ERRORS OF ARTIFICIAL LENSES. 435 



oblique pencils which proceed from the extremities or circumference 

 of the object, a and c, undergo similar, though not such regular refrac- 

 tion as the divergent rays of the direct pencil, and after passing ob- 

 liquely through the lens, converge to their respective common foci, a! , 

 c f , on the opposite sides of the common focus of the direct pencil, b. 

 In the same manner, all the rays proceeding from points between the 

 centre and the extremities or circumference of the object, after being 

 refracted, converge to their respective intermediate common foci, so that 

 an inverted image, a f ', b f , c f , of the object, a, b, c, is thus formed. The 

 formation of such an inverted image, may be readily shown by holding 

 a lighted candle on one side of a lens, and a screen of white paper on 

 the other; it is of special interest to the physiologist, for this optical 

 phenomenon actually takes place in the eye. 



In the production of images by artificial lenses, there are several 

 sources of imperfection. It has already been mentioned that the 

 different colored rays into which solar light may be decomposed, have 

 different degrees of refrangibility ; it is in consequence of this unequal 

 refraction, that the images of bodies illuminated by solar or other 

 compound light, formed by an ordinary lens, are surrounded by a fringe 

 of prismatic colors. This defect is called the error of dispersion or 

 chromatic aberration*. 



The degree of refraction of the rays which fall on the curved sur- 

 face of a double convex lens, becomes relatively greater, the greater 

 their distance from the axis of the lens, because they fall upon, and 

 issue from, its surfaces, with greater and greater obliquity. Hence, 

 the peripheral rays are brought to a focus sooner than the central 

 rays, so that every part of the image becomes more or less indistinct 

 and confused. This is called spherical aberration. The effect on a 

 small pencil of light, is the production of the so-named circles of dis- 

 sipation. 



By cutting off the peripheral rays, by means of perforated stops or 

 diaphragms, both chromatic and spherical aberration may be diminished. 

 They may be almost completely corrected, by building up lenses of 

 two pieces of glass, having different curves, and also different disper- 

 sive powers, so that the dispersive and undue marginal refractive effects 

 of one portion of the lens, are counteracted by the influence of the 

 other. Such lenses are called achromatic. 



If an object be situated at such a distance from the lens, that the 

 rays issuing from it are parallel, the best image is formed in the prin- 

 cipal focus of the lens. The nearer the object approaches the lens, 

 the more the focus recedes, until at last, the object having reached the 

 principal focus of the lens in front, the rays emerging from the lens 

 become parallel, and accordingly, no image is formed. Hence, in 

 order to obtain a distinct image of any object, the distance between 

 the lens and the screen for the reception of the image, must be varied, 

 that is, increased or diminished, according to the nearness or distance 

 of the object. In optical instruments, provision is made for the 

 proper adjustment of the focal distance, by having the lenses, or the 

 screen, made movable. The defect arising from imperfect adjustment 

 of the focus, is known as distantial aberration. 



