Works of Johann Wolfgang von Goethe
Page 309
310
How little therefore we have here to do with single sun-rays, bundles or fasces of rays, cylinders of rays, pencils, or whatever else of the kind may be imagined, is strikingly evident. For the convenience of certain diagrams the sun-light may be assumed to arrive in parallel lines, but it is known that this is only a fiction; a fiction quite allowable where the difference between the assumption and the true appearance is unimportant; but we should take care not to suffer such a postulate to be equivalent to a fact, and proceed to further operations on such a fictitious basis.
311
Let the aperture in the window-shutter be now enlarged at pleasure, let it be made round or square, nay, let the whole shutter be opened, and let the sun shine into the room through the whole window; the space which the sun illumines will always be larger according to the angle which its diameter makes; and thus even the whole space illumined by the sun through the largest window is only the image of the sun plus the size of the opening. We shall hereafter have occasion to return to this.
312 (199)
If we transmit the image of the sun through convex glasses we contract it towards the focus. In this case, according to the laws before explained, a yellow border and a yellow-red edge must appear when the spectrum is thrown on white paper, But as this experiment is dazzling and inconvenient, it may be made more agreeably with the image of the full moon. On contracting this orb by means of a convex glass, the coloured edge appears in the greatest splendor; for the moon transmits a mitigated light in the first instance, and can thus the more readily produce colour which to a certain extent accompanies the subduing of light: at the same time the eye of the observer is only gently and agreeably excited.
313 (200)
If we transmit a luminous image through concave glasses, it is dilated. Here the image appears edged with blue.
314
The two opposite appearances may be produced by a convex glass, simultaneously or in succession; simultaneously by fastening an opaque disk in the centre of the convex glass, and then transmitting the sun’s image. In this case the luminous image and the black disk within it are both contracted, and, consequently, the opposite colours must appear. Again, we can present this contrast in succession by first contracting the luminous image towards the focus, and then suffering it to expand again beyond the focus, when it will immediately exhibit a blue edge.
315 (201)
Here too what was observed in the subjective experiments is again to be remarked, namely, that blue and yellow appear in and upon the white, and that both assume a reddish appearance in proportion as they mingle with the black.
316 (202, 203)
These elementary phenomena occur in all subsequent objective experiments, as they constituted the groundwork of the subjective ones. The process too which takes place is the same; a light boundary is carried over a dark surface, a dark surface is carried over a light boundary. The edges must advance, and as it were push over each other in these experiments as in the former ones.
317 (204)
If we admit the sun’s image through a larger or smaller opening into the dark room, if we transmit it through a prism so placed that its refracting angle, as usual, is underneath; the luminous image, instead of proceeding in a straight line to the floor, is refracted upwards on a vertical surface placed to receive it. This is the moment to take notice of the opposite modes in which the subjective and objective refractions of the object appear.
318
If we look through a prism, held with its refracting angle underneath, at an object above us, the object is moved downwards; whereas a luminous image refracted through the same prism is moved upwards. This, which we here merely mention as a matter of fact for the sake of brevity, is easily explained by the laws of refraction and elevation.
319
The luminous object being moved from its place in this manner, the coloured borders appear in the order, and according to the laws before explained. The violet border is always foremost, and thus in objective cases proceeds upwards, in subjective cases downwards.
320 (205)
The observer may convince himself in like manner of the mode in which the appearance of colour takes place in the diagonal direction when the displacement is effected by means of two prisms, as has been plainly enough shown in the subjective example; for this experiment, however, prisms should be procured of few degrees, say about fifteen.
321 (206, 207)
That the colouring of the image takes place here too, according to the direction in which it moves, will be apparent if we make a square opening of moderate size in a shutter, and cause the luminous image to pass through a water-prism; the spectrum being moved first in the horizontal and vertical directions, then diagonally, the coloured edges will change their position accordingly.
322 (208)
Whence it is again evident that to produce colour the boundaries must be carried over each other, not merely move side by side.
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XXIII.Conditions of the Increase of Colour.
323 (209)
Here too an increased displacement of the object produces a greater appearance of colour.
324 (210)
This increased displacement occurs,
1. By a more oblique direction of the impinging luminous object through mediums with parallel surfaces,
2. By changing the parallel form for one more or less acute angled.
3. By increased proportion of the medium, whether parallel or acute angled; partly because the object is by this means more powerfully displaced, partly because an effect depending on the mere mass co-operates.
4. By the distance of the recipient surface from the refracting medium so that the coloured spectrum emerging from the prism may be said to have a longer way to travel,
5. When a chemical property produces its effects under all these circumstances: this we have already entered into more fully under the head of achromatism and hyperchromatism.
325 (211)
The objective experiments have this advantage that the progressive states of the phenomenon may be arrested and clearly represented by diagrams, which is not the case with the subjective experiments.
326
We can observe the luminous image after it has emerged from the prism, step by step, and mark its increasing colour by receiving it on a plane at different distances, thus exhibiting before our eyes various sections of this cone, with an elliptical base: again, the phenomenon may at once be rendered beautifully visible throughout its whole course in the following manner: — Let a cloud of fine white dust be excited along the line in which the image passes through the dark space; the cloud is best produced by fine, perfectly dry, hair-powder. The more or less coloured appearance will now be painted on the white atoms, and presented its whole length and breadth to the eye of the spectator.
327
By this means we have prepared some diagrams, which will be found among the plates. In these the appearance is exhibited from its first origin, and by these the spectator can clearly comprehend why the luminous image is so much more powerfully coloured through prisms than through parallel mediums.
328 (212)
At the two opposite outlines of the image an opposite appearance presents itself, beginning from an acute angle; the appearance spreads as it proceeds further in space, according to this angle. On one side, in the direction in which the luminous image is moved, a violet border advances on the dark, a narrower blue edge remains next the outline of the image. On the opposite side a yellow border advances into the light of the image itself, and a yellow-red edge remains at the outline.
329 (213)
Here, therefore, the movement of the dark against the light, of the light against the dark, may he clearly observed.
330 (214)
The centre of a large object remains long uncoloured, especially with mediums of less density and smaller angles; but at last the opposite borders and edges touch each other, upon w
hich a green appears in the centre of the luminous image.
331 (215)
Objective experiments have been usually made with the sun’s image: an objective experiment with a dark object has hitherto scarcely been thought of. We have, however, prepared a convenient contrivance for this also. Let the large water-prism before alluded to be placed in the sun, and let a round pasteboard disk be fastened either inside or outside. The coloured appearance will again take place at the outline, beginning according to the usual law; the edges will appear, they will spread in the same proportion, and when they meet, red will appear in the centre. An intercepting square may be added near the round disk, and placed in any direction ad libitum, and the spectator can again convince himself of what has been before so often described.
332 (216)
If we take away these dark objects from the prism, in which case, however, the glass is to be carefully cleaned, and hold a rod or a large pencil before the centre of the horizontal prism, we shall then accomplish the complete immixture of the violet border and the yellow-red edge, and see only the three colours, the external blue, and yellow, and the central red.
333
If again we cut a long horizontal opening in the middle of a piece of pasteboard, fastened on the prism, and then cause the sunlight to pass through it, we shall accomplish the complete union of the yellow border with the blue edge upon the light, and only see yellow-red, green and violet. The details of this are further entered into in the description of the plates.
334 (217)
The prismatic appearance is thus by no means complete and final when the luminous image emerges from the prism. It is then only that we perceive its elements in contrast; for as it increases these contrasting elements unite, and are at last intimately joined. The section of this phenomenon arrested on a plane surface is different at every degree of distance from the prism; so that the notion of an immutable series of colours, or of a pervading similar proportion between them, cannot be a question for a moment.
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XXIV. Explanation of the Foregoing Phenomena.
335 (218)
As we have already entered into this analysis circumstantially while treating of the subjective experiments, as all that was of force there is equally valid here, it will require no long details in addition to show that the phenomena, which are entirely parallel in the two cases, may also be traced precisely to the same sources.
336 (219)
That in objective experiments also we have to do with circumscribed images, has been already demonstrated at large. The sun may shine through the smallest opening, yet the image of the whole disk penetrates beyond. The largest prism may be placed in the open sun-light, yet it is still the sun’s image that is bounded by the edges of the refracting surfaces, and produces the accessory images of this boundary. We may fasten pasteboard, with many openings cut in it, before the water-prism, yet we still merely see multiplied images which, after having been moved from their place by refraction, exhibit coloured edges and borders, and in these mere accessory images.
337 (235)
In subjective experiments we have seen that objects strongly relieved from each other produce a very lively appearance of colour, and this will be the case in objective experiments in a much more vivid and splendid degree. The sun’s image is the most powerful brightness we know; hence its accessory image will be energetic in proportion, and notwithstanding its really secondary dimmed and darkened character, must be still very brilliant. The colours thrown by the sun-light through the prism on any object, carry a powerful light with them, for they have the highest and most intense source of light, as it were, for their ground.
338
That we are warranted in calling even these accessory images semi-transparent, thus deducing the appearances from the doctrine of the semi-transparent mediums, will be clear to every one who has followed us thus far, but particularly to those who have supplied themselves with the necessary apparatus, so as to be enabled at all times to witness the precision and vivacity with which semi-transparent mediums act.
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XXV. Decrease of the Appearance of Colour.
339 (243)
If we could afford to be concise in the description of the decreasing coloured appearance in subjective cases, we may here be permitted to proceed with still greater brevity while we refer to the former distinct statement. One circumstance, only on account of its great importance, may be here recommended to the reader’s especial attention as a leading point of our whole thesis,
340 (244, 247)
The decline of the prismatic appearance must be preceded by its separation, by its resolution into its elements. At a due distance from the prism, the image of the sun being entirely coloured, the blue and yellow at length mix completely, and we see only yellow-red, green, and blue-red. If we bring the recipient surface nearer to the refracting medium, yellow and blue appear again, and we see the five colours with their gradations. At a still shorter distance the yellow and blue separate from each other entirely, the green vanishes, and the image itself appears, colourless, between the coloured edges and borders. The nearer we bring the recipient surface to Axe prism, the narrower the edges and borders become, till at last, when in contact with the prism, they are reduced to nothing.
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XXVI.Grey Objects.
341 (218)
We have exhibited grey objects as very important to our inquiry in the subjective experiments. They show, by the faintness of the accessory images, that these same images are in all cases derived from the principal object. If we wish here, too, to carry on the objective experiments parallel with the others, we may conveniently do this by placing a more or less dull ground glass before the opening through which the sun’s image enters. By this means a subdued image would be produced, which on being refracted would exhibit much duller colours on the recipient plane than those immediately derived from the sun’s disk; and thus, even from the intense sun-image, only a faint accessory image would appear, proportioned to the mitigation of the light by the glass. This experiment, it is true, will only again and again confirm what is already sufficiently familiar to us
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XXVII. Coloured Objects.
342 (260)
There are various modes of producing coloured images in objective experiments. In the first place, we can fix coloured glass before the opening, by which means a coloured image is at once produced; secondly, we can fill the water-prism with coloured fluids; thirdly, we can cause the colours, already produced in their full vivacity by the prism, to pass through proportionate small openings in a tin plate, and thus prepare small circumscribed colours for a second operation. This last mode is the most difficult; for owing to the continual progress of the sun, the image cannot be arrested in any direction at will. The second method has also its inconveniences, since not all coloured liquids can be prepared perfectly bright and clear. On these accounts the first is to be preferred, and deserves the more to be adopted because natural philosophers have hitherto chosen to consider the colours produced from the sun-light through the prism, those produced through liquids and glasses, and those which are already fixed on paper or cloth, as exhibiting effects equally to be depended on, and equally available in demonstration.
343
As it is thus merely necessary that should be coloured; so the large water-prism before alluded to affords us the best means of effecting this. A pasteboard screen may be contrived to slide before the large surfaces of the prism, through which, in the first instance, the light passes uncoloured. In this screen openings of various forms may be cut, in order to produce different images, and consequently different accessory images. This being done, we need only fix coloured glasses before the openings, in order to observe what effect refraction produces on coloured images in an objective sense.
344
A series of glasses may be prepared in a mode similar to that
before described (284); these should be accurately contrived to slide in the grooves of the large water-prism. Let the sun then shine through them, and the coloured images refracted upwards will appear bordered and edged, and will vary accordingly: for these borders and edges will be exhibited quite distinctly on some images, and on others will be mixed with the specific colour of the glass, which they will either enhance or neutralize. Every observer will be enabled to convince himself here again that we have only to do with the same simple phenomenon so circumstantially described subjectively and objectively.
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XXVIII. Achromatism and Hyperchromatism.
345 (285, 290)
It is possible to make the hyperchromatic and achromatic experiments objectively as well as subjectively. After what has been already stated, a short description of the method will suffice, especially as we take it for granted that the compound prism before mentioned is in the hands of the observer.
346
Let the sun’s image pass through an acute-angled prism of few degrees, prepared from crown-glass, so that the spectrum be refracted upwards on an opposite surface; the edges will appear coloured, according to the constant law, namely, the violet and blue above and outside, the yellow and yellow-red below and within the image. As the refracting angle of this prism is undermost, let another proportionate prism of flint-glass be placed against it, with its refracting angle uppermost. The sun’s image will by this means be again moved to its place, where, owing to the excess of the colouring power of the prism of flint-glass, it will still appear a little coloured, and, in consequence of the direction in which it has been moved, the blue and violet, will now appear underneath and outside, the yellow and yellow-red above and inside.