Chap. 6.] Focus cf diverging Rays. 439 



other, or in general it may be faid of all thefe lenfes, 

 that the parallel rays converge or diverge after refrac- 

 tion according as the middle of the glafs is thicker or 

 thinner than its extremities. 



Upon the fame principles alib may be found the 

 foci of lenfes, fuppofing them to be compofed of fub- 

 fiances rarer inftead of deafer than the furrounding 

 medium. 



Having found the principal focus of a lens, we fhall 

 with the fame eafe find the focus of rays diverging 

 from a point, and intercepted by a lens, as we did 

 when they were intercepted by a fingle furface. Let Q 

 (Plate XIX. Fig. 35.) be the focus of diverging rays 

 incident on the lens A B, and let F, /, be the principal 

 foci of rays incident on the furfaces B or A, in a con- 

 trary direction, and let Qj reprefent an incident ray, 

 With E as a center, and E F radius, defcribc the arc 

 F G interfering Qj in G, join EG, and draw Aq pa- 

 rallel to E G, then with E as a center, and E/ radius, 

 defcribe the arc fg interjecting iq in g, and join E. 

 The ray QJ will be affected in the fame manner, whe- 

 ther it is considered as diverging from Q^or G; but 

 *fmce rays parallel to E G, incident on the furface B, 

 are by the refraction of the lens made to converge to 

 G, a ray diverging from G will, after the refraction of 

 the lens, move parallel to E G ; therefore the ray QJ 

 ttill be made by the lens to move in the direction Aq. 

 Again, if the ray was turned back, it might be confi- 

 dered as diverging from g, and by the lens it would be 

 made to move in the direction /Q^, parallel to E<?. 

 Hence we have two triangles, QJ3 E, Egy, fimijar 

 to each other, and QG : GE :: Eg : gq- t that is, the 

 nearer * is to E, the nearer will this proportion be to 

 that of QJF : F E : : E/ : fq t a proportion fimilar i 

 that which we found before with fingle furfacejs. 



The, 



