PRELIMINARY DIOPTRIC CONSIDERATIONS. 



825 



The distance of the image from the lens may be readily calculated by the 

 following formula, in which 1 represents the distance of the point of light, b the 

 distance of the image, and f the focal distance of the lens: 





Examples: Let 1 = 24 cm., f = 6 cm. Then JL = JL JL = JL; therefore 



b 6 24 

 b = 8 cm., that is, the image is formed 8 cm. behind the lens. Further: Let 



1 = 10 cm., f = 5 cm. (or 1 = 2f). Then JL = JL J_ = JL; therefore b = 10 



b 5 10 10 



cm., that is, the image is double the focal distance from the lens. Finally, let 



1 = oo. Then * - = JL- -L, or b = f , that is, the focus for parallel rays, coming 



from an infinite distance, is in the principal focus of the lens. 



Index of Refraction. A ray of light passing from one medium to another 

 medium of different density, in a direction perpendicular to the surface, passes 

 through the latter without changing its direction If, therefore (Fig. 273) G D. 

 is perpendicular to A B, then D D is also perpendicular to A B. For a horizontal 

 surface A B the axis of incidence is the vertical line G D, while for a spherical 



FIG. 273. 



FIG. 274. 



surface the axis of incidence is the prolonged radius. If the ray of light strikes 

 the surface obliquely, it is refracted, that is deflected from its original direction. 

 The incident and refracted rays lie, however, in the same plane. If the oblique, 

 incident ray passes from a rarer medium to a denser one (for example, from air 

 into water), the refracted ray is deflected toward the perpendicular. Conversely, 

 if the ray passes from a denser medium into a rarer one, it is deflected away from 

 the perpendicular. The angle that the incident ray (S D) forms with the per- 

 pendicular (G D), (angle i) is called the angle of incidence. The angle that the re- 

 fracted ray (D S x ) forms with the prolonged perpendicular (D D) is called the 

 angle of refraction (angle r) . The degree of the refraction is expressed by the index 

 of refraction (or exponent of refraction) ; it is represented for each substance by 

 the relation of the sine of the angle of incidence to the sine of the angle of refrac- 

 tion of a ray passing from air into that substance. Thus, n = sine i : sine 

 r = a b : c d. In comparing the indices of refraction of two media, it is assumed 

 that the ray of light passes from the air into the media. In passing from air into 

 water, the ray of light is deflected to such a degree that the ratio of the sine of the 

 angle of incidence to the sine of the angle of refraction is as 4 : 3 ; the index of 

 refraction is therefore ^ (more exactly = 1.336). With glass the ratio is 3 : 2 



