Chap, 4.] Catoptrics. 217 



upon a plain and fimple principle, which has been al- 

 ready explained, viz. that the angle of reflexion is al- 

 ways equal to the angle of incidence. Thus let Q^ a 

 Plate XL (fig. i,) be a point from which rays diverg- 

 ing fall on the reflecting furface A B, and let QJD, 

 QJi, be two incident rays. At D, E draw the per- 

 pendiculars D C, E F to A B, and make the angles 

 C D G, H E F equal to QJD C,. QjL R and the rays 

 QJD, QJ will be reflected by the furface in the di- 

 rections D G, E H. 



The point Q^, from which the rays diverge, is 

 called the focus of diverging rays j and as, after re- 

 flexion, the rays appear to have diverged from a point 

 behind the furface, that point is called the focus of re- 

 flected rays. To find this point, produce the lines 

 G D, H E till they meet the perpendicular drawn 

 from Q^on the reflecting furface produced, if necef- 

 fary. Let QJVE q be this perpendicular, which G D 

 meets in q j then, fince QJD C is equal to GDC, 

 QJD M is equal to G D B, but G D B is equal to 

 M D q ; in the two triangles QJD M, M D ^, there 

 are two angles in the one equal to two angles in the 

 other, and one fide M D common to both, therefore 

 Q^M is equal to M g. The fame may be proved 

 alfo of the interfection of the lines H E q and Q^M q. 

 Therefore the focus of rays reflected by a plane fur- 

 face is at the fame diftance behind the furface, as the 

 focus of diverging rays is before it. 



If, inftead of rays diverging from one point they 

 diverge from feveral, the correfponding foci will be 

 found in the fame manner. Let QJR. (fig. 2.) be a 

 furface, from every point of which draw perpendicu- 

 lars to the reflecting furface as before, and q r will be 

 the image of QJR, or all the rays diverging from 



