OPTICAL INSTRUMENTS. 



rian Tzetzes : " When the fleet of Mar- 

 cellus was within bowshot, the old man 

 Archimedes brought an hexagonal mir- 

 ror, which he had previously prepared, 

 at a proper distance from which he also 

 placed other smaller mirrors of the same 

 kind that moved in all directions on 

 hinges, which when placed in the sun's 

 rays directed them upon the Roman 

 fleet, whereby it was reduced to ashes." 

 We are also informed that Proclus in 

 the same way destroyed the fleet of 

 Vitellius at the siege of Byzantium. 



CHAPTER I. Mirrors Plane Looking- 

 Glasses Concave Mirrors Burning 

 Mirrors Convex Mirrors. 



(1 .) Mirrors are surfaces of polished me- 

 tal, or glass silvered on its posterior side, 

 capable of reflecting the rays of light 

 from objects placed before them, and 

 exhibiting to us their image. There are 

 three classes of mirrors, distinguishable 

 by the figure of their reflecting surface. 

 These are plane, concave, and convex. 

 The reflection of light by either of these 

 mirrors observes this constant law, that 

 the angle which the incident ray makes 

 with the reflecting surface, is equal to 

 the angle of reflection. We may explain 

 this law by a figure. Let c d, (fig* 1 .) 

 be a section of the reflecting surface : 



Fig. \. 



c7 



an object before the mirror ; and a 

 rays proceeding to the surface in the 

 point a. The angle O ac which the rays 

 make with the surface of the mirror is 

 called the angle of incidence ; and the 

 direction in which an observer will see 

 the object O in the mirror at a, must be 



1 a, the angle of reflection I a d being 

 equal to the angle of incidence O a c. 

 If we suppose O I to be two persons 

 viewing each other in a plane mirror or 

 looking-glass c d, the direction in which 

 each observeth the other at the point a is 

 a o or a i, but the apparent place of their 

 images will be behind the glass at the 

 point i or o, the distance behind corres- 

 ponding with that of their situation before 

 the mirror. This deception proceeds from 



our common experience, which leads us 

 to expect the object to be in the direction 

 in which the rays come to our eyes, in- 

 stead of in the real place of the object. 

 The illusion is so complete, that domes- 

 tic animals, when viewing themselves in 

 a looking-glass for the first time, often 

 have their passions strongly excited. 

 When a person is viewing himself in 

 a Booking- glass, if he measure the size 

 which he appears on the glass, the 

 image will be one half his real magni- 

 tude, let his distance from the glass be 

 in any manner varied. For, as it was 

 stated above that the image appears 

 behind the glass exactly at the same dis- 

 tance as the object is before it, it must 

 be evident that as the mirror is half way 

 between him and his apparent image, it 

 will cut in half the cone of rays which 

 proceed from his image to his eye. This 

 is shown mfig. 2, where c c? is a section 



Fig. 2. 



of a plane mirror or looking-glass, and 

 a b the face of a person viewing himself 

 in it ; now rays from every part of his 

 face fall upon the reflector, from which 

 they are sent to the eye, forming a cone 

 of rays whose apex enters the pupil ; 

 consequently, as this cone is cut by the 

 glass halfway between the apex and its 

 base, which base is himself, the mea- 

 sure of the line ef will be half of a b. 



(2.) Concave Mirrors are those whose 

 polished surfaces are spherically hollow. 

 The properties of these mirrors may be 

 easily understood, when we consider 



Fig. 3. 



