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THE PHOTOGRAPHIC NEWS. 715 In a previous lesson, it has been shown that any lens may be supposed as primarily made up of a series of infinitely small pieces of prisms. Now, as a prism refracts different rays differently, it is manifest that what would be the focus for one colour will not be the focus for other colo irs. The violet rays being most refracted, the focus of this colour with a convex lens will be nearer to the lens than that of the red, and between these two points will be the focus for intermediate colours. The ultra-violet rays, which are still more refracted than the violet, will have a focus still nearer to the lens than even the latter. [This is always true, except in a case most unlikely to be met with in photography, when the source of light is between the centre of the lens and the principal focus of rays incident in the contrary direction.] With a concave lens the reverse is evidently the case. Suppose the lens C to be free from spherical aberra tion, (fig. 43), and that parallel rays of light pro ceeding from a distant point, made up of violet and red rays travel along the axis of the lens, the focus of the violet rays will be at v, and of the red rays at r. If a screen be placed at v the image of a point of light will be a point in which violet predominates, surrounded by a red disc of diameter a b • and if at r, the image will be a point in which red predominates, surrounded by a violet disc of diameter c d; atgf, the screen would show approximately the original coloured light; but the image of the point of light would in this case be a disc of the diameter g f. If all intermediate colours between red and violet were in the incident beam of light as is the case in white light, it is evident that in every position between v and » there will be a point in which one colour predominates surrounded by discs made of all the other coloured rays in varying proportions. Can this chromatic aberration be diminished without out making a combination of lenses ? If Fig. 43 be ex amined, it will be seen that as the aperture of B A the lens is diminished, so will the coloured disc be diminished in diameter, till by sufficiently reducing it, the coloured disc may be reduced to the limits of the disc of admissible confusion.* For some purpose in photography an ordinary spectacle lens can thus be used. Achromatic Prisms.—If we construct two prisms of diffe rent materials, so that the mean deviations are the same, and if we place the base of one prism in contact with the refracting angle of the other, the mean ray of light would emerge from the two prisms, so placed without suffering Fig. 44. any deviation ; but owing to the “ irrationality of disper sion,” if received on a white screen, would show colours bounding the white point of light so projected. A little consideration will show that by a judicious selection of the angles of the prisms, any two colours may be made to mute, and at the same time to have a given deviation ; thus, the yellow ray, D, and the indigo, G, may be made o unite to form the refracted image, the other colours form- Jens of suihowe ver, be bo n in mind that such is the case only when a interreretttaote focal length is chosen, otherwise deffraction phenomena ing a secondary spectrum by the overlap of the two spectra which arise from the two prisms. [The angle may be found thus when the prisms have but small refracting angles.] Let i and e be the refracting angles of the two prisms, u and u, the indices of refraction for one colour, p-+a and u,—b the indices of refraction for another colour. Of these, i, u, u,, a, and b* are known, and 0 has to be found. It can readily be shown since i and 0 are small by hypo thesis, that the deviations for the first colour in each prism are— (u—1)i and (uy—1)0 and for the other colour— (u+a—1)i and (u+b—1)0 The total deviation in the first case will be— (u-1)i + (u—1)0 (i) and in the other— (u+a- 1)i + (u+b—1)« (ii) If, then, the deviations for the two colours are to be the same as we have supposed, i.e., that the colours are united after passing through the two prisms, then (i) must equal (ii), aud we have— 0=ai+be , at or, e= — — b The minus sign shows that the base of one prism has to be placed against the point of the other as in figure. If there be three different materials of which the prisms are made, three different colours may be made to combine ; if 4, 4, and so on. Achromatism of lenses.—As regards a combination of lenses in contact, as in the ordinary photographic use, we may briefly state the rule which governs the combination. In order to be achromatic for two colours, take the difference of refraetve index for the two colours for one material, and divide by the index of refraction less unity of the colour most refracted, and again divide by the focal length of the lens for that same colour. Do the same for the other lens, and the two results must equal one another, from which [Mathematically it may be expressed thus. Let u and u, be the refractive radius of the two materials for the colour of greatest refrangibility, f and fi the principal focal length of the two lenses for that colour, a and b the dispersion or difference between the refractive indices of the two colours for each lens respectively. Then, in order that achromatism for the two colours may ensue, a 14 _b . 1=o (m—1) f u—l fi Evidently one must have a negative focus, and the other positive ; hence one must be a concave and the other a convex lens. From this the focal length of an achromatizing lens may be calculated, and its curvature can be found from the formulae given in Lesson IV., it being presumed that the indices of refraction for the colours to be united are known in both cases.] patent Jntclligence. Application for Letters Patent. 5204. Harrison Garside,, of the city of Manchester, in the county of Lancaster, photographer, for an invention of “ An improved method of producing surfaces for methanical or ink printing by means of photography.”—Dated 2nd November, 1883. Notice to Proceed. 4732. John Edwin Atkinson, of Greenwich, in the county of Kent, for an invention of “ Improvements in apparatus for use in transporting and exposing sensitized photographic plates or films.”—Dated 4th October, 1883. • a and b are very small compared with u and H1, see table.