Works of Johann Wolfgang von Goethe
Page 310
347
If the whole image be now moved a little upwards by a proportionate prism of crown-glass, the hyperchromatism will disappear, the sun’s image will be moved from its place, and yet will appear colourless.
348
With an achromatic object-glass composed of three glasses, this experiment may be made step by step, if we do not mind taking out the glasses from their setting. The two convex glasses of crown-glass in contracting the sun’s image towards the focus, the concave glass of flint-glass in dilating the image beyond it, exhibit at the edges the usual colours. A convex glass united with a concave one, exhibits the colours according to the law of the latter. If all three glasses are placed together, whether we contract the sun’s image towards the focus, or suffer it to dilate beyond the focus, coloured edges never appear, and the achromatic effect intended by the optician is, in this case, again attained.
349
But as the crown-glass has always a greenish tint, and as a tendency to this hue may be more decided in large and strong object-glasses, and under certain circumstances produce the compensatory red, (which, however, in repeated experiments with several instruments of this kind did not occur to us,) philosophers have resorted to the most extraordinary triodes of explaining such a result; and having been compelled, in support of their system, theoretically to prove the impossibility of achromatic telescopes, have felt a kind of satisfaction in having some apparent ground for denying so great an improvement. Of this, however, we can only treat circumstantially in our historical account of these discoveries.
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XXIX. Combination of Surjective and Orjective Experiments.
350
Having shown above (318) that refraction, considered objectively and subjectively, must act in opposite directions, it will follow that if we combine the experiments, the effects will reciprocally destroy each other.
351
Let the sun’s image be thrown upwards on vertical plane, through a horizontally-placed prism. If the prism is long enough to admit of the spectator also looking through it, he will see the image elevated by the objective refraction again depressed, and in the same place in which it appeared without refraction.
352
Here a remarkable case presents itself, but at the same time a natural result of a general law. For since, as often before stated, the objective sun’s image thrown on the vertical plane is not an ultimate or unchangeable state of the phenomenon, so in the above operation the image is not only depressed when seen through the prism, but its edges and borders are entirely robbed of their hues, and the spectrum is reduced to a colourless circular form.
353
By employing two perfectly similar prisms placed next each other, for this experiment, we can transmit the sun’s image through one, and look through the other.
354
If the spectator advances nearer with the prism through which he looks, the image is again elevated, and by degrees becomes coloured according to the law of the first prism. If he again retires till he has brought the image to the neutralized point, and then retires still farther away, the image, which had become round and colourless, moves still more downwards and becomes coloured in the opposite sense, so that if we look through the prism and upon the refracted spectrum at the same time, we see the same image coloured according to subjective and objective laws.
355
The modes in which this experiment may be varied are obvious. If the refracting angle of the prism, through which the sun’s image was objectively elevated, is greater than that of the prism through which the observer looks, he must retire to a much greater distance, in order to depress the coloured image so low on the vertical plane that it shall appear colourless, and vice versa.
356
It will be easily seen that we may exhibit achromatic and hyperchromatic effects in a similar manner, and we leave it to the amateur to follow out such researches more fully. Other complicated experiments in which prisms and lenses are employed together, others again, in which objective and subjective experiments are variously intermixed, we merle for occasion, when it will be our object to trace such effects to the simple phenomena with which we are now sufficiently familiar.
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XXXX. Transition.
357
In looking back on the description and analysis of dioptrical colours, we do not repent either that we have treated them so circumstantially, or that we have taken them into consideration before the other physical colours, out of the order we ourselves laid down. Yet, before we quit this branch of our inquiry, it may be as well to state the reasons that have weighed with us,
358
If some apology is necessary for having treated the theory of the dioptrical colours, particularly those of the second class, so diffusely, we should observe, that the exposition of any branch of knowledge is to be considered partly with reference to the intrinsic importance of the subject, and partly with reference to the particular necessities of the time in which the inquiry is undertaken. In our own case we were forced to keep both these considerations constantly in view. In the first place we had to state a mass of experiments with our consequent convictions; next, it was our especial aim to exhibit certain phenomena (known, it is true, but misunderstood, and above all, exhibited in false connection,) in that natural and progressive development which is strictly and truly conformable ‘to observation; in order that hereafter, in our polemical or historical investigations, we might be enabled to bring a complete preparatory analysis to bear on, and elucidate, our general view. The details we have entered into were on this account unavoidable; they may be considered as a reluctant consequence of the occasion. Hereafter, when philosophers will look upon a simple principle as simple, a combined effect as combined; when they will acknowledge the first elementary, and the second ‘complicated states, for what they are; then, indeed, all this statement may be abridged to a narrower form; a labour which, should we ourselves not be able to accomplish it, we bequeath to the active interest of contemporaries and posterity.
359
With respect to the order of the chapters, it should, be remembered that natural phenomena, which are even allied to each other, are not connected in any particular sequence or constant series; their efficient causes act in a narrow circle, so that it is in some sort indifferent what phenomenon is first or last considered; the main point is, that all should be as far as possible present to us, in order that we may embrace them at last from one point of view, partly according to their nature, partly according to generally received methods.
360
Yet, in the present particular instance, it may be asserted that the dioptrical colours are justly placed at the head of the physical colours; not only on account of their striking splendour and their importance in other respects, but because, in tracing these to their source, much was necessarily entered into which will assist our subsequent enquiries.
361
For, hitherto, light has been considered as a kind of abstract principle, existing and acting independently; to a certain extent self-modified, and on the slightest cause, producing colours out of itself. To divert the votaries of physical science from this mode of viewing the subject; to make them attentive to the fact, that in prismatic and other appearances we have not to do with light as an uncircumscribed and modifying principle, but as circumscribed and modified; that we have to do with a luminous image; with images or circumscribed objects generally, whether light or dark: this was the purpose we had in view, and such is the problem to be solved.
362
All that takes place in dioptrical cases, — especially those of the second class which are connected with the phenomena of refraction, — is now sufficiently familiar to us, and will serve as an introduction to what follows.
363
Catoptrical appearances remind us of the physiological logical phenomena, but as we ascribe a more objective character to the former, we thought oursel
ves justified in classing them with the physical examples. It is of importance, however, to remember that here again it is not light, in an abstract sense, but a luminous image that we have to consider.
364
In proceeding onwards to the paroptrical class, the reader, if duly acquainted with the foregoing facts, will be pleased to find himself once more in the region of circumscribed forms. The shadows of bodies, especially, as secondary images, so exactly accompanying the object, will serve greatly to elucidate analogous appearances.
365
We will not, however, anticipate these statements, but proceed as heretofore in what we consider the regular course.
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XXXI. Catoptrical Colours.
366
Catoptrical colours are such as appear in consequence of a mirror-like reflection. We assume, in the first place, that the light itself, .as well as the ,surface from which it is reflected, is perfectly colourless. In this sense the appearances in question come under the head of physical colours. They arise in consequence of reflection, as we found the dioptrical colours of the second class appear by means of refraction. Without further general definitions, we turn our attention at once to particular cases, and .to the conditions which are essential to the exhibition of these phenomena.
367
If we unroll a coil of bright steel-wire, and after suffering it to spring confusedly together again, place it at a window in the light, we shall see the prominent parts of the circles and convolutions illumined, but neither resplendent nor iridescent. But if the sun shines on the wire, this light will be condensed into a point, and we perceive a small resplendent image of the sun, which, when seen near, exhibits no colour. On retiring a little, however, and fixing the eyes on this refulgent appearance, we discern several small mirrored suns, coloured in the most varied manner; and although the impression is that green and red predominate, yet, on a more accurate inspection, we find that the other colours are also present,
368
If we take an eye-glass, and examine the appearance through it, we find the colours have vanished, as well as the radiating splendour in which they were seen, and we perceive only the small luminous points, the repeated images of the sun. We thus find that the impression is subjective in its nature, and that the appearance is allied to those which we have adverted to under the name of radiating halos (100).
369
We can, however, exhibit this phenomenon objectively. Let a piece of white paper be fastened beneath a small aperture in the lid of a camera-obscura, and when the sun shines through this aperture, let the confusedly-rolled steel-wire be held in the light, so that it be opposite to the paper. The sun-light will impinge on and in the circles of the wire, and will not, as in the concentrating lens of the eye, display itself in a point; but, as the paper can receive the reflection of .the light in every part of its surface will be seen in hair-like lines, which are also iridescent.
370
This experiment is purely catoptrical; for as we cannot imagine that the light penetrates the surface of the steel, and thus undergoes a change, we are soon convinced that we have here a mere reflection which, in its subjective character, is connected with the theory of faintly acting lights, and the after-image of dazzling lights, and as far as it can be considered objective, announces even in the minutest appearances, a real effect, independent of the action and reaction of the eye.
371
We have seen that to produce these effects not merely light but a powerful light is necessary; that this powerful light again is not an abstract and general quality, but a circumscribed light, a luminous image. We can convince ourselves still further of this by analogous cases.
372
A polished surface of silver placed in the sun reflects a dazzling light, but in this case no colour is seen. If, however, we slightly scratch the surface, an iridescent appearance, in which green and red are conspicuous, will be exhibited at a certain angle. In chased and carved metals the effect is striking: yet it may be remarked throughout that, in order to its appearance, some form, some alternation of light and dark must co-operate with the reflection; thus a window-bar, the stem of a tree, an accidentally or purposely interposed object produces a perceptible effect. This appearance, too, may be exhibited objectively in the camera-obscura.
373
If we cause a polished plated surface to he so acted on by aqua fortis that the copper within is touched, and the surface itself thus rendered rough, and if the sun’s image be then reflected from it, the splendour will be reverberated from every minutest prominence, and the surface will appear iridescent. So, if we hold a sheet of black unglazed paper in the sun, and look at it attentively, it will be seen to glisten in its minutest points with the most vivid colours.
374
All these examples are referable to the same conditions. In the first case the luminous image is reflected from a thin line; in the second probably from sharp edges; in the third from very small points. In all a very powerful and circumscribed light is requisite. For all these appearances of colour again it is necessary that the eye should be at a due distance from the reflecting points.
375
If these observations are made with the microscope, the appearance will be greatly increased in force and splendour, for we then see the smallest portion of the surfaces, lit by the sun, glittering in these colours of reflection, which, allied to the hues of refraction, now attain their highest degree of brilliancy. In such cases we may observe a vermiform iridescence on the surface of organic bodies, the further description of which will be given hereafter.
376
Lastly, the colours which are chiefly exhibited in reflection are red and green, whence we may ‘infer that the linear appearance especially consists of a thin line of red, bounded by blue on one side and yellow on the other. If these triple lines approach very near together, the intermediate space must appear green; a phenomenon which will often occur to us as we proceed.
377
We frequently meet with these colours in nature. The colours of the spider’s web might be considered exactly of the same class with those reflected from the steel wire, except that the non-translucent quality of the former is not so certain as in the case of steel; on which account some have been inclined’ to class the colours of the spider’s web with the phenomena of refraction.
378
In mother-of-pearl we perceive infinitely fine organic fibres and lamellae in juxtaposition, from which, as from the scratched silver before alluded to, varied colours, but especially red and green, may arise.
379
The changing colours of the plumage of birds may also be mentioned here, although in all organic instances a chemical principle and an adaptation of the colour to the structure may be assumed; considerations to which we shall return in treating of chemical colours.
380
That the appearances of objective halos also approximate catoptrical phenomena will be readily admitted, while we again do not deny that refraction as well may here come into the account. For the present we restrict ourselves to one or two observations; hereafter we may be enabled to make a fuller application of general principles to particular examples.
381
We first call to mind the yellow and red circles produced on a white or grey wall by a light placed near it (88). Light when reflected appears subdued, and a subdued light excites the impression of yellow, and subsequently of red.
382
Let the wall be illumined by a candle placed quite close to it. The farther the light is diffused the fainter it becomes; but it is still the effect of the flame, the continuation of its action, the dilated effect of its image. We might, therefore, very fairly call these circles reiterated images, because they constitute the successive boundaries of the action of the light, and yet at the same time only present an extended image of the flame.
383
If the sky is white and luminous round the sun owing to the atmosp
here being filled with light vapours; if mists or clouds pass before the moon, the reflection of the disk mirrors itself in them; the halos we then perceive are single or double, smaller or greater, sometimes very large, often colourless, sometimes coloured,
384
I witnessed a very beautiful halo round the moon the 15th of November, 1799, when the barometer stood high; the sky was cloudy and vapoury. The halo was completely coloured, and the circles were concentric round the light as in subjective halos. That this halo was objective I was presently convinced by covering the moon’s disk, when the same circles were nevertheless perfectly visible.
385
The different extent of the halos appears to have a relation with the, proximity or distance of the vapour from the eye of the observer.
386
As window-panes lightly breathed upon increase the brilliancy of subjective halos, and in some degree give them an objective character, so, perhaps, with a simple contrivance in winter, during a quickly freezing temperature, a more exact definition of this might be arrived at,
387
How much reason we have in considering these circles to insist on the image and its effects, is apparent in the phenomenon of the so-called double suns. Similar double images always occur in certain points of halos and circles, and only present in a circumscribed form what takes place in a more general way in the whole circle. All this will be more conveniently treated in connexion with the appearance of the rainbow, — Note Q.
388
In conclusion it is only necessary to point out the affinity between the catoptrical and paroptical colours. We call those paroptical colours which appear when the light passes by the edge of an opaque colourless body. How nearly these are allied to the dioptrical colours of the second class will be easily seen by those who are convinced with us that the colours of refraction take place only at the edges of objects. The affinity again between the catoptrical and par-optical colours will be evident in the following chapter.