252 FERGUSON'S LECTURES. 



LECT. be reflected back from that mirror, and meet in a point 

 m. at half the distance of the surface of the mirror from 



^^^V^^^ 



C, the center of its concavity : for they will be reflected 

 at as great an angle from the perpendicular to the sur- 

 face of the mirror,, as they fell upon it, with regard to 

 that perpendicular ; but on the other side thereof. Thus, 

 Jet C be the center of concavity of the mirror A b B, and 

 let the parallel rays d fa, Cm b, and el c, fall upon it at 

 the points a, b, and c. Draw the lines Cia, Cmb, 

 and C h c, from the center C to these points ; and all 

 these lines will be perpendicular to the surface of the 

 mirror, because they proceed thereto like so many radii 

 or spokes from its center. Make the angle Cah equal 

 to the angle da C, and draw the line amh, which will 

 be the direction of the ray dfa, after it is reflected from 

 the point a of the mirror : so that the angle of incidence 

 d a C, is equal to the angle of reflection Cah; the rays 

 making equal angles with the perpendicular Cia on its 

 opposite sides. 



Draw also the perpendicular C h c to the point c, 

 where the ray e Ic touches the mirror ; and, having made 

 the angle Cci equal to the angle Cce, draw the line 

 cm i, which will be the course of the ray elc, after it is 

 reflected from the mirror. 



The ray Cmb passes through the center of concavity 

 of the mirror, and falls upon it at b, the perpendicular 

 to it ; and is therefore reflected back from it in the 

 same line bmC. 



All these reflected rays meet in the point m ; and in 

 that point the image of the body which emits the pa- 

 rallel rays da, Cb, and ec, will be formed : which point 

 is distant from the mirror equal to half the radius b M C 

 of its concavity. 



The rays which proceed from any celestial object 

 may be esteemed parallel at the earth ; and therefore, 

 the images of that object will be formed at m, when the 

 reflecting surface of the concave mirror is turned <li- 



