OPTICS. 237 



to twice the radius of the sphere, of which the 

 lens is a portion. 



When parallel rays, as A B (Fig. 6.) fall upon a 

 double convex lens, they will be refracted, so as to 

 meet in a focus, whose distance is equal to the 

 radius, or semi-diameter of the sphere of the lens. 



But if a lens be more convex on one side than 

 on the other, the rule for rinding the focal distance 

 is this : as the sum of the semi-diameters of both 

 convexities is to the semi-diameter of either, so is 

 double the semi-diameter of the other to the dis- 

 tance of the focus; or, divide the double product 

 of the radii by their sums, and the quotient will be 

 the distance sought. 



If another glass, F G, of the same convexity as 

 D E, be placed in the rays at the same distance 

 from the focus, it will refract them so as that, 

 after going out of it, they will be all parallel, as 

 b c; % and go on in the same manner as they came 

 to the first glass D E, but on the contrary sides of 

 the middle ray. 



The rays diverge from any radiant point, as 

 from a principal focus; therefore, if a candle be 

 placed aty, in the focus of the convex-glass F G, 

 the diverging rays in the space F/G, will be so 

 refracted by the glass, that, after going out of it, 

 they will become parallel, as shown in the space 

 c b. 



If the candle be placed nearer the glass than its 

 focal distance, the rays will diverge after passing 

 through the glass, more or less, as the candle is 

 more or less distant from the focus. 



If the candle be placed farther from the glass 

 than its focal distance, the rays will converge after 

 passing through the glass, and meet in a point, 

 which will be more or less distant from the glass, 



