Chap. 4.] Refrafiion by concave Surfaces. 209 



towards the perpendiculars /C and g C ; and are con- 

 fequently divergent. 



Converging rays falling on the fame concave furface 

 will be rendered lefs convergent, as in fig. 2. For 

 the rays ab, de (fig. 6.) which would have converged 

 at O, if their progrefs had not been intercepted, will 

 be refracted towards the perpendiculars /C and g C, 

 and will unite only at i. If the convergence was lefs, 

 they might by the refraction be rendered parallel or 

 even divergent. 



Diverging rays proceeding from the center of con-? 

 cavity will not fuffer any refraction, for the reafons al- 

 ready afligned. 



If, however, diverging rays proceed from any point 

 nearer the refracting furface than the center of concav- 

 ity, they will be rendered lefs divergent, as in fig. j. 

 For the two diverging rays kb and ke (fig. 7.) inftead 

 of proceeding to d and h, are refracted towards the per- 

 pendiculars/C and^C. 



If, on the contrary, which is the mod general cafe, 

 the diverging rays proceed from a point more diftant 

 from the furface than the center of concavity, their di- 

 vergence will be increafed as in fig. 4. For the di- 

 verging rays Ib and le (fig. 7.) which tend towards 

 m and n, are refracted towards the perpendiculars /C 

 and g C, and become more divergent than they would 

 otherwife have been. 



When rays pafs from a denfe into a rarer medium, 

 and the denfe medium is terminated by a concave fur- 

 face, then 



Parallel rays become divergent; for the parallel rays 

 de, gi (fig. 8.) when they reach the concave furface 

 e D /, inftead of continuing their courfe in the direct 

 lines towards /and b, proceed towards m and^>, being 



VOL. I. P refracted 



