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The photographic news
- Bandzählung
- 12.1868
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- 1868
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- Hochschule für Grafik und Buchkunst Leipzig
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- Bandzählung
- No. 527, October 9, 1868
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Zeitschrift
The photographic news
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Band
Band 12.1868
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- Titelblatt Titelblatt I
- Kapitel Preface III
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- Register The Index To Volume XII 619
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Band 12.1868
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484 THE PHOTOGRAPHIC NEWS, be made for B as in the first case for A. One of these arrangements would, of course, be adopted when the defini tion of one of the points is required to be the best possible, while that of the other is of comparatively no moment. Such occasions arise, but in pictorial photography it would be generally desirable that both objects should be fairly repre sented, and that the definition of one should not be entirely sacrificed in order to improve the other. In such a case the focussing would not be made on either A or B, but on a point (approximately) half way between them, so that neither A nor B would be perfectly defined, but would be represented on the plate by circles of light equal to each other, but of only half the magnitude of that which repre sented one point in the first and second cases. This readily suggests the question, would not a lens affected by spherical aberration be capable of giving as good a representation as this of A and B on the screen ? It is true that in actual photography there would be generally some third object, and so situated that the peculiar power of the lens would be brought out in perfectly defining it; but this would be rather a drawback than an advantage, as a tolerably uniform definition is usually desirable. We are thus naturally led to enquire what effect the introduction of spherical aberra tion would have on the definition of objects situated at various distances from the lens. With this end in view it is necessary to examine carefully the nature of the bundle of rays which proceed from towards the screen after refrac tion by an uncorrected lens. In the first place it is to be noticed that the rays which are refracted by one part of the lens do not, in general, reach the axis at the same point with those which come from a different part; so that if we divide the lens into rings, proceeding from the centre outwards, each small ring may be supposed to act as a perfect lens; but there is a variation of focal length in passing from one ring to another. Thus the focal length of the outermost ring C A, and that of the central part C F, the intermediate rings having inter mediate focal lengths. The least section of the assemblage of rays is at Q, where the curve F Q H, touched by all the rays, and called in optics the caustic, meets those from the edge of the lens, which, having cut the axis in A, again diverge. But it does not follow, as might at first be supposed, that the screen should be placed there in order to get the best possible definition of the object 0. The reason of this will appear presently. Between the lens and Q the space occupied by the rays is bounded by the curved caustic surface, but beyond Q by the cone, whose vestex is at A, formed by the above, refined to extreme rays. A second radient point, 0' nearer the lens (say) will pro duce an approximately similar system of rays to the above, only displaced somewhat towards the right, or from the lens. But instead of considering the two systems of rays as cut by a fixed screen, as in actual practice, it is allowable and more convenient for explanation to confine ourselves to one system, and conceive that intersected by parallel planes at varying positions along the axis. This substitution pro ceeds on the assumption that the objects are not at very different distances from the lens in relation to its focal length. In order to avoid continual reference to them, it will be supposed in what follows that the aperture and focal length of the lens are given, or do not vary under the circumstances contemplated, which of course does not prevent the aberra tion changing its amount within certain limits. The distances between the two cutting planes which we have to consider is given as soon as the positions of 0 O' are fixed. And as, in the case of a corrected lens, the definition of objects slightly out of focus may be measured by the diameter of the small circle which represents a point, the question is suggested, where must the sections in the pre sent instance be taken to make their diameters equal ? In Conington’s Optics there is a remark to the effect that such a quality as definition cannot haye a measure. Thus I [OCTOBER 9, 1868 suppose one definition could not be said to be twice as good as another. But neither could the same be said of two temperatures, at least, prior to modern discoveries, which does not prevent the ordinary thermometer from being a very useful measure of temperature. The planes will evidently lie on opposite sides of Q but not equally distant from it, inasmuch as the obliquity of the caustic surface to the axis on the left is less than that of the cone which bounds the section on the right of Q. A definite result can of course be obtained by the application ot mathematics, and it will, I believe, be found that the magnitude of the aberration may be so chosen as to make the diameters of the section smaller than it is for a corrected lens ; so that it would appear that for the equal definition of 0 0' a corrected lens is not the best. On referring to the original calculation I find that this statement is not quite correct. As the aberration increases from zero up to a certain point, the definition (as measured by the size of the section) would remain unaltered, and after that point would deteriorate. The correction in view of what follows is of no moment. About a year ago I went through the calculation alluded to, but I was aware that it would give no adequate idea of the advantage of an uncorrected lens, on account of the fundamental assumption on which it proceeds, namely, that the diameter of the section of the pencil made by the screen may be taken as a measure of the distinctness, or rather indistinctness, of the image. This, though admissible enough for a corrected lens, is by no means equally so when there is a spherical aberration, for then the light is not impartially distributed over the area of the section, nor according to any other fixed law, the same for all sections. There is, in fact, a series of points where the illumination is much (according to the ordinary theory of rays, infinitely) greater than it is elsewhere, such points being situated on the caustic surface, and also in a line along the axis between A and F. That this is bo will be admitted when it is remembered that all the rays pass through the line A. The result is that a section taken between H and A has a bright rim, but nothing peculiar about the illumination at the centre. On passing A, however, while the bright circumference continues, a spot of intense light makes its appearance at the centre, anil this state of things remains until Q is past. At this point the bright circle leaves the boundary of the illuminated area, continuing to contract, while the latter begins to expand. Soon after passing F the illumination becomes comparatively uniform over the whole area of the section. All this may be easily observed by admitting the sun's rays into a darkened room through a hole in the shutter in which is fixed a lens of short focus. If the rays diverging from the small image of the sun thus formed be allowed to fall on a lens which possesses a considerable amount of spherical aberration (such as a microscopic or magic lantern condenser), the circumstances of the preceding paragraph are sensibly realized, and the construction of tho refracted pencil can be examined by receiving it on a movable paper screen. A very beautiful modification of this experiment has been made by Professor Stokes, who avails himself of the power possessed by certain substances of rendering visible and dis persing the blue and ultra-blue rays of the spectrum, a phe nomenon to which he gave the name of fluorescence. The sun’s rays, reflected horizontally, by a mirror placed outside the window, are admitted into the darkened room through a blue glass, and, after refraction by the lens, pass into a glass trough filled with a weak solution of oesculine placed close behind it. The blue glass is not absolutely neces sary, but much increases the brilliancy of the experiment. A solution sufficient for the purpose may be made by soaking a few chips of the inner bark of the horse-chestnut in a jug of water, but it soon decomposes. The path of the rays 13 marked by the luminosity of the liquid, somewhat as in » smoky atmosphere, and the bright line along the axis 18
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