20 



OPTICS. 



become equal to M N. When M N 

 recedes from the mirror, m n will be- 

 come less and less, and recede from the 

 mirror also ; and when M N is infinitely 

 distant, m n will be at E, the virtual 

 focus of parallel rays. Objects, there- 



fore, are always seen diminished in a 

 convex mirror, unless when they touch 

 it. 



Formation of images by concave mir- 

 rors. -Let M N (ftg. 25'.) be an object 

 at a considerable distance from a con- 



Fig. 25. 



cave mirror R S, whose centre is C and 

 principal focus F: then, as the rays from 

 M fall diverging on the mirror, they will 

 be reflected to a focus at m, a little 

 without its principal focus, and there 

 form a representation of the point m ; 

 in like manner the rays diverging from 

 N will be reflected to n, and there form a 

 picture of N ; so that there will be an in- 

 verted image n in of the object formed a 

 little without the principal focus F. This 

 image seems to be suspended in the air, 

 and has a very singular appearance when 

 it is received on a thin blue smoke from 

 a chafing dish placed below m. As the 

 object M N recedes from the mirror, the 

 image m n approaches to F, with which 

 it coincides when M N is infinitely 

 distant. This is the principle of the Re- 

 flecting telescope. If we conceive m n 

 to be a small object, then the rays di- 

 verging from it will form an enlarged 

 image of it at M N, which may be 

 either viewed by the eye, or, which is 

 better, by a convex lens, in which case it 

 constitutes a Reflecting microscope. 



If we consider the image m n as a new 

 object, and place a small concave mirror 

 r s behind it, so as to form an enlarged 

 image of that image, the rays of which 

 pass through a hole E, in the large mirror 

 RS ; then, this second, or enlarged image, 

 maybe either vie wed by the eye behind E, 

 or magnified still more by a convex lens. 

 In this case, the combination becomes 

 the Gregorian reflecting telescope. If we 

 make the small mirror rs convex, and 

 place it between F and n m, so as to 

 intercept the rays before they actually 

 meet their virtual foci, n m, then an en- 

 larged image of this virtual image will 

 be formed somewhere about E, and 

 may be magnified, as before, with a 

 convex lens. In this case, the combi- 



nation constitutes the Cassegrainian 

 reflecting telescope. The former instru- 

 ment is called after its inventor, James 

 Gregory ; the latter after its inventor, 

 Monsieur Cassegrain. In these teles- 

 copes, the magnifying power is de- 

 termined in the very same manner as 

 for . convex lenses, or combinations of 

 them ; the size of the image being 

 always to the size of its object, as the 

 distance of the image from the mirror 

 is to the distance of the object. 



When the object is placed nearer a 

 concave mirror than its principal focus 

 F, the rays will not have their locus in 

 front of the mirror, but will diverge 

 as already shewn, from conjugate foci 

 behind the mirror, where they will form 

 a correct representation of the object. 

 The image is ihighly magnified when the 

 object is near the focus, but it gra- 

 dually diminishes as the object ap- 

 proaches the mirror, and it becomes 

 equal to it when the object touches the 

 mirror. 



CHAPTER VII. On Spherical Aberra- 

 tion in Lenses and Mirrors. 



IN treating of the refraction of rays at 

 the surfaces of spheres and lenses, we 

 have supposed that all the rays meet 

 exactly in the focus. This, however, is 

 not exactly true ; for if, in//^-. 6, the ray 

 A C is refracted by the sphere L L to 

 the point/, another ray falling upon the 

 sphere nearer the axis,, any where be- 

 tween C and H, will have its focus, or 

 will intersect the axis, at a point /' 

 farther from the sphere than/. This is 

 easily proved by actually projecting the 

 refracted rays, and if it is done for those 

 rays farthest from the axis, and for those 



