OF NEWTON'S OPTICS. 



27 



tion of the sine of incidence and refrac- 

 tion for the red, green, and violet, sup- 

 posed to pass from air into glass, to be 

 as follows : 



Red Sin. inc. Sin.ref. : : 77 50 

 Green Sin . inc. Sin . ref. : : 77| 50 

 Violet Sin . inc. Sin . ref. : : 78 50 

 he proceeded to investigate the effect 

 which this difference in the proportion 

 produces on the images of objects formed 

 by the object-glasses of refracting tele- 

 scopes. When the curvature of the 

 object-glass is not great, compared with 

 its diameter, the angles of incidence of 

 rays proceeding from a point at any 



Fig. 



OAUV^J VI T^l Y OHIO,!!, Ctll^lVO GUW 



ne proportion as the angles themselves: 

 1, therefore, in the case to which we 



considerable distance are very small, the 

 rays being evidently very nearly perpen- 

 dicular to the surface of the glass. By 

 a well known principle of mathematics, 

 the sines of very small angles are in the 

 samei 

 and, 



now allude, the angles of incidence will 

 be to those of refraction as the above 

 numbers, and the deviations of the rays 

 above mentioned will be as the differences 

 of those numbers. That is to say, the 

 deviations of the red, green, and violet, 

 will be as 27, 2 7i, and 28. 



Let L be a lens presented to a dis- 



30. 



tant object from which the rays may 

 be considered parallel. Let V be the 

 focus to which the violet, or most refran- 

 gible rays are collected ; and R the point 

 to which the red, or least refrangible rays 

 are collected ; and let G be the focus of 

 the medium or green rays. The places 

 of the points, V, G, R, may be determined 

 by geometrical reasoning, if the propor- 

 tions of the sines of incidence and refrac- 

 tion as above given, and the curvature of 

 the lens, be known. The result is, that if 

 twice the distance, LG, be divided into 

 55 equal parts, the space VRis equal to 

 one of these parts. 



It may also be proved that if O be a 

 ucid point, and V, G, R, the foci of the 

 violet, green and red light from it, and 

 as before twice the distance L G be di- 

 vided into 55 equal parts, V R will have 

 the same proportion to one of those 

 parts as O G has to O L. 



It will be observed that the violet rays 

 diverging from V meet the red rays con- 

 verging towards R at a certain point be- 

 tween V and R, and that at this distance 

 all the rays which are refracted by the 

 lens are collected into the smallest pos- 

 sible circle. The diameter of this circle 

 being computed when the incident rays 

 are parallel, was found to be about the 

 55th part of the diameter of the lens. 



(36.) To verify these inferences, Newton 

 repeated again the experiment described 

 in (19), but adopted the method men- 

 tioned in p. 24, of rendering the pris- 

 matic light homogeneous. In the course 

 of these experiments he encountered 

 many practical difficullies arising from 

 imperfections, such as veins, air bubbles, 

 &c. in the glass of which his prisms 



were formed, of which, as well as of his 

 efforts to avoid or remove them, he gives 

 a very detailed and interesting account. 

 He also found considerable difficulty in 

 determining the exact foci of the lights 

 of blueish character at the upper end of 

 the spectrum, owing to their extreme 

 faintness. On the whole, however, he 

 succeeded in satisfying himself that the 

 foci of the rays of different colours were 

 at those points to which the computation 

 made on their supposed unequal re- 

 frangibility assigned them. Thus it ap- 

 peared that the object glass of a refract- 

 ing telescope formed as many distinct 

 images of an object placed before it, as 

 there are lights of different degrees of 

 refrangibility : that these images dif- 

 fered in colour, the blueish ones being 

 nearest to the object glass, and the red- 

 dish most remote from it, and that be- 

 tween these were included images of a 

 greenish and yellowish hue ; that these 

 images extended over a space along the 

 axis of the telescope, equal to about 

 2-55ths of the focal length of that glass ; 

 and that the smallest space into which 

 the innumerable images of the same 

 point in the object can be collected on a 

 plane at right angles to the axis of the 

 telescope, is a circle, whose diameter 

 amounts to about a 55th part of the 

 diameter of the object glass. " So that 

 it is a wonder," says Newton, " that 

 lelescopes represent objects so distinct 

 as they do. But were all the rays of 

 light equally refrangible, the error arising 

 only from the sphericalness of the figures 

 of glasses would be many hundred times 

 less." 

 The effect called spherical aberration, 



