16 



OPTICS. 



CHAPTER V. CATOPTRICS. 



Reflexion of Light Law of Reflexion 

 'Reflexion from Plane, Concave, and 

 Convex Mirrors. 



HITHERTO we have considered only the 

 light which is transmitted through 

 transparent bodies; but in every case 

 where light falls upon a body, a portion 

 of it is thrown back or reflected from its 

 surface, according to a regular law. 

 The branch of optics which treats of the 

 reflexion of light is called Catoptrics, 

 from two Greek words, one of which 

 signifies from or against, and the other 

 to see, because things are seen by light 

 reflected from bodies. 



When a ray of light, AC, (fig. 1 8) falls 

 upon a polished surface, either plane 

 like R C S, or curved like r C s, at the 

 point C, it will be reflected in such a 

 direction C B, that the angle AGP, 

 which the ray makes with C P, a line 

 perpendicular to the surface at C, is 

 equal to the angle B C P, which the 

 reflected ray makes with the same per- 

 pendicular. The angle A C P is called 

 the angle of incidence, and B C P the 

 angle of reflexion. When the ray falls 

 in the direction P C, it is reflected back 

 in the same line; and when the ray 

 falls in the direction R C, it is reflected 

 in the direction C S. 



These results maybe easily proved by 

 reflecting the light of the sun or a can- 

 dle from a piece of looking-glass ; and 

 hence we may consider it as a general 

 law, that the angle of reflexion is equal 

 to the angle of incidence. 



The bodies which are used to reflecl 

 light are called mirrors, or specula, and 

 are commonly pieces of metal or glass, 

 having their surface highly polished. 

 Those made of glass are generally quick- 

 silvered on one side, so as to reflect 

 more light ; but in the following obser- 

 vations it is supposed that the mirror is 

 made of metal. Mirrors are either 

 plane, concave, or convex, according as 

 they are bounded by plane or by sphe- 

 rical surfaces. 



Reflexion of rays from plane mirrors. 

 When parallel rays fall upon a plane 

 mirror they will be parallel after re- 

 flexion. If A C, A' C' ( fig. 1 8) are two 

 parallel rays falling upon the plane mir- 

 ror R S', they will be reflected into the 

 parallel directions C B, C'B': since 

 C P, C' P are both perpendicular to the 

 same plane, they are parallel ; and be- 

 cause A C is parallel to A C', and C P 

 to C' P', the angle A C P will be equal 



to A' C' P. Hence B C P is equal to 

 to B'C'P, and CB parallel to C'B'. 

 The same truth may be easily proved 

 experimentally. 



When diverging rays fall upon a 

 plane mirror, they will have the same 

 divergency after reflexion. Let the rays 

 AB, AD, AF, diverging from A (fig. 

 19.) fall upon the plane mirror RS; 



draw B C, D E, F G, so as to make the 

 angle C B P equal to A B P ; E D P' 

 equal to A DP, and GFP" equal to 

 A F P" ; then by continuing the lines 

 C B, E D, G F backwards, they will be 

 found to meet at A', so that A' B, A D, 

 and A' F are respectively equal to 

 AB, AD, and AF ; and B AF equal 

 to B A F. 



When converging rays fall upon a 

 plane mirror they will have the same 

 convergency after reflexion. This is 

 obvious, from fig. 1 9, where the rays 

 C B, E D, and C F fall upon the mirror 

 R S, and would have met in a point at 

 A', if the mirror had not intervened. 

 Since the lines FA, DA, BA form 

 equal angles with the perpendicular at 

 F, D, and B, they will be the reflected 

 rays which will meet at A, in the same 

 manner as they would have done at A', 

 had there been no mirror to reflect 

 them. 



Reflexion of parallel rays by con- 

 cave and convex mirrors. Let M N 



