OPTICAL INSTRUMENTS. 



their surface as composed of an indefinite 

 number of small planes all of which make 

 a determinate angle with each other, so 

 as to throw all the rays to a point. (See 

 fig. 3.) Let a b c be a concave mirror, 

 and let d be the centre of curvature, 

 and ooo rays of light from a distant 

 object (the cross in the wood-cut must 

 be supposed at a considerable distance) 

 falling on the mirror at a b c, making 

 different angles with its surface ; these 

 rays when reflected at equal angles to 

 their incidence, as may be seen by the 

 dotted lines which are perpendicular, 

 will meet in a point /, called the focus 

 of the mirror, where* an image of the 

 object will be formed in an inverted po- 

 sition. The distance of this focal point 

 from the surface of the mirror, when the 

 curvature is moderate, will be equal to 

 half its radius d b. The importance of 

 concave mirrors in the construction of 

 reflecting telescopes, in which construc- 

 tion they are commonly called specula, 

 will be shown hereafter under that head. 

 The employment of concave mirrors 

 in collecting the heat of the sun's rays 

 from the whole of its' surface to a single 

 point, thus accumulating a very great 

 degree of heat, for the combustion and 

 fusion of various natural substances 

 that are infusible in the greatest heat 

 capable of being produced from ordi- 

 nary fire, may be exemplified, amongst 

 those of modern date, by the burning 

 mirror of M.deVillette. The diameter 

 of this metal speculum was 3 feet 1 1 

 inches, and its focal distance or pointy 

 from the surface was 3 feet 2 inches. The 

 composition of this metal was of tin 

 and copper, which reflects the light very 

 powerfully, and is capable of a high de- 

 gree of polish. When exposed to the 

 rays of the sun, by Drs. Hams and De- 

 saguliers, a silver sixpence was melted 

 in 7| seconds when placed in its focus ; 

 a copper halfpenny melted in 16 seconds 

 and liquefied in 34 seconds ; tin was 

 melted in 3 seconds ; and a diamond, 

 weighing 4 grains, lost iths of its weight*. 

 The intensity of heat, obtained by burn- 

 ing mirrors or lenses, will always be as 

 the area of the reflecting surface ex- 

 posed to the sun is to the area of the 

 small circle of light collected in its 

 focus ; thus, the diameter of the spot 



* The burning mirror constructed by Count Buffon, 

 was a polyhedron, 6 feet broad and as many high, con- 

 sisting of 168 small mirrors, or flat pieces of looking- 

 glass, each 6 inches square. By means of this instru- 

 ment, with the faint rays of the sun in the month of 

 March, he set on fire boards of beech wood at 150 



at the focus of 

 was 0.358 of an inch, and the diameter 

 of the mirror 47 inches ; hence the area 

 of these circles was as 0.358 2 to 47 a , 

 that is, the intensity of the sun's rays 

 was increased 17257 times at the focal 

 point. The loss of light occasioned in 

 passing through the medium of which 

 the lens is composed, together with that 

 lost by reflection from the surface of 

 mirrors, must, however, be deducted 

 from this theoretical calculation. See 

 Photometers. 



Concave mirrors afford many curious 

 and pleasing illustrations of their pecu- 

 liar properties. For example : when a 

 person stands in front of a concave mir- 

 ror, a little further from its surface 

 than its focus (or half the radius of its 

 concavity), he will observe his own 

 image pendant in the air before him, 

 and in an inverted position : this 

 image will advance and recede with 

 him ; and, if he stretch out his hand, 

 the image will do the like. Exhibitions 

 have been brought before the public 

 in which a singular deception was ob- 

 tained by a large concave mirror. A 

 man being placed with his head down- 

 wards, in its focus an erect image of 

 him was exhibited, while his real per- 

 son was concealed, and the place of 

 the mirror darkened; the spectators 

 were then directed to take a plate of 

 fruit from his hand, which in an instant 

 was dexterously changed for a dagger, 

 or some other dangerous weapon. 



(3.) Convex mirrors are chiefly em- 

 ployed as ornaments in apartments. 

 The objects viewed in these are dimi- 

 nished, but seen in an erect position ; 

 the images appear to emanate from a 

 point behind the mirror; this point, 

 which is its focus, will be half the radius 

 of convexity behind their surface, and 

 is called the negative, or imaginary 

 focus, because the rays are not actually 

 collected as by a concave mirror, whose 

 focus is called virtual.* 



feet distance. This machine had the conrenience of 

 burning downwards, or horizontally at pleasure, each 

 speculum being moveable, so as, by the means of 

 three screws, to be set to a proper inclination lor 

 directing the rays towards any given point. It thns 

 turned either in its greater focus or in any nearer 

 interval, possessing this great superiority over com- 

 mon burning glasses whose foci are fixed and deter- 

 mined. Buifon at another time burnt wood at the 

 distance of more than 120 feet, and silver was fused 

 at 50 feet. See the article Burning Apparatus in 

 the Edinburgh Encyclopaedia. 



The reflecting surfaces of cylinders have been 

 occasionally used in optical amusements, for render- 

 ing anamorphoses (distorted or deformed pictures) of 

 their proper shape when reflected from its surface. 

 B2 



