RAINBOW. The rainbow is a circular image of the sun, variously coloured. It is thus produced : the solar rays, entering the drops of falling rain, are refracted to their further surfaces, and thence, by one or more reflections, transmitted to the eye : at their emergence f'rom the drop, as well as at their entrance, they suffer a refraction, by which the rays are separat ed into their different colours, and these, therefore, are exhibited to an eye pro perly placed to receive them. That this is the true account of the formation of the rainbow, appears from the following considerations : 1. That a bow is never seen but when rain is falling, and the sun shining at the same time, and that the sun and bow are always in opposite quar ters of the heavens : this every one's ex perience can testify. 2. That the same appearance can be artificially represent ed by means of water thrown into the air, when the spectator is placed in a pro per position with his back turned to the sun : experiment will shew this. 3. That its formation, as above described, can be clearly explained from the properties of light, already demonstrated in the former parts of this dictionary.
Let A B, (Plate XIII. Miscel. fig. 10) be a drop of water, and C a penCil of solar rays incident thereon ; if all the rays of any one colour, as red, belonging to the pencil C D, be refracted to the same point, C, and thence reflected, they will fall on the space, R Q, with the same obliquity, and at the same distances from each other as the refracted rays, if pro ceeding backward from G, would fall on the space, T S, but these, at their refrac tion, would emerge into T D, C S, &c parallel to each other; the rays, G 11, G Q, will emerge from the drop parallel to each other, and therefore will enter an eye properly placed copiously enough to cause a sensation ; a red colour will therefore appear in the direction of these rays, and so of others. But if the re fracted rays do not meet in the same point, the reflected rays, (fig. 11) I V, P Q, will not fall on the surface at the same distance from each other that P T and I S do, though their obliquity to the sur face be equal to that of the latter ; there fore, the refracted rays will emerge, diverging from each other, and conse quently will not enter the eye copiously enough to cause a perception of their co lour. It is plain, that where the rays of any colour emerge parallel, all these emerging rays will be inclined to the in cident rays in the same angle. And by calculation it is found, that the red rays, when they emerge parallel to each other, make with the incident rays an angle, A B 0, (fig. 12) of 42° 2', and the violet an angle, A C 0, of 40° 17', and the rays of the other colours, angles greater than the latter, and less than the former.
If through the eye which receives the emerging rays, there be drawn a line, A X, parallel to the incident rays, it will make, with the emerging rays of each colour, angles, R A X, and V A X, &c. equal to the above. This line, A X, is called the axis of vision. The several drops placed in the lines, A 11, A V, &c. will exhibit to the eye at A, the several prismatic colours respectively, as appears from what has been said ; and if those lines be supposed to revolve with a coni cal motion round the axis of vision, it is evident, for the same reason, that all the drops placed in each of the conic sur faces, so generated, will transmit the rays of each colour respectively to the • eye, and therefore, that a number of cir cular, concentric arches of the prismatic colours, adjoining to each other, will be exhibited to the eye. This explanation
relates to the interior bow, whose co. loins, beginning from the outside, are red, orange, &c. as in the prismatic spec trum. This bow can never be seen if the sun be elevated more than 42° 2' above the horizon ; for the horizon, II 0, (fig. 13) always makes with the axis of vision, A X, an angle equal to the eleva tion of the sun, In the case here stated, the line, A Q, marking the vertex of a rainbow, would fall entirely below the horizon. • As the anterior bow is formed by one reflection and two refractions, the exterior bow is formed by two reflections and two refractions at the surfaces of the drops of falling rain. If the red rays of any pencil, C D, (fig. 14) of solar rays, after refraction intersect each other at It, so that when reflected at T V, they may proceed parallel within the drop, after a second reflection at X Q, they will pro ceed to L M, intersecting each other at S, equally distant from X Q, as R. is from T V : and as the rays, QT, X V, if they proceeded backward, would, after reflec tion, so fall on the surface, N 0, as to be refracted into air parallel to each other ; so X M, Q L, falling on the surface pre cisely in the same circumstances, shall be refracted to the eye parallel to each other, and therefore will enter it copiously enough to cause a perception of their colour, (and so of the rest). The red rays, when emerging parallel after two reflections, are by calculation 'found to make with the incident rays, and there fore with the axis of vision, an angle of 50 57'. The violet rays, when emerging parallel, are found to make with their in cident rays, and therefore with the axis of vision, art angle of 54° 7': the other emerging rays meet the axis of vision in the intermediate angles. From hence it is easy to explain the generation of the exterior bow, (fig. 12) in the same man ner as that of the interior. It is to be re marked, that the order of colours in the exterior bow is the reverse of that in the interior, and the reason of this appears in the above explanation ; for A E, which marks the direction of the violet rays in the outer bow, contains with A X, the axis of vision, a greater angle than A D, which marks the direction of the red rays, contains with the same axis. The reverse is the case with the interior bow. It is evident, (for a reason similar to that given in the case of the interior bow) that an exterior bow cannot be seen when the elevation of the son is above 54° 7'.
lunar. The Moon some times also exhibits the phenomenon of an iris, by the refraction of her rays in drops of rain in the night time.