Chap. 5-] Rules for finding the Focus of fefleaed Rays. 223 



diftance from the center of the furface will be a mean 

 proportional between its diftances from the foci of di- 

 Yerging and reflected rays. 



In Plate XIII. fig. 7. the proportion is in the fame 

 manner demonftrated, by faying, that rays appearing 

 to diverge from w, were reflected by the furface in- 

 tercepting rays converging to ;/, and vice ver.fa. 



The foci of diverging and reflected rays are always 

 on the fame fide as the principal focus. The greater 

 the diftance of Q_ from T, the lefs is the diftance 

 of q from T ; as, Q, approaches to T,-y recedes from 

 it j they medt together when rays are reflected by a 

 concave furface in the center. When the focus of 

 diverging rays is between the center and the princi- 

 pal focus, the focus of reflected rays is on the other 

 fide of the center. When Q^is ki T, the reflected 

 rays are parallel ; when QJs between T and the fur- 

 face, the rays appear to diverge from a point on the 

 other fide of the furface. When rays are reflected by 

 the convex furface, the focus of the reflected rays is 

 always between the principal focus and the furface. 



Having found the focus of reflected rays for a fingle 

 point, we can, as before, find the fituation of the image 

 of any object, by confidering the object as made up 

 of innumerable foci of diverging rays. Let QJR. 

 (fig. 8.) reprefent an object before a fpherical reflector, 

 then join QJ3 D, and in the line QJ3 find the point 

 q, the focus of rays after reflexion, by the proportion 

 laid down in the preceding inftance. In the fame 

 manner find the point r, and, if neceflary, find the 

 correfponding foci to other points in the object Q^R, 

 then q r is its image. This image will be either erect 

 or inverted, according to the nature of the reflector, 

 and the pofirion of the object. Firft, if the reflector 

 is a fpherical concave, as in fig. 8, and the diftance of 



the 



