10 



OPTICS. 



distance C/is called the focal distance 

 of the lens, and in a double and equally 

 convex lens of glass, whose index of re- 

 fraction is 1.500, it is equal to the radius 

 of the spherical surfaces of the lens. If 

 the lens is a piano convex lens, as E,y?g\ 

 3, it is equal to twice the radius of its 

 spherical surface. If the lens is un- 

 equally convex, its focal distance may 

 be found by the following rule : Mul- 

 tiply the two radii of its surfaces, and 

 divide twice that product by the sum of 

 the radii the quotient will be the focal 

 distance required. 



When converging rays or rays which 

 proceed to one point, such as R F, R F, 

 R F (fig. 8), are intercepted by or fall 

 upon a convex lens L L, whose princi- 

 pal focus is O, their convergency is 

 hastened, and they will be refracted to 

 a focus /nearer the lens. As the point 

 of convergence F recedes from the lens, 

 the point /also recedes from it towards 

 O, beyond which it never goes ; and as F 

 approaches the lens, /' also approaches 

 to it. The points F and/ are called con- 



Fig. 9. 



jugate foci, because the place of the one 

 varies with the place of the other, and 

 though every lens has only one princi- 

 pal focus, yet its conjugate foci are in- 

 numerable. The conjugate focal distance 

 C/ may be found by the following rule : 

 Multiply the principal focal distance, or 

 O C by F C, the distance of the point of 

 convergence, and divide that product by 

 the sum of the same numbers. The 

 quotient will be the distance C/. 



When diverging rays, or rays which 

 proceed from one point F, such as R L, 

 R C, R L (fig. 9), fall upon a convex 



lens L L, whose principal focus is O, 

 the refraction of the lens will make them 

 converge to a focus/ beyond O. As the 



Eoint of divergence F recedes from the 

 ;ns, the focus /will approach to it, and 

 when F is infinitely distant, /will coin- 

 cide with O, for the rays diverging from 

 F have now become parallel rays. If F 

 approaches to O, the focus /will recede 

 from O, and when F coincides with O, 

 /will be infinitely distant, or the re- 

 fracted rays will be parallel. When F 

 is between O and C, as at F', the re- 

 fracted rays will diverge like L r, L r, as 

 if they came from a focus/' beyond O, 

 and in front of the lens. The points F 

 and/ are called conjugate foci as before, 

 and the conjugate focal distance may be 

 thus found : ' Multiply the principal 

 focal distance by F C, the distance of the 

 point of divergence, and divide that pro- 

 duct by the difference of the same num- 

 bers. The quotient will be the distance 



e/ 



Refraction through concave lenses. 



Light is refractei through concave 

 lenses in the same manner as through 

 prisms, and the direction of the refracted 

 rays may in every case be found by the 

 method already described for a prism. 

 Let LL (fig. 10.) be a double concave 



lens, whose axis is R/C, and C its 

 middle point : then it will be found that 

 parallel rays R L, R L will be refracted 

 into the directions L r, L r, so as to di- 

 verge as if they proceeded from /, a 

 point before the lens which is the prin- 

 cipal focus of the lens. The principal 



