To estimate the relative brightness of the image and object, suppose, for simplicity, all the light which enters the telescope from the object to reach the eye. Then the quantity of light which enters the eye from the image is greater than that which would enter the unaided eye from the object, in the ratio of aperture of the object-glass, C, to the aperture of the pupil of the eye. But it is spread over a magnified image. If the image be as much larger than the object as the object-glass is larger than the pupil of the eye, the object and image will appear equally bright. Taking the aperture of the pupil as Tif in., the object-lens would require an aperture of 10 in., with a magni fying power of 100 times, in order that brightness should not be lost. Practically, the most formidable difficulty in attaining very high magnifying powers is that due to the enormous size of lenses and mirrors which are required to give the necessary brightness to the enlarged image. It is easy to see that it is impossible to render the final image brighter than the object by any increase of dimensions in the object-lens.
After what we have said about the common astronomical telescope, the reader will have no difficulty, from a combination of figures 2 and 3, in understanding the construc tion of the Newtonian or Herschelian reflecting telescope.
We proceed to the second part of our proposed scheme of treatment of the subject, viz., the unavoidable imperfections of the telescope, and their reduction to a minimum.
In the first place, then, even with a mirror—where we are not annoyed by the break ing up of white light into its component colors, since the law of reflection (q.v.) is the same for all rays—it is impossible to form a perfectly sharp image of more than one defin ite point at a time. In order to do even this, the mirror must be formed as part of the prolate spheroid produced by the rotation, about its longer axis, of an ellipse (q.v.), one of whose foci is the object-point, the other the image. If the object-point be, like a star, practically at an infinite distance, the requisite form of the mirror is that formed by the rotation of a parabola (q.v.) about its axis. The axis of the mirror must then be directed to the object-point, and all rays from it will, after reflection, pass accurately through the focus. But this is not strictly true for any other object-point in the field of view, although so nearly true that no inconvenience is practically found to result from it.. But, if the mirror used be part of a sphere, no point can be found such that rays diverg ing from it shall all be brought after reflection accurately to one point of the image; and this defect, called spherical aberration, increases proportionally to the surface of the mir ror so that by increasing that surface, for the attainment of brightness, we increase pro portionally the indistinctness of the image. To give an idea of the delicate manipula tion required in the construction of a reflecting telescope, we take the case of a specu lum of 4 ft. aperture and 40 ft. focus, as calculated by sir J. Herschel. If this be first
ground to a truly spherical form, it must have a radius of SO ft., as we have seen above. Now, such a mirror will give a very indistinct image, even under the most favorable cir cumstances; yet to grind it to the parabolic form, which is practically perfect, leaving the middle untouched, and grinding more and more away from its surface as we pro ceed outward to the edges, even at the edges we have to remove a film of metal of only the „i„ part of an inch, somewhere about the part of the thickness of the paper on which this is printed ! Lenses, whether the object-lens or the eye-lens, have this defect also; but, as a rule, the spherical aberration in lensesis almost negligible compared with chromatic aberration, which arises from the different refrangibilities (see REFRACTION) of the various colored rays; and leads to the formation, by a lens, of a separate image of a bright object for each colored ray. The remedy consists in achromatizing (see ACHROMATIC, REFRAC TION) the lens—i.e., forming it of two or more lenses of different kinds of glass—so that the colors, separated by one, shall be reunited by the others. With a double achro matic lens, in which a convex lens of crown glass is united to a concave of flint-glass, the focal lengths of the separate lenses can be easily adjusted so as to bring, when in. combination, any two assigned rays of the spectrum (q.v.) simultaneously to a focus; and, by a judicious selection of these two rays, we may reduce the consequences of irra tionality of dispersion (See REFRACTION) to a minimum. But this is not all. To con struct a lens of a given material which shall have a given focal length, is an indetermin ate problem; we may assign the curvature of either surface at then that of the other is definite, and can be calculated. Thus, the achromatism of a double-lens can be secured in an infinite variety of ways, and we mar impose further conditions; i.e., that the curvatures of the convex and concave surfaces shall be adjusted so as to de stroy to as far as possible the spherical aberration. Other imperfections, such as those due to (q.v.), etc., cannot be here more than alluded to, as they do not admit, within any reasonable limits, of being popularly explained. Nor can we enter upon questions connected with the correction of chromatic and spherical aberra tions in eye-pieces, which is effected by the combination of two or more lenses (generally of the same material) placed at a certain distance from each other. We may only mention that the defect (for terrestrial purposes) of the common astro nomical telescope, the inversion of the image, is overcome by combining two such telescopes, the smaller to examine the image formed by the larger, and therefore to reinvert it. This practically comes to constructing the eye-piece of three lenses at a dis tance from each other; though, for greater distinctness, four are usually employed.