OPTICS. 



21 



nearest the axis, the difference//' be- 

 tween the foci of these rays is called the 

 spherical aberration, or the aberration 

 or straying of the rays from the focus, 

 caused by the spherical figure of the lens. 

 That this aberration arises from the cur- 

 vature of the glass being equal or sphe- 

 rical at C and at H is evident, for if the 

 glass was rounder or more convex at H 

 than it is, it would have a focus nearer 

 the sphere, and the ray which it now re- 

 fracts only to/' would" be refracted to/; 

 or if when H remains the same, the glass 

 were made flatter at C than it is, it 

 would refract the rays to a more distant 

 point than at /. Hence, in order to re- 

 fract rays at different distances from the 

 axis to the same point, the glass must 

 have different degrees of curvature at 

 different distances from the axis. 



By actually projecting the refracted 

 rays' for spheres and lenses of different 

 kinds, which we strongly recommend to 

 the student, he will obtain the follow- 

 ing results : 



1. In a plano-convex lens with its 

 plane side turned towards parallel rays, 

 that is, turned outwards, if it is to form 

 an image behind it, as in the object glass 

 of a telescope ; or inwards, if it is to be 

 used as a single microscope, the aberra- 

 tion is 4^ times its thickness*. 



2. In SL plano-convex lens with its con- 

 vex side towards parallel rays, the aber- 

 ration is 1 T y^dths of its thickness. Hence 

 in using a plano-convex lens, the paral- 

 lel rays should always be incident on its 

 convex surface, or emerge from it. 



3. In a double convex lens with equal 

 convexities, the aberration is l T Vodths 

 of its thickness. 



4. In a double convex lens whose radii 

 are as 2 to 5, the aberration is the same 

 as in the piano convex lens ($1,) if the 

 side with the radius 5 is turned towards 

 parallel rays ; and the same as the 

 plano-convex lens ($ 2,) if the side with 

 the radius 2 is turned towards parallel 

 rays. 



5. The lens with least spherical aber- 

 ration is a double convex one, whose 

 radii are as 1 to 6, the side whose radius 

 is 1 being turned towards parallel rays. 

 The aberration is thenl T <>dths of its 

 thickness. When the side with the 

 radius 6 is turned to parallel rays, its 

 aberration is 3 T Vodths of its thickness. 



If we call the aberration of the pre- 

 ceding lens 1, Mr. Herschel has shewn 



, L. 



that the following are the aberrations of 

 other lenses. 



Best form as in 5 - 1.00 



Double convex or concave 1 .567 



Plano-convex or concave, curved 



surface towards parallel rays 1.081 

 Plano-convex or concave, plane 

 surface towards parallel rays 4.2 

 As it is desirable to reduce the aberra- 

 tion below once the thickness of the lens, 

 and as this cannot be done by a single 

 one, we must have recourse to two lenses 

 put together. Mr. Herschel has shewn 

 that if two plano-convex lenses are put 

 together as in/?g-. 26, the aberration will 

 Fig. 26. 



be only 0.2481, or one-fourth of that of 

 a single lens in its best form. The focal 

 length of the first of these lenses must 

 be to that of the second, as 1 to 2 . 3. If 

 their focal lengths are equal, the aberra- 

 tion will be . 603, or nearly one half. 



The spherical aberration, however, 

 may be entirely destroyed by combining 

 a meniscus and double convex lens, as 

 shewn in fig. 27 and 28, the convex sides 



Fig. 27. 



being turned to the eye when they are 



used as lenses, and to parallel rays when 



they are used as burning glasses. Mr. 



Fig. 28. 



Herschel has computed the following 

 curvatures for these lenses : 



