178 OPTICAL PRINCIPLES. 



coloured rays will become parallel and meet at a 

 single focus. 



This may be elucidated by considering the lenses 

 as composed of prisms. Thus, let fig. 28 represent 

 the compound lens, the two halves of the doubly 

 convex lens acting as two triangular prisms (fig. 19) 

 with their bases opposed, converging the compound 

 white rays w w, and dispersing the coloured elemen- 

 tary rays, which would form spectra at ss. In the 

 plano-concave lens the triangular prisms may be 

 considered as placed with their apices towards each 

 other, and so would tend to disperse the coloured 

 rays in the opposite direction, to form spectra at 1 1. 

 Then, supposing the dispersions to be equal and in 

 opposite directions, the coloured rays would become 

 parallel and meet at a definite focus, the colour being 

 destroyed. At the same time, the spherical action 

 of the concave lens being opposite to that of the 

 convex, the converging action of the latter will be 

 diminished, so that the focus of the compound lens 

 will be longer than that of the convex alone ; but as 

 the dispersive power of the concave is greater rela- 

 tively than that of the convex, the mean refraction is 

 less altered than the refraction or dispersion of the 

 separate coloured rays ; so that the concave wholly 

 opposes or corrects the dispersion produced by the 

 convex, while it only partially corrects its mean 

 refraction. 



A lens in which the chromatic and spherical aber- 

 rations are corrected or destroyed is commonly called 

 achromatic; although the term properly applies to 

 the correction of the colour only. 



If in a compound lens the chromatic aberration is 

 only partially corrected, so that the red rays still 

 meet at a focus beyond the violet, as in a simple 

 uncorrected lens (fig. 20), the lens is said to be under- 

 corrected, or the aberration to be positive ; while if 

 the correcting action of the plano-concave lens be too 



