Fig. 44.—Diagram Explaining the Formation of an Achromatic Lens. A, crown-glass prism; B, flint-glass prism of less angle, but giving the same amount of colour; C, the two prisms combined, giving a colourless yet deviated band of light at D˝.
Another method of showing the same thing is to bring a V-shaped water-trough into the path of the rays from the lantern; then, while no water is in it, the beam of light passing through it is absolutely uncoloured and undeviated. In this case we have no water inclosed by these surfaces, and it is not acting as a prism at all. If, however, a prism of flint glass, a substance of high dispersive power, is introduced into it, with its refracting edge upwards, it destroys the condition we had before, and we have a coloured band on the screen, because the glass that the prism is made of has the faculty of strong dispersion in addition to its deviation. We can get rid of that dispersion by throwing dispersion in a contrary direction by filling up the trough with water, and so making, as it were, a water prism on either side of the glass one, water being a substance of low dispersive power. We have a colourless beam thrown on the screen, which is deviated from the original level, because the water prisms are together of a greater angle than the glass one.
The experiments of Hall and Dolland have resulted in our being able to combine lenses in the same way that we have here combined prisms, bearing in mind what has been said in reference to the action of lenses being like that of so many prisms; and we may consider two lenses, one of crown and the other of flint glass, Fig 45. The crown glass being of a certain curvature will give a certain dispersion; the flint glass, in consequence of its great dispersive power, will require less curvature to correct the crown glass. What will happen will be this: assuming the second lens to be away, the rays will emerge from the first (convex) lens and form a coloured image at A. But if the second flint-glass concave lens be interposed it will, by means of its action in a contrary direction, undo all the dispersion due to this first lens and a certain amount of deviation, so that we shall get the combination giving an almost colourless image at B.
Fig. 45.—Combination of Flint- and Crown-glass Lenses in an Achromatic Lens.
It will not be absolutely colourless, for the reasons which will be now explained. If light be passed through different substances placed in hollow prisms, or through prisms of flint and crown glass, and the spectra thus produced be observed, we find there are important differences. When we expand the spectra considerably, we see that the action of these different substances is not absolutely uniform, some colours extending over the spectrum further than others. In the case of one kind of glass the red end of the spectrum is crushed up, while in the other we have the red end expanded.
This is called the irrationality of the spectrum produced by prisms of different substances. The crown and the flint-glass lenses—and for telescopes we must use such glass—give irrational spectra, so that the achromatic telescope is not absolutely achromatic, in consequence of this peculiarity; for if R, G, B, Fig. [46], are the centres of the red, green, and violet in the spectrum given by a prism composed of the glass of which one lens is made, and R´, G´, B´, are those of the other, if the lenses are placed so as to counteract each other, and are of such curves that the reds and violets are combined, the greens will remain slightly outstanding. Suppose, as in the drawing, the second prism disperses the violet as much as the first one does, then, when these are reversed they will exactly compensate red and violet. But the second one acts more strongly on the green than the first, which will be over-compensated; and if we weaken the second prism so that the green and red are correct, then the violet will be slightly outstanding, which in practice is not much noticed, except with a very bright object when there is always outstanding colour.
Fig. 46.—Diagram Illustrating the Irrationality of the Spectrum.