OPTICS. 



between the said perpendicular DC, and 

 the reflected ray CM, viz. the angle DC.VI. 

 The angle of refraction, is that contained 

 between the retracted ray CS, and the per- 

 pendicular CN, viz. the angle FCK. The 

 angle of deviation, is that which is con- 

 tained between the line of direction of an 

 incident ray AL, and the direction of the 

 same ray CF, utter it is refracted; thus 

 the angle LCF is the angle of deviation. 



A lens, is glass ground into such a form 

 as to collect or disperse the rays of light 

 which pass through it. These are of dif- 

 ferent shapes, and from thence receive 

 different names. A plano-convex, has one 

 side flat, and the other convex, as A (fig. 

 3.) A plano-concave, is flat on one side, 

 and concave on the other, as B. A dou- 

 ble convex, is convex on both sides, as C. 

 A double concave, is concave on both 

 sides, as D. A meniscus, is convex on one 

 side, and concave on the other, as E. A 

 line passing through the centre of a lens, 

 as F G, is called its axis. 



Of Refraction. If the rays of light, after 

 passing through a medium, enter another 

 of a different density perpendicular to its 

 surface, they proceed through this medi- 

 um in the same direction as before. Thus 

 the ray OP (h'g. 2.) proceeds to K, in the 

 same direction. But if they enter ob- 

 liquely to the surface of a medium, either 

 denser or rarer than what they moved in 

 before, they are made to change their di- 

 rection in passing through that medium. 

 If the medium which they enter be denser, 

 they move through it in a direction near- 

 er to the perpendicular drawn to its sur- 

 face. Thus, AC, upon entering the den- 

 ser medium HGK, instead of proceeding 

 in the same direction AL, is bent into the 

 direction CF, which makes a less angle 

 with the perpendicular OP. On the con- 

 trary, when light passes out of a denser 

 into a rarer medium, it moves in a direc- 

 tion farther from the perpendicular. 

 Thus, if SC were a ray of light which 

 had passed through the dense medium 

 HGK, on arriving at the rarer medium 

 it would move in the direction CA, 

 which makes a greater angle with the 

 perpendicular. This refraction is great- 

 er or less, that is, the rays are more or 

 less bent or turned aside from their 

 course, as the second medium through 

 which they pass is more or less dense 

 than the first. Thus, for instance, light 

 is more refracted in passing from air into 

 glass, than from air into water ; glass be- 

 ing denser than water. And, in general, 

 in any two given media, the sine of any 

 one angle of incidence has the same ratio 



to the sine of the corresponding angle cf 

 refraction, as the sine of any other angle 

 of incidence has to the sine of its corres- 

 ponding angle of refraction. Hence, 

 when the angle of incidence is increased, 

 the corresponding angle of refraction is 

 also increased; because the ratio of their 

 sines cannot continue the same, unless 

 they be both increased ; and if two angles 

 of incidence be equal, the angles of refrac- 

 tion will be equal. The angle of deviation 

 must also vary with the angle of incidence. 

 If a ray of light, AC, (fig. 2) pass obliquely 

 out of air into glass, A D, the sine of the 

 angle of incidence A C D, is to N S, the 

 sine of the angle of refraction N C S, 

 nearly as 3 to 2 ; therefore, supposing the 

 sines proportional to the'angles, the sine 

 of F C L, the angle of deviation, is as the 

 difference between AD and N S, that 

 is as 3 2, or 1, whence the sine of inci- 

 dence is to the sine of the angle of devia- 

 tion as 3 to 1. In like manner it may be 

 shewn, that when the ray passes oblique- 

 ly out of glass into air, the sine of the an- 

 gle of incidence will be to that of devia- 

 tion, as N S to A D N S, that is, as 2 

 to 1. In passing out of air into water, 

 the sine of the angle of incidence is to 

 that of refraction, as 4 to 3, and to that of 

 deviation, as 4 to 4 3, or 1 ; and in pass- 

 ing out of water into air, the sine of the 

 angle of incidence is to that of refraction, 

 as 3 to 4, and to that of deviation, as 3 to 

 1. Hence a ray of light cannot pass out 

 of water into air at a greater angle of in- 

 cidence than 48 36', the sine of which is 

 to radius as 3 to 4. Out of glass into air 

 the angle must not exceed 40 11', be- 

 cause the sine of 40 11' is to radius as 2 

 to 3 nearly ; consequently, when the sine 

 has a greater proportion to the radius 

 than that mentioned, the ray will not be 

 refracted. It must be observed, that when 

 the angle is within the limit for light to 

 be refracted, some of the rays will be re- 

 flected. For the surfaces of all bodies 

 are for the most part uneven, which oc- 

 casions the dissipation of much light by 

 the most transparent bodies; some be- 

 ing reflected, and some refracted, by the 

 inequalities on the surfaces. Hence a per- 

 son can see through water, and his image 

 reflected by it at the same time. Hence 

 also, in the dusk, the furniture in a room 

 may be seen by the reflection of a win- 

 dow, while objects that are without are 

 seen through it. 



Upon a smooth board, about the cen- 

 tre C, describe a circle H O K P ; draw 

 t\vo diameters of the circle, OP, H K, 

 perpendicular to each other ; draw ADM 



