A 



L 



1. A prism, shown at A, is a solid, 

 having two plane surfaces, A R, A S, 

 inclined to one another. 



2. A plane glass, shown at B, has two 

 plane surfaces parallel to one another. 



3. A sphere or spherical lens* , shown 

 at C, has every point in its surface 

 equally distant from a common cen- 

 tre. 



4. ^double convex lens, shown at D, 

 is bounded by two convex spherical 

 surfaces, whose centres are on oppo- 

 site sides of the lens. It is equally con- 

 vex when the radii of both surfaces 

 (that is, the distances from the centres 

 to the circumferences of the circle they 

 belong to) are equal, and unequally 

 convex, when their radii or distances 

 are unequal. 



5. Kplano-convex lens, shown at E, is 

 bounded by a plane surface on one side, 

 and by a convex one on the other. 



6. A double concave lens, shown at 

 F, is bounded by two concave spherical 

 surfaces, whose centres are on opposite 

 sides of the lens. 



7. A plano-concave lens, shown at G, 

 is bounded by a plane surface on one 

 side, and a concave one on the other. 



8. A meniscus, shown at H, is 

 bounded by a concave and a convex 

 spherical surface ; and these two sur- 

 faces meet, if continued. 



9. A concavo-convex lens, shown at I, 

 is bounded by a concave and a convex 

 surface ; but these two surfaces do not 

 meet though continued. 



The axis of these lenses is a straight 

 line M N, in which are situated the cen- 

 tres of their spherical surfaces, and to 

 which their plane surfaces are perpen- 

 dicular. If we suppose the sections from 

 B to I to revolve round the line INI N, 

 they will generate the different solids 

 which they are intended to represent ; 

 but in treating of the refraction of the 

 lenses we shall still use these sections, 

 because, since every section of the same 

 lens passing through the axis M N, has 



* /,cr?, a Latin word signifying a lentile, a small 

 flat kind of bean. 



the very same form, what is true of 

 one section must be true of the whole 

 lens. 



Refraction through prisms. Let R S, 

 R' S' (fig. 4,) be the faces of a prism of 



Fig. 4. 



glass having its refractive power 1.525, 

 and A C a ray of light falling upon the 

 face R S at C. Through C draw P Q 

 perpendicular to R S, and from any 

 scale of equal parts take in the com- 

 passes 1.525, or 15.25, or 152.5, or 1525 

 parts, and setting one foot of the com- 

 passes on C A, move it along to some 

 point A till the other foot falls only on 

 one point of C P as at D ; then upon C , as 

 a centre, describe a circle A P Q passing 

 through A. From the same scale take 

 in the compasses 1.000 or 10.00 or 

 100.00 or 1000, and setting one foot on 

 the line C Q, move it along till the other 

 falls upon E in the circle A P Q, taking 

 care that the point F is such that, when 

 one foot is placed at E, the other foot 

 can touch C Q in no other point but F. 

 But A D is the sine of the angle of inci- 

 dence, and E F the sine of the angle of 

 refraction, hence the line G E C' drawn 

 through E will be the refracted ray. 



Again, as the ray C C' meets the 

 second refracting surface at C', through 

 C' draw P' Q' perpendicular to R' S , 

 and from any scale of equal parts take 

 in the compasses 1.000 or 10.000, Sec. 

 and setting one foot in the line G A', 

 move it along to some point A' till the 

 other foot falls only on one point of 

 C' P', as at D'. In like manner, take from 

 the same scale 1.525, or 15.25, &c. and 

 setting one foot of the compasses in 

 C'Q', move it towards some point F'- 



