22 OPTICS. 



Fig. 27. 



Focal length of t he convex lens + 1 .000 . 



Radius of its first surface + 5.833. 



Radius of its second surface 35.000. 



Focal length of the Meniscus -fl 7.829 . 



Radius of its first surface + 3.688. 



Radius of its second surface + 6.291 . 



Fig. 28. 

 + ] 0.000 



Focal length of the compound lens 

 A single lens may be made free from 

 aberration for parallel rays, provided the 

 surface which receives the parallel rays 

 is part of an ellipsoid, (or prolate sphe- 

 roid, formed by the revolution of an 

 ellipse round its greater axis,) whose 

 greater axis is the index of refraction of 

 the substance, the distance between its 

 foci being 1 ; and provided that the 

 second surface is concave, and whose 

 centre is the farther focus of the spheroid. 

 A single lens may also be made free of 

 aberration for parallel rays, provided the 

 surface which receives parallel rays is' 

 plane, and the other surface part of a 

 hyperboloid, formed by the revolution of 

 a hyperbola, whose greater axis is the 

 index of refraction of the substance, the 

 distance between the foci being 1. 



Spherical Aberration of Mirrors. 

 In determining the focus of paraDel 

 rays reflected by a concave spherical 

 mirror, M N (Jig. 20.) it has been proved 

 that the focus /is always so situated in 

 the line C E, that for any ray R A, C/ 

 is equal to/ A : but if/' is the focus of 

 rays very near RE, so that C/' is equal 

 to /' E, then, as /'A is greater than 

 /' E, /' cannot be the focus of the 

 ray R A ; and, consequently, its focus 

 must be nearer E, or at/ in order that 

 C/ may be equal to /A. As the ray 

 R A recedes from the axis R E, / A 

 will become greater and greater in pro- 

 portion to/' E ; and, therefore, the focus 

 /must come nearer and nearer to E, in 

 proportion as the ray R A recedes from 

 R E. The distance//' for any ray R A 

 or R B, or for a spherical mirror, whose 

 diameter is A B, is called its spherical 

 aberration. This aberration obviously 

 increases in the same mirror with the 

 diameter A B of its aperture ; and, in mir- 

 rors of different curvature, it increases 

 with the curvature, for it is clear that if 

 the surface A E B is more concave,/ A 

 will increase faster in proportion to/E. 

 Hence, it is plain, that ii we had a curve 

 of such a nature that a line R A parallel 

 to its axi& C E, and another line A/ 

 drawn from A to a fixed point/, should 

 always form an equal angle with C A, a 

 line perpendicular to the curve at A, we 

 should then have a surface which would 

 reflect parallel rays to a focus or ma~ 



-r- 6.407 

 thematical point /. 



35.000 

 + 5.497 

 + 2.051 

 + 8.128 

 + 3.474 



Now this curve is 



actually a parabola, and hence the spe- 

 cula, or mirrors, of all reflecting tele- 

 scopes are ground into the shape of a 

 paraboloid, or a surface formed by the 

 revolution of a parabola round its axis. 

 By the same reasoning it may be 

 shewn that when rays fall diverging 

 from any point R (fig. 21.) on a concave 

 spherical mirror A B, they will not be 

 refracted to the same focus, as the rays 

 near the axis, such as RE, and that 

 such rays can only be reflected to the 

 same focus with those near the axis, 

 when the surface A E B is such that 

 lines drawn from two points R, / form 

 equal angles with a line C A, perpen- 

 dicular to the surface at the point where 

 the ray falls. Such a surface is that of 

 an ellipsoid, whose foci are R and/; so 

 that when rays diverge from one focus 

 of an ellipsoid, they are accurately re- 

 flected to the other focus. Hence, in 

 reflecting microscopes, the mirror should 

 be always a portion of an ellipsoid, in 

 one focus of which is the object, and in 

 the other the image. 



CHAPTER VIII. CHROMATICS. 



Decomposition of White Light into 

 Colours Different refrangibility of 

 differently coloured Rays decompo- 

 sition of white light. 



HITHERTO we have considered light as 

 a simple substance, and all its parts or 

 rays as refracted in the very same manner, 

 by the lenses upon which they fall. This, 

 however, is not the case. The white 

 light, which comes irora the sun, or 

 from any other luminous body, is actu- 

 ally composed or made up ot seven dif- 

 ferent kinds of light of different colours, 

 viz., red, orange, yellow, green, blue, in- 

 digo, and violet. These colours often ap- 

 pear by themselves, and the white light 

 from which they are produced is decom- 

 posed, or separated into its elements, 

 by different processes, which we shall 

 presently explain. 



That branch of optics, which treats 

 of the colours of light, of their physical 

 properties, and of the laws according to 

 which white light is decomposed, and. 



