36 Transactions of the Amebic an Institute. 



real image will be formed ; but there will be a negative or imaginaiy 

 image on the same side of the lens as the object. If the eye of an 

 observer be placed behind the lens, looking toward the object, this 

 imaginary image will appear to be real, and Avill be the thing seen. 

 Spherical lenses do not produce true foci. Hence the images formed 

 by single lenses are imperfect. When parallel rays are transmitted 

 through a convex lens the focus of the central rays is more distant 

 than that of the marginal. Intermediate rays form foci at interme- 

 diate distances. The space along the axis of the lens through which 

 these several foci are distributed is called the spherical aberration of 

 the lens. If a lens is unequally curved on its two sides, the amount of 

 its aberration will differ according as one or the other side is pre- 

 sented to parallel rays. Generally speaking, parallel rays should be 

 received on the side having the largest curvature. 



The aberration of concave lenses is the reverse of that of convex. 

 A concave lens, combined wntli a convex of greater power, will 

 lengthen the focus, but not prevent its formation. Such a concave 

 lens in the position of maximum aberration, coml)ined with a convex 

 in the j^osition of minimum aberration, will neutralize aberration 

 entirely, and produce a perfect focus. This is the principle on which 

 the first of the grave difficulties in the construction of the microscope 

 is overcome. Aberration would be less in lenses formed of substances 

 more highly refracting than glass — as diamond, sapphire, topaz, and 

 other gems. Such lenses would be thinner than glass lenses of 

 equivalent power, and aberration is in a definite ratio to the thickness. 

 In a plano-convex lens it is four and one-half times the thickness with 

 the flat side toward parallel rays, and only one-sixth of the thickness 

 with the convex side toward parallel rays. But the costliness of 

 these gems, the difficulty of grinding them, the color of some of thera, 

 and the property of double-refraction which they all possess, are 

 disadvantages greater than the evil they are proposed to remedy. 

 Moreover, this evil has been effectually eliminated, and tliey arc not 

 needed. But there is another aberration no less troublesome than 

 the spherical, which is called the chromatic. Common white light is 

 composed of elementary rays diftering from each other very sensibly 

 in refrangibility, and also in color. The familiar experiment with 

 the prism illustrates this. The extreme colors are the red and the 

 violet ; but as the violet is very faint, we may regard for our present 

 purposes the red and the blue as representing the limits. The blue 

 rays exceeding the red in refrangibility, will form an image nearer to 



