933 



RAINBOW. 



RAINBOW. 



931 



and if the angles c E o or D E o were nearly equal to 52, the eye would 

 be affected by the sensation of brightness as explained above ; therefore, 

 if the lines A E, B E, &e., were to revolve conically about E o as an axis, 

 all the globules of rain upon the conical surfaces so described would 

 send pencils of parallal rays to the eye, and two concentric arches of 

 bright light would be seen in the heavens. This hypothesis accounts 

 satisfactorily for the existence of two concentric bows of bright light, 

 but it affords no indication of the bands of colours of which they con- 

 sist. Descartes, however, very sagaciously refers their cause to the 

 decomposition of light on entering and quitting the drops of rain, 

 observing that the convex surfaces of the drops must produce effects 

 similar to those which take place when light is made to pass through 

 the plane faces of a triangular prism of water. 



But when Newton had discovered the different degrees of refrangi- 

 bility in the different coloured rays which composed a pencil of white 

 or compounded light, he was able to assign immediately the cause of 

 the coloured bands in the rainbow, the order of then- position, and the 

 breadth which they must occupy. Thus, if the incident pencil s I 

 (fys. 1 and 2) had consisted only of violet-coloured light (for example), 

 tlir .ingle A I s must have had that particular value which alone would 

 allow the rays of the emergent pencil to be parallel to one another ; 

 but if the incident pencil were supposed to consist of light of another 

 colour, as red, it should have fallen a little further from the centre 

 of the drop, in order that the angle A 1 8 might have the particular 

 value which would allow the rays of the emergent pencil to be 

 parallel to one another. It may be proved without difficulty that 

 the total deviation, when consecutive emergent rays of a given 

 colour come out parallel to one another, is less for red rays than for 

 violet ; and if K E be the direction in which the latter emerge from a 

 drop, K r in both figures may represent the direction hi which the 

 former would emerge, the variation of the course before emergence 

 being omitted in the figures to avoid confusion ; and if the eye were 

 situated so as to receive the pencil K E, it would have the impression 

 of a violet colour ; while, if it were situated so as to receive the pencil 

 K F, it would have that of a red colour. We have mentioned, for sim- 

 plicity, only the violet and red rays, which form the two extremes of 

 the coloured spectrum ; but it is easy to conceive that a like explana- 

 ti"ii might be given for rays of the intermediate colours. And since 

 th"' pencils of all the different colours diverge from one another on 

 quitting a rain-drop, it is evident that the spectator whose eye receives 

 one of the pencils will be affected by the colour of that pencil only, 

 the other pencils passing either above or below his eye. 



Newton has determined by computation that when the angle A E o 

 ( f'J- 3 ) = 40 1 T, the violet rays alone, after two refractions and 

 one reflection, will enter the eye of the spectator at E, the other 

 rays falling below; and when / BEO =42 2', the red rays alone 

 will enter the eye, the violet rays passing above. Again, when 

 L c E o = 50 59', the red rays only will enter the eye, after two 

 refractions and two reflections, the violet rays falling below; and 

 when / D E o = 54 9', the violet rays alone will enter, the red passing 

 above. If the interval between the drops A and B, and also between 

 thr drops c and D, were occupied by other drops, it may readily be 

 imagined that the pencils of parallel rays which come from them to 

 the eye would be of all the prismatic colours between the red and 

 violet, and that thus there would appear in the heavens two narrow 

 spectra : the length of that between A and B would be 1 45', and of 

 that between c and D would be 3 Itf. Therefore, if all the lines drawn 

 to E from the drops in the two spectra were to revolve conically about 

 E O as an axis, the drops on these lines would be in situations to send 

 to the eye rays of their own proper colours, and thus there would exist 

 the appearance in the heavens of two concentric bands of variously 

 coloured light. 



But it has been here supposed that the pencils s A, B B, Ac., come 

 from the centre only of the sun's disc, whereas each point of the disc 

 produces two bows similar to those which have been described : 

 therefore the lower extremity of the interior bow will be a violet band 

 whose breadth is equal to half the diameter of the sun (suppose 15'), 

 and which is situated immediately below the violet line formed by the 

 centre of the disc ; and in like manner the upper extremity of the 

 interior bow will be a red band whose breadth is also = 15', and which 

 in situated immediately above the red line formed by the centre of the 

 disc : consequently the whole breadth of the interior bow is about 

 = 2 15'. Similarly 30' (the measure of the nun's diameter) must be 

 added to the breadth of the outer bow, as before determined, which 

 thus becomes about =3 40'. In both bows, the colours between the 

 violet and red are less distinct than those two colours, because of the 

 mixture of the coloured light from all parts of the disc. 



On account of the two reflections which take place in the interior of 

 the drops which give rise to the outer bow, while there is but one 

 reflection in those which produce the inner bow, there must be a 

 greater quantity of light lost by transmission through the drops in the 

 former case than in the latter ; and hence the outer bow ia always 

 fainter than the other. 



The effect of the light of any given colour which comes out of the 

 drop in a divergent state has been neglected in the preceding inves- 

 tigation, but it is by no means insensible, especially in the neighbour- 

 hood of the bow, where the divergence is not great. If a ray which 

 emerged after one or two internal reflections be first supposed to be 



.ncident along a line passing through the centre of the drop, and the 

 ine of incidence be then conceived to move parallel to itself until 

 laving passed through si in Jig. 1 or 2, it just grazes the surface, it 

 will be found by calculation that the deviation, at first 180 or 360, 

 decreases until the position is reached in which consecutive rays come 

 out parallel, after which it increases again. In Jig. 1, the deviation 

 lakes place in the direction of the motion of the hands of a watch, and 

 m (i. ~i in the contrary direction. Hence the rays which emerge with 

 *reater deviation than K E, are situated (as to their directions) above 

 K E in fy. \ , and below K E in fg. 2 ; and therefore in fig. 3 the drops to 

 which they refer would be situated below A or B in the former case, 

 and abm-e c or D in the latter. Hence, considering light of one colour 

 only, and again regarding the sun as a mere point, we ought instead 

 of two bright circles in the sky, in the positions determined above, 

 'jo have two bows, in each of which the brightness terminates abruptly 

 on the side towards the other, and fades oft' on the other side. Hence, 

 considering the joint effect of all the colours, we see that they must 

 be more mixed together, especially about the blue and violet, than 

 would otherwise have been the case. In a vivid solar rainbow the 

 darkness of the space between the bows compared with the space 

 immediately within the primary bow is readily seen. 



There is one part of the phenomenon which cannot be explained 

 merely by geometrical optics, namely, the existence of what have been 

 called supernumerary boics. In the upper part of the primary solar 

 rainbow two or even three maxima of red may frequently be seen on 

 the inside of the principal maximum, forming as many additional or 

 supernumerary bows, decreasing in vividness and in breadth on 

 receding from the principal bow inwards. Even the secondary bow, 

 notwithstanding its comparative faintness, shows symptoms of the 

 same phenomenon. The existence of these bows was first explained by 

 Dr. Young, who pointed out that the light corresponding to any par- 

 ticular direction within the bow was double, and tliat the two portions 

 were in a condition to interfere. The explanation, however, resulting 

 from the application of the principle of interference to two systems of 

 rays whose courses are determined by geometrical optics is imperfect, 

 and would make the illumination increase to infinity on passing from the 

 illuminated side to the place of the geometrical bow, and then ceases 

 abruptly. Whenever such results follow from the calculations of 

 geometrical optics, it is found that they are modified in practice by 

 the phenomena of diffraction. The complete explanation of the super- 

 numerary bows, according to the principles of the undulatory theory, 

 has been given by Mr. Airy, in a paper ' On the Intensity of Light 

 in the neighbourhood of a Caustic ' (' Camb. Phil. Trans.,' vol. vii., 

 p. 379), and hia results have been verified by the observations of 

 Professor Miller. 



A rainbow can never be greater than a semicircle, if the spectator 

 be not on elevated ground ; for if it were, the centre of the bow would 

 be above the horizon, and the sun, which is in a line drawn through 

 that centre and the eye, would then be below the horizon ;' but, in this 

 case, the sun could not shine on the drops of rain, and consequently 

 there would be no bow. When the rain-cloud ia of small extent, there 

 is seen only that portion of the bow which, the cloud can form ; yet 

 the bow is sometimes seen against the blue sky, which happens when 

 the rain in falling is seen on a part of the sky which is free from cloud ; 

 and a portion of a bow is frequently seen hi an inverted position on the 

 ground by the refraction of the light in drops of rain adhering to the 

 grass or the leaves of trees. It may be added that a coloured bow 

 similar to that which is produced by rain may be observed in the 

 spray from a waterfall, or from a fountain, when the jet of water is 

 agitated by the wind, and also in the mists which at times lie upon 

 low grounds. 



The lunar rainbows appear in general in white ; and when they are 

 coloured, they differ from those produced by the sun only in the 

 colours being much more faint. The faintness of the colour, or its 

 entire absence, is accounted for by the fact that when light is exces- 

 sively faint, all perception of colour is lost. 



The circle of light which is occasionally seen surrounding the sun 

 or moon at a considerable distance from the disc of the luminary is 

 called a lialo, and ia caused by the refractions of light in particles of 

 ice which float in the air. It must not be confounded with a corona, 

 which consists in one or two coloured rings immediately surrounding 

 the luminary, and is distinguished from a halo by the variability and 

 comparative smallness of its diameter, and by the order of the colours, 

 red outside, blue inside which is the reverse of the order in a halo. 

 The corona is due to the globules of water constituting a thin veil of 

 cloud, and is a phenomenon of interference, which may be imitated by 

 viewing a caudle seen against a dark background through a piece of glass 

 dusted with lycopodium. The two halns most commonly seen have 

 radii of about 22 and 46. The phenomenon of halos having some 

 resemblance to that which has been just described, a brief explanation 

 of it may be with propriety introduced in this place. 



The cause of the halo was first investigated by Des Cartes, who 

 observes ^' Meteora,' cap. is.) that this phenomenon diSers from the 

 rainbow, inasmuch as the latter is seen only while rain is falling, 

 whereas halos are never seen at such times; and he ascribes their 

 formation to refractions of light in star-shaped crystals of ice, which 

 he remarks are thicker in the middle than at the edges, and are there- 

 fore proper to produce refractions. 



