744 



FORMATION OF IMAGES BY CONVEX LENSES. 



With regard to the size and distance of the image from the lens, there are the following 

 ca8( . s .__/) If the object be placed at twice the focal distance from the lens, the image of the 

 same ismst the same size and at the same distance from the lens as the object is. (b) If the 

 object be nearer than the focus, the image recedes and at the same time becomes larger, (c) If 



i . 



m 



Di 



Fig. 525. Fig. 526. 



the olject be farther removed from the lens than twice the focal distance, then the image is 

 nearer to the lens and at the same time becomes smaller. 



Position of the focal point. The distance of the focal point from the lens is readily calcu- 

 lated according to the following formula : Where Z = the distance of the luminous point, J = the 



111 111 

 distance of the image, ond/=the focal distance of the lens : -+ =^ , or 



o /' 



Thi|4-S-| ; ' 0<hEt6, 



Example. Let Z = 24 centimetres, /=6 cm. 

 image is formed 8 cm. behind the lens. Further, let 1 = 10 cm.,/=5 cm. {i.e., 1 = 2 f). 



so that 6 10, i.e., the image is placed at twice the focal distance of the lens, 



8 cm., i.e., the 

 Then 



10 



10' 



Lastly, let l = oo, 



Thenl=) 



so that b=f, i.e., the image of parallel rays coming from 



infinity lies in the focal point of the lens. 



Refractive Indices. A ray of light, which passes in a perpendicular direction from one 

 medium into another medium of different density, passes through the latter without changing 

 its course or being refracted. In fig. 525, if G D, is A B, then so is D D, j, A B ; for a plane 

 surface A B is the horizontal, and G D the vertical line. If the surface be spherical, then the 

 vertical line is the prolonged radius of this sphere. If, however, the ray of light fall obliquely 

 upon the surface, it is " refracted," i.e., it is bent out of its original course. The incident and 

 the refracted ray nevertheless lie in one plane. When the oblique incident ray passes from a 

 less dense medium (e.g., air) into one more dense (e.g., water), the refracted or excident ray is 

 bent Uncards the perpendicular. If, conversely, it pass from a more dense to a less dense medium, 

 it is bent away from the perpendicular. The angle (i, G D S) which the incident ray (S D) forms 

 with the perpendicular (G D) is called the angle of incidence, the angle formed by the refracted 

 ray (D S,) with the prolonged perpendicular (D D) is called the angle of refraction, D D S 2 

 (r). The refractive power is expressed as the refractive index. The term refractive index 

 (n) means, that number which shows for a certain substance, how many times the sine of the 

 angle of incidence is greater than the sine of the angle of refraction, when a ray of light passes 

 from the air into that substance. Thus, w= sin. i : sin. r=ab, : cd. On comparing the refractive 

 indices of two media, we always assume that the ray passes from air into the medium. On 

 passing from the air into water, the ray of light is so refracted that the sine of the angle of 



incidence is to the sine of the angle of refraction, as 4 : 3 ; the refractive index = - (or more 



3 

 exactly =1-336). ^ With glass the proportion is = 3 : 2 ( = V5B5Snellius, 1620; Descartes). 

 The sine of the incident and refractive-angles are related as the velocity of light with both 

 media. 



The construction of the refracted ray, the refractive index being given, is simple : Example 

 Suppose in fig. 526, L=the air, G = a dense medium (glass) with a spherical surface, xy, and 



