in the line OE must send the most refrangible rays most copiously to the eye, and so strike the sense with the deepest violet colour in that region. In like manner, the angle SFO being equal to the angle POF, or 42° 2′, will be the greatest in which the least refrangible rays after one reflection can emerge out of the drops, and therefore those rays must come most copiously to the eye from the drops in the line OF, and strike the sense with the deepest red colour in that region. And, by the same argument, the rays which have the intermediate degrees of refrangibility will come most copiously from drops between E and F, and strike the senses with the intermediate colours in the order which their degrees of refrangibility require; that is, in the | progress from E to F, or from the inside of the bow to the outside, in this order, violet, indigo, blue, green, yellow, orange, red. But the violet, by the mixture of the white light of the clouds, will appear faint, and inclined to purple.

Again, the angle SGO being equal to the angle POG, or 50° 57′, will be the least angle in which the least refrangible rays can, after two reflections, emerge out of the drops, and therefore the least refrangible rays must come most copiously to the eye from the drops in the line OG, and strike the sense with the deepest red in that region. And the angle SHO being equal to the angle POH, or 54° 7′, will be the least angle in which the most refrangible rays, after two reflections, can emerge out of the drops, and therefore those rays must come most copiously to the eye from the drops in the line OH, and strike the sense with the deepest violet in that region. And, by the same argument, the drops in the regions between G and H will strike the sense with the intermediate colours in the order which their degrees of refrangibility require; that is, in the progress from G to H, or from the inside of the bow to the outside, in this order, red, orange, yellow, green, blue, indigo, and violet. And since the four lines OE, OF, OG, OH may be situated any where in the above-mentioned conical superficies, what is said of the drops and colours in these lines, is to be understood of the drops and colours every where in those superficies.

Thus there will be made two bows of colours, an interior and stronger, by one reflection in the drops, and an exterior and fainter by two; for the light becomes fainter by every reflection; and their colours will lie in a contrary order to each other, the red of both bows bordering upon the space GF, which is between the bows. The breadth of the interior bow, EOF, measured across the colours, will be 1° 15′, and the breadth of the exterior GOH, will be 3° 10′, also the distance between them GOF, will be 8° 55′, the greatest semidiameter of the innermost, that is, the angle POF, being 42° 2′, and the least semidiameter of the outermost POG being 50° 57′. These are the measures of the bows as they would be, were the sun but a point; but by the breadth of his body, the breadth of the bows will be increased by half a degree, and their distance diminished by as much; so that the breadth of the inner bow will be 2° 15′, that of the outer 3° 40′, their distance 8° 25′; the greatest semidiameter of the interior bow 42° 17′, and the least of the exterior 50° 42′. And such are the dimensions of the bows in the heavens found to be, very nearly, when their colours appear strong and perfect.

The light which comes through drops of rain by two refractions without any reflection, ought to appear strongest at the distance of about 26 degrees from the sun, and to decay gradually both ways as the distance from the sun increases and decreases. And the same is to be understood of light transmitted through spherical hailstones. If the hail be a little flatted, as it often is, the light transmitted may grow so strong at a little less distance than that of 26°, as to form a halo about the sun and moon; which halo, when the stones are duly figured, may be coloured, and then it must be red within, by the least refrangible rays, and blue without, by the most refrangible ones.

The light which passes through a drop of rain after two refractions, and three or more reflections, is scarce strong enough to cause a sensible bow.

As to the dimension of the Rainbow, Des Cartes first determined its diameter by a tentative and indirect method; laying it down, that the magnitude of the bow depends on the degree of refraction of the fluid; and assuming the ratio of the sine of incidence to that of refraction, to be in water as 250 to 187. But Dr. Halley, in the Philos. Trans. number 267, gave a simple direct method of determining the diameter of the Rainbow from the ratio of the refraction of the fluid being given; or, vice versa, the diameter of the Rainbow being given, to determine the refractive power of the fluid. And Dr. Halley's principles and construction were farther explained by Dr. Morgan, bishop of Ely, in his Dissertation on the Rainbow, among the notes upon Rohault's System of Philosophy, part 3, chap. 17.

From the theory of the Rainbow, all the particular phenomena of it are easily deducible. Hence we see, 1st, Why the iris is always of the same breadth; because the intermediate degrees of refrangibility of the rays between red and violet, which are its extreme colours, are always the same.

2dly, Why the bow shifts its situation as the eye does; and, as the popular phrase has it, flies from those who follow it, and follows those that fly from it; the coloured drops being disposed under a certain angle, about the axis of vision, which is different in different places: whence also it follows, that every different spectator sees a different bow.

3dly, Why the bow is sometimes a larger portion of a circle, sometimes a less: its magnitude depending on the greater or less part of the surface of the cone, above the surface of the earth, at the time of its appearance; and the higher the sun, always the less the Rainbow.

4thly, Why the bow never appears when the sun is above a certain altitude; the surface of the cone, in which it should be seen, being lost in the ground at a little distance from the eye, when the sun is above 42° high.

5thly, Why the bow never appears greater than a semicircle, on a plane; since, be the sun never so low, and even in the horizon, the centre of the bow is still in the line of aspect; which in this case runs along the earth, and is not at all raised above the surface. Indeed if the spectator be placed on a very considerable eminence, and the sun in the horizon, the line of aspect, in which the centre of the bow is, will be considerably raised above the horizon. And if the eminence be very high, and the rain near, it is possible the bow may be an entire circle.

6thly, How the bow may chance to appear inverted, or the concave side turned upwards; viz, a cloud happening to intercept the rays, and prevent their shining on the upper part of the arch: in which case, only the lower part appearing, the bow will seem as if turned upside down; which has probably been the case in several prodigies of this kind, related by authors. |

Lunar Rainbow. The moon sometimes also exhibits the phenomenon of an iris, by the refraction of her rays in the drops of rain in the night-time.

Aristotle says, he was the first that ever observed it; and adds, it is never seen but at the time of the full moon; her light at other times being too faint to affect the sight after two refractions and one reflection.

The lunar iris has all the colours of the solar, very distinct and pleasant; only fainter, both from the different intensity of the rays, and the different disposition of the medium.

Marine Rainbow. This is a phenomenon sometimes observed in a much agitated sea; when the wind, sweeping part of the tops of the waves, carries them aloft; so that the sun's rays, falling upon them, are refracted, &c, as in a common shower, and there paint the colours of the bow. These bows are less distinguishable and bright than the common bow: but then they exceed as to numbers, there being sometimes 20 or 30 seen together. They appear at noon day, and in a position opposite to that of the common bow, the concave side being turned upwards, as indeed it ought to be.

RAIN-Gage, an instrument for measuring the quantity of rain that falls. It is the same as OMBROMETER, or Pluviameter, which see.

RAKED Table, or Raking Table, in Architecture, a member hollowed in the square of a pedestal, or elsewhere.