OPTICAL IMAGES. 



attained, admits of an explanation, which after what has been 

 stated above will be easily understood. 



Let an object o o, fig. 35, be placed before a convex lens, c c, 

 and let v be its violet, and E its red image, the dispersion being 



Fig. 35. 



consequently v E. Now, let F F be a concave lens, through which 

 the rays proceeding from c c will be transmitted. This lens being 

 concave, will have the effect of diminishing the convergency of 

 the rays, and of throwing both the violet and red images to a 

 greater distance ; but it will have a greater effect on the violet 

 than on the red rays, the former being more refrangible. Now, 

 suppose that the material of which the lens F F is made, be such 

 that at a certain distance from it, at v' for example, the quantity 

 of dispersion it would produce would be exactly equal to v E. In 

 that case it is evident that the extreme images of o o, the violet 

 image and the red image would be equally affected in contrary 

 directions by the two lenses c c and F F. By c c, the violet image 

 would be brought back, and the red image thrown forward, so as 

 to separate them by the distance v E ; but by the lens F F, on the 

 contrary, the violet image is thrown forward, and the red driven 

 back, in exactly the same degree, so that the two images are made 

 to coalesce at E' v'. As to the intermediate images, although they 

 do not actually coalesce, their dispersion becomes so insignificant 

 as to produce no perceptible chromatic aberration. 



The production of this effect depends on the relative dispersive 

 and refractive powers of the material of the two lenses, and on 

 their forms. 



This important principle may be further elucidated as follows : 



Let i/ i/ (fig. 36, p. 113) be a diverging lens and let it be 



supposed to receive rays proceeding from a white object which, 



if not intercepted, would produce a real image of the object at 



a point o, within the focal distance of the lens i/ 1/. In that case 



the lens L' i/, according to what has been explained, will produce 



a series of coloured images of the object at a greater distance 



116 



