10 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



The values of the same lines for the flint glass are as follows : 

 D, 1-7174=^; F, 1-73489= M '; 0, 1-71055=/*". 

 u'-ii" 1-73489-1-71055 -02434 



- 1 "1-7174 -1 



7174 



-==0339. 



So the dispersive power of the flint between the lines C and F is 

 slightly more than twice that of the crown for the same region of 

 the spectrum. In the above formula the expression /u' /*" is usually 



written b u ; in full it is therefore 



Having thus traced a ray 

 experimentally through a 

 prism, our next step is to show 

 that a convex lens is only a 

 curved form of two suck prisms 

 with their bases in contact, 

 as is shown in A, fig. 6, , 

 where the curved line shows 

 the lenticular character and 

 the shaded elements the two 

 prisms. A concave lens is in 

 effect two prisms reversed, 

 that is, with their apices in 

 contact, as in B, fig. 6, where, 

 again, the curved line shows 

 the form of the lens and the 





 /i- 1 



FIG. 6. Convex and concave 

 lenses are related to the 

 prism. 



FIG. 7. Proof that a lens may be considered 

 as an assemblage of prisms. (From the 

 ' Forces of Nature.') 



shaded parts its relation to a pair of prisms. The fact that a lens is, 

 in effect, as such, but an assemblage of superposed prisms is seen in 

 fig. 7, the refracting angle of the prism being more acute as the 

 principal axis is approached, and the deviation being greater as the 

 angle is more obtuse. 



In fig. 8 let P be the axis in each case ; then, from what we 

 have seen, it is manifest that rays parallel to the axis falling on the 

 prisms with their bases in contact and acting like a convex lens will 

 be refracted towards the axis O P. But in the other case, where 

 the prisms have their apices together, as in fig. 9, acting as a con- 

 cave lens, the light is refracted away from the axis O P. 



