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 befbre. Thus the ray OP (fig. 2.) proceeds to K, in the same direction. But if they enter ob. liquefy 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 of 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 1), 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 A D and N 5, 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 0 K P; draw two diameters of the circle, 0 P, H K, perpendicular to each other ; draw A DM perpendicular to 0 P; cut off D T and C I equal to three-fourths D A; through T I, draw T I S, cutting the circumference in S ; N S drawn from S, perpendicularly upon 0 1', w ill be equal to D T, or three fourths of D A. Then if pins be stuck perpendicularly at A, C, and S, and the board be dipped in the water as far as the line H K, the pin at S will appear in the same line with the pins at A and C. This shews, that the ray which comes from the pin S is so refracted at C, as to come to the eye along the line C A; whence the sine of incidence A D is to the sitie of re fraction N S, as 4 to 3. If other pins were fixed along C S, they would all ap pear in A C produced ; which shews that the ray is bent at the surface only. The Same may be shewn, at different inclina tions of the incident ray, by means of a moveable rod turning upon the centre C, tvhich always keep the ratio of the sines A D, N S, as 4 to 3. Also the sun's sha dow, coinciding with A C, may be shewn to be refracted in the same manner. The image L, of a small object S, plac ed under water, is one-fourth nearer the surface than the object. And hence the bottom of a pond, river, &c. is one third deeper than it appears to a specta tor.