In order to make large reflectors perfect—large telescopes of short focus, because that is one of the requirements of the modern astronomer—we have to battle against spherical aberration.
We have already seen that the power of substances to refract light differs for different colours, and we have seen the varied refraction of different parts of the spectrum, and the necessity of making lenses achromatic. Now there is one enormous advantage in favour of the reflector. We do not take our light to bits and put it together again as with an achromatic lens. But curiously enough, there is a something else which quite lowers the position of the reflector with regard to the refractor. Although, in the main all the light falling in parallel lines on a concave surface is reflected to a focus, this is only true in a general sense, because, if we consider it, we find an error which increases very rapidly as the diameter of the mirror increases or as the focal length diminishes. For instance, D I, Fig. 58, is the segment of a circle, or the section of a sphere—if we deal with a solid figure. D C, E G and H I, are three lines representing parallel rays falling on different parts of it. According to that law which we have considered, we can find where the ray E G will fall. We draw a line L, G, from the centre to the point of reflection, and make the angle F G L, equal to the angle of incidence E G L; then F will be the focus, so far as this part of the mirror is concerned. Now let us repeat the process for the ray H I, and we shall find that it will be reflected to K, a point nearer the mirror than F, and it will be seen that the further the rays are from the axis D C, the further from the point F is the light reflected; so that if we consider rays falling from all parts of the reflecting surface, a not very large but a distinctly visible surface is covered with light, so that a spherical surface will not bring all the rays exactly to a point, and with a spherical mirror we shall get a blurred image. We can compare this imperfection of the reflector, called spherical aberration, with the chromatic aberration of the object-glass.
FIG. 58.—Diagram Illustrating Spherical Aberration. ]