And thus, while the angle of incidence or distance of the point of incidence from в 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 to fay, 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, 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 в and w, with which the greatest poffible distance between the point of reflection and, and the greatest poffible angle between the incident and emergent reflected ray will correfpond. So that a ray incident nearer to в fhall, at its emergence after reflection, form a less angle with the incident, by reafon of its more direct reflection from a point nearer to Q; and a ray incident nearer to w, fhall at its emergence form a lefs 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 confiderable space in the vicinity of that point of incidence with which the greateft angle of emergence correfponds, will, after emerging, form an angle with the incident rays differing infenfibly from that greatest angle, and confequently will proceed nearly parallel to each other; and those rays which fall at a diftance from that point will emerge at various angles, and confequently will diverge. Now, to a fpectator, whofe back is turned towards T 2 N towards the radiant body, and whofe eye is at a confiderable distance from the globe or drop, the divergent light will be fcarcely, if at all, perceptible; but if the globe be fo fituated, that those rays which emerge parallel to each other, or at the greatest poffible angle with the incident, may arrive at the eye of the fpectator, he will, by means of those rays, behold it nearly with the same splendor at any distance. In like manner, those rays which fall parallel on a globe, and are emitted after two reflections, fuppofe at the points F and G, will emerge, at H, parallel to each other, when the angle they make with the incident, A N, is the leaft poffible; and the globe must be seen very refplendent, when its pofition is fuch, that those parallel rays fall on the eye of the spectator. The quantities of these angles are determined by calculation, the proportion of the fines of incidence and refraction to each other being known. And this proportion being different (264, G) in rays which produce different colours, the angles muft vary in each. Thus it is found, that the greatest angle in rain-water for the leaft refrangible, or red rays, emitted parallel after one reflection is 42° 2', and for the moft 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, о Suppofe now, that 'o (fig. 82) is the fpectator's p eye, and op a line drawn parallel to the Sun's rays, and let POE, POF, POG, POH, be angles of 40° 17', 42° 2′, 50° 57′, and 54° 7′ refpectively, and these angles turned about their common fide op, will, with their other fides o E, OF, OG, OH describe the verges of two rainbows as in the figure. For, if E, F, G, H be drops placed any where in the conical fuperficies defcribed 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 moft refrangible rays can, after one reflection, be refracted to the eye, and therefore all the drops in the line o E must send the most refrangible rays moft copiously to the eye, and thereby strike the fenfe with the deepest violet colour in that region. And in like manner the angle SFO being equal to the angle Po F, or 42° 2′, will be the greatest in which the leaft 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 ftrike the sense with the deepest red colour in that region. And, by the fame argument, the rays which have the intermediate degrees of refrangibility will come moft copiously from drops between E and F, and ftrike the fenfes with the intermediate colours in the order which their degrees of refrangibility require; that T 3 |