Page:Optics.djvu/121

 Now this is in some degree the case with respect to flint- and crown-glass: they do not disperse the different coloured rays proportionally, and in consequence, if two lenses be matched so that their dispersions are equal and opposite for the extreme rays, there will still be some aberration of green and blue rays uncorrected.

132.Dr. Brewster in his excellent "Treatise on new Philosophical Instruments" details some experiments tending to shew that prisms and lenses of the same substance might be combined so as to correct each other's dispersion, without destroying all the refraction.

He found that when a beam of light passed through a flint-glass prism, so that the deviation was a minimum, (the angles of incidence and emergence being equal,) and the dispersion was corrected by a smaller prism of the same substance, inclined to increase its refraction, the colourless pencil was still considerably refracted from its original direction, by the prism with the greater refracting angle.

This combination, represented in Fig. 144, he proposes to imitate with a pair of lenses, by making them of the form shewn in Fig 145.

The reason why the preceding theory did not lead to any such conclusions as these, appears to be as follows:

It was taken for granted, that a given substance has always the same dispersive power into whatever form it be put, or however its surface be inclined to the light, that is, that the dispersion bears a constant ratio to the mean refraction. Thence it was argued that the dispersion of a lens was as the dispersive power of the substance, and the power of the lens, jointly, or as the dispersive power directly, and focal length inversely, and that therefore the dispersions of a convex and concave-lens might be made equal and opposite, if the fraction $dispersive power⁄focal length$ was the same in each: but it appears from Dr. Brewster's experiments, that our premises are not true, for that when the angle of incidence is changed, the ratio of refraction is not constant for each kind of primitive light.

133.Dollond, who first constructed achromatic compound-lenses, made them of three different parts, as represented in Fig. 146,