1 8 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



tion of R and Y would only be half as great as that effected by the 

 prism in the figure. 



Then if another prism were made of the same material as that 

 assumed in fig. 5, but with only half the refracting angle, viz. 25, 

 the dispersion between R and Y would also be but half that repre- 

 sented. Also a prism having 50 of refracting angle gives the same 

 amount of dispersion as that from a prism of 25 of refracting angle, 

 but of twice its dispersive power. 



Under these conditions, when one prism, exactly like another in 

 angle and dispersive power, is placed close to it in an inverted 

 position, the dispersion of the first prism is entirely neutralised by 

 that of the second because it is precisely equal in amount :md 



opposite in power. 

 This will be under- 

 stood by a glance at 

 fig. 20. But it will 

 be seen that not only 

 is dispersion reversed, 

 but refraction also 

 is neutralised, the 

 emergent ray being 

 parallel to the in- 

 cident ray. Therefore 

 the equal and inverted 

 system of prisms can 

 be of no possible use 

 to the practical opti- 

 cian in the correc- 

 tion of lenses because 

 the convergence and divergence of rays are both essential to the 

 construction of optical instruments. The dispersion, in fact, must 

 be destroyed without neutralising all the refraction. 



Suppose we take a prism with an angle of 50, composed of glass 

 having a certain dispersive power, and invert next it a prism of 25 

 angle, composed of glass having twice the dispersive power of the 

 former. Dispersion will be manifestly destroyed, because it is equal 

 in amount and opposite in nature to that possessed by the prism of 

 50 ; but the prism with an angle of 25 will not neutralise all the 

 refraction effected by the prism of 50. 



These conditions plainly suggest the solution of the problem, for 

 part of the convergence is maintained while the whole of the 

 dispersion is destroyed. 



The spherical lenses which answer to these prisms are a crown 

 biconvex, fitting into a flint plano-concave of double the dispersive 

 power 



It has been pointed out above that all the other colours lie in 

 their proper order between the rays R and Y (fig. 5). Let us select 

 one, green, and represent it by G. Now if G lies midway between 

 R and Y in the prism of 50 of angle, and also between R and Y in 

 the prism of 25 of angle, its dispersion will also be neutralised. 

 This means that when the dispersion between the three colours in 



FIG. 20. Recomposition of light by prisms. (From 

 tlie 'Forces of Nature.') 



