Chap. 6.] Convergence of Rays explained. 233 



imift necerTarily be I Qj therefore I Q^is parallel to 

 Cp. We have hence two fimilar triangles QJ 3 C, 

 Cpq and QJP : PC :: Cp :pq. Now if I is very 

 near to E, Qj 3 , PC, Cp, pq will be very nearly equal 

 to QT, TC, C /, tq, and by making as QJT to TC, 

 fo C t to / q, we fhall find a point q near to which all 

 the rays diverging from Q^will by refraction be made 

 to converge. 



Hence QT varies inverfely as tq- t that is, the 

 greater the diftance of Q^from T, the lefs will be that 

 of q from /, for C T and C /, remain invariable in the 

 proportion, however the pofition of Q^may be va- 

 ried. 



The points Q^and q are always on oppofite fides of 

 T and /. 



If the point Q^was at fuch a diftance, that the rays 

 diverging from it might be confidered as parallel, q 

 and / would coincide. As Qjwas brought nearer to T, 

 q would recede from t ; when Qjmd T coincide, little 

 q will be ho longer in the line E q y but the refradled 

 rays will now be parallel. As Qjnoves from T to E, 

 q appears at a great diftance from E on the fame fide 

 of the furface with Q^and overtakes it at E. 



Diverging rays incident on the convex furface of a 

 clenfer medium, or the concave furface of a rarer me- 

 dium, are made to converge or diverge according to 

 the fituaticn of their foci with rcfpecl to the principal 

 focus. When they are incident en the convex fur- 

 face of a rarer medium, or the concave furface of a 

 denfer medjum, their progrels may be feen in Figures 

 20, 21. 



The ray QJ diverging from Q^will be affected in 



the fame manner as if it was fuppofed to converge to 



P the principal focus of rays incident on the concave 



furface , but a ray converging to P, will by refra&ion 



9 of 



