Concave Surfaces. [Book III, 



of the convex furface be made to proceed in a direc- 

 tion parallel to C P, therefore q I will be parallel to 

 CP. Again, a ray incident on a concave furface con- 

 verging to q t may be confide, red as converging to p t 

 the focus of parallel rays on the convex furface, and 

 therefore by refraction of the concave furface, it will 

 be made to proceed in a direction parallel to C/>. 

 Hence as before the triangles QJ?C, qpC are fimi- 

 lar, and the fame proportion is deduced QJT : T C : : 

 /C : tq. 



Rays diverging from any point, and intercepted by 

 the convex furface of a rarer or concave furface of a 

 de nfer medium will by refraction, we have before feen, 

 be made always to diverge more. Upon the fame prin- 

 ciples, and in the fame manner, the effects of fpherical 

 furfaces on converging rays is fhewn, which are ex- 

 actly oppofite to thofe of diverging rays, and a learner 

 may profitably exercife himfelf by trying the effect on 

 paper on rays converging or diverging, refracted by 

 the convex or concave furface of different mediums. 



Having thus difcovered the progrefs of rays of light 

 diverging from any point, and intercepted by a refract- 

 ing fpherical furface, we (hall find no difficulty in ac- 

 counting for the apparent places of objects feen in dif- 

 ferent mediums bounded by fpherical liirfaces. 



Let QM (Plate XVII. Fig. 22.) be an object in a 

 glafs medium, and q the focus of refracted rays diverg- 

 ing from Q. > m the focus of refracted rays diverging 

 from M. Then q m will be the image of QM. Lee 

 O be the place of the fpectator, and join O q, O m, 

 then r s is the part of the glafs through which he fees 

 the object, and Qr O, M s O are the extreme rays by 

 which it is feen. Let a denfe medium be now bound- 

 ed by a convex furface, Fig. 23. and an object QJM 

 be at fuch a diftancc from it, that its image fhaU be 



