Works of Johann Wolfgang von Goethe
Page 306
184
Objects seen through mediums more or less transparent do not appear to us in the place which they should occupy according to the laws of perspective. On this fact the dioptrical colours of the second class depend.
185
Those laws of vision which admit of being expressed in mathematical formulae are based on the principle that, as light proceeds in straight lines, it must be possible to draw a straight line from the eye to any given object in order that it be seen. If, therefore, a case arises in which the light arrives to us in a bent or broken line, that we see the object by means of a bent or broken line, we are at once informed that the medium between the eye and the object is denser, or that it has assumed this or that foreign nature.
186
This deviation from the law of right-lined vision is known by the general term of refraction; and, although we may take it for granted that our readers are sufficiently acquainted with its effects, yet we will here once more briefly exhibit it in its objective and subjective point of view.
187
Let the sun shine diagonally into an empty cubical vessel, so that the opposite side be illumined, but not the bottom: let water be then poured into this vessel, and the direction of the light will be immediately altered; for a part of the bottom is shone upon. At the point where the light enters the thicker medium it deviates from its rectilinear direction, and appears broken: hence the phenomenon is called the breaking (brechung) or refraction. Thus much of the objective experiment.
188
We arrive at the subjective fact in the following mode: — Let the eye be substituted for the sun: let the sight be directed in like manner diagonally over one side, so that the opposite inner side be entirely seen, while no part of the bottom is visible. On pouring in water the eye will perceive a part of the bottom; and this takes place without our being aware that we do not see in a straight line; for the bottom appears to us raised, and hence we give the term elevation (hebung) to the subjective phenomenon. Some points, which are particularly remarkable with reference to this, will be adverted to hereafter.
189
Were we now to express this phenomenon generally, we might here repeat, in conformity with the view lately taken, that the relation of the objects is changed or deranged.
190
But as it is our intention at present to separate the objective from the subjective appearances, we first express the phenomenon in a subjective form, and say, — a derangement or displacement of the object seen, or to be seen, takes place.
191
But that which is seen without a limiting outline may be thus affected’ without our perceiving the change. On the other hand, if what we look at has a visible termination, we have an evident indication that a displacement occurs. If, therefore, we wish to ascertain the relation or degree of such a displacement, we must chiefly confine ourselves to the alteration of surfaces with visible boundaries; in other words, to the displacement of circumscribed objects.
192
The general effect may take place through parallel mediums, for every parallel medium displaces the object by bringing it perpendicularly towards the eye. The apparent change of position is, however, more observable through mediums that are not parallel.
193
These latter may be perfectly spherical, or may be employed in the form of convex or concave lenses. We shall make use of all these as occasion may require in our experiments. But as they not only displace the object from its position, but alter it in various ways, we shall, in most cases, prefer employing mediums with surfaces, not, indeed, parallel with reference to each other, but still altogether plane, namely, prisms. These have a triangle for their base, and may, it is true, be considered as portions of a lens, but they are particularly available for our experiments, inasmuch as they very perceptibly displace the object from its position, without producing a remarkable distortion.
194
And now, in order to conduct our observations with as much exactness as possible, and to avoid all confusion and ambiguity, we confine ourselves at first to
SUBJECTIVE EXPERIMENTS,
in which, namely, the object is seen by the observer through a refracting medium. As soon as we have treated these in due series, the objective experiments will follow in similar order.
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XII. Refraction Without the Appearance of Colour.
195
Refraction can visibly take place without our perceiving an appearance of colour. To whatever extent a colourless or uniformly coloured surface may be altered as to its position by refraction, no colour consequent upon refraction appears within it, provided it has no outline or boundary. We may convince ourselves of this in various ways.
196
Place a glass cube on any larger surface, and look through the glass perpendicularly or obliquely, the unbroken surface opposite the eye appears altogether raised, but no colour exhibits itself. If we look at a pure grey or blue sky or a uniformly white or coloured wall through a prism, the portion of the surface which the eye thus embraces will be altogether changed as to its position, without our therefore observing the smallest appearance of colour.
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XIII. Conditions of the Appearance of Colour.
197
ALTHOUGH in the foregoing experiments we have found all unbroken surfaces, large or small, colourless, yet at the outlines or boundaries, where the surface is relieved upon a darker or lighter object, we observe a coloured appearance.
198
Outline, as well as surface, is necessary to constitute a figure or circumscribed object. We therefore express the leading fact thu: circumscribed objects must be displaced by refraction in order to the exhibition of an appearance of colour.
199
We place before us the simplest object, a light disk on a dark ground (A). A displacement occurs with regard to this object, if we apparently extend its outline from the centre by magnifying it. This may be done with any convex glass, and in this case we see a blue edge (B).
200
We can, to appearance, contract the circumference of the same light disk towards the centre by diminishing the object; the edge will then appear yellow (C). This may be done with a concave glass, which, however, should not be ground thin like common eye-glasses, but must have some substance. In order, however, to make this experiment at once with the convex glass, let a smaller black disk be inserted within the light disk on a black ground. If we magnify the black disk on a white ground with a convex glass, the same result takes place as if we diminished the white disk; for we extend the black outline upon the white, and we thus perceive the yellow edge together with the blue edge (D).
201
These two appearances, the blue and yellow, exhibit themselves in and upon the white: they both assume a reddish hue, in proportion as they mingle with the black.
202
In this short statement we have described the primordial phenomena of all appearance of colour occasioned by refraction. These undoubtedly may be repeated, varied, and rendered more striking; may be combined, complicated, confused; but, after all, may be still restored to their original simplicity.
203
In examining the process of the experiment just given, we find that in the one case we have, to appearance, extended the white edge upon the dark surface; in the other we have extended the dark edge upon the white surface, supplanting one by the other, pushing one over the other. We will now endeavour, step by step, to analyse these and similar cases.
204
If we cause the white disk to move, in appearance, entirely from its place, which can be done effectually by prisms, it will be coloured according to the direction in which it apparently moves, in conformity with the above laws. If we look at the disk a through a prism, so that it appear moved to 6, the outer edge will appear blue and blue-red, according to the law of the figure (fig, 1), the other edge being yellow, and yellow-red, according to the
law of the figure c (fig. 1). For in the first case the white figure is, as it were, extended over the dark boundary, and in the other case the dark boundary is passed over the white figure. The same happens if the disk is, to appearance, moved from a to c, from a to d, and so throughout the circle.
205
As it is with the simple effect, so it is with more complicated appearances. If we look through a horizontal prism (a b) at a white disk placed at some distance behind it at e, the disk will be raised to f, and coloured according to the above law. If we remove this prism, and look through a vertical one (c d) at the same disk, it will appear at h, and coloured according to the same law. If we place the two prisms one upon the other, the disk will appear displaced diagonally, in conformity with a general law of nature, and will be coloured as before; that is, according to its movement in the direction, e. g.:
206
If we attentively examine these opposite coloured edges, we find that they only appear in the direction of the apparent change of place. A round figure leaves us in some degree uncertain as to this: a quadrangular figure removes all doubt.
207
The quadrangular figure a moved in the direction a b, or a d, exhibits no colour on the sides which are parallel with the direction in which it moves: on the other hand, if moved in the direction a c, parallel with its diagonal, all the edges of the figure appear coloured.
208
Thus, a former position (203) is here confirmed; viz. to produce colour, an object must be so displaced that the light edges be apparently carried over a dark surface, the dark edge’s over a light surface, the figure over its boundary, the boundary over the figure. But if the rectilinear boundaries of a figure could be indefinitely extended by refraction, so that figure and background might only pursue their course next, but not over each other, no colour would appear, not even if they were prolonged to infinity.
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XIV. Conditions Under Which the Appearance of Colour Increases.
209
We have seen in the foregoing experiments that all appearance of colour occasioned by refraction depends on the condition that the boundary or edge be moved in upon the object itself, or the object itself over the ground, that the figure should be, as it were, carried over itself, or over the ground. And we shall now find that, by increased displacement of the object, the appearance of colour exhibits itself in a greater degree. This takes place in subjective experiments, to which, for the present, we confine ourselves, under the following conditions.
210
First, if, in looking through parallel mediums, the eye is directed more obliquely.
Secondly, if the surfaces of the medium are no longer parallel, but form a more or less acute
Thirdly, owing to the increased proportion of the medium, whether parallel mediums be increased in size, or whether the angle be increased, provided it does not attain a right angle,
Fourthly, owing to the distance of the eye armed with a refracting medium from the object to be displaced,
Fifthly, owing to a chemical property that may be communicated to the glass, and which may be afterwards increased in effect.
211
The greatest change of place, short of considerable distortion of the object, is produced by means of prisms, and this is the reason why the appearance of colour can be exhibited most powerfully through glasses of this form. Yet we will not, in employing them, suffer ourselves to be dazzled by the splendid appearances they exhibit, but keep the above well-established, simple principles calmly in view.
212
The colour which is outside, or foremost, in the apparent change of an object by refraction, is always the broader, and we will henceforth call this a border: the colour that remains next the outline is the narrower, and this we will call an edge.
213
If we move a dark boundary towards a light surface, the yellow broader border is foremost, and the narrower yellow-red edge follows close to the outline, If we move a light boundary towards a dark surface, the broader violet border is foremost, and the narrower blue edge follows.
214
If the object is large, its centre remains uncoloured. Its inner surface is then to be considered as unlimited (195): it is displaced, but not otherwise altered: but if the object is so narrow, that under the above conditions the yellow border can reach the blue edge, the space between the outlines will be entirely covered with colour. If we make this experiment with a white stripe on a black ground, the two extremes will presently meet, and thus produce green. We shall then see the following series of colours: —
Yellow-red.
Yellow.
Green
Blue
Blue-red.
215
If we place a black band, or stripe, on white paper, the violet border will spread till it meets the yellow-red edge. In this case the intermediate black is effaced (as the intermediate white was in the last experiment), and in its stead a splendid pure red will appear. The series of colours will now be as follows: -
Blue.
Blue-red
Red.
Yellow-red.
Yellow.
216
The yellow and blue, in the first case (214), can by degrees meet so fully, that the two colours blend entirely in green, and the order will then be,
Yellow-red.
Green.
Blue-red
In the second case (215), under similar circumstances, we see only
Blue.
Red.
Yellow.
This appearance is best exhibited by refracting the bars of a window when they are relieved on a grey sky.
217
In all this we are never to forget that this appearance is not to be considered as a complete or final state, but always as a progressive, increasing, and, in many senses, controllable appearance. Thus we find that, by the negation of the above five conditions, it gradually decreases, and at last disappears altogether.
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XV. Explanation of the Foregoing Phenomena.
218
Before we proceed further, it is incumbent on us to explain the first tolerably simple phenomenon, and to show its connexion with the principles first laid down, in order that the observer of nature may be enabled clearly to comprehend the more complicated appearances that follow.
219
In the first place, it is necessary to remember that we have to do with circumscribed objects. In the act of seeing, generally, it is the circumscribed visible which chiefly invites our observation; and in the present instance, in speaking of the appearance of colour, as occasioned by refraction, the circumscribed visible, the detached object solely occupies out attention.
220
For our chromatic exhibitions we can, however, divide objects generally into primary and secondary. The expressions of themselves denote what we understand by them, but our meaning will be rendered still more plain by what follows.
221
Primary objects may be considered firstly as original, as images which are impressed on the eye by things before it, and which assure us of their reality. To these the secondary images may be opposed as derived images, which remain in the organ when the object itself is taken away; those apparent after-images, which have been circumstantially treated of in the doctrine of physiological colours.
222
The primary images, again, may be considered as direct images, which, like the original impressions, are conveyed immediately from the object to the eye. In contradistinction to these, the secondary images may be considered as indirect, being only conveyed to us, as it were, at second-hand from a reflecting surface. These are the mirrored, or catoptrical, images, which in certain cases can also become double images:
223
When, namely, the reflecting body is, transparent, and has two parallel surfaces, one behind the other: in such a case, an image may be reflected to the eye from both surfaces, and thus aris
e double images, inasmuch as the upper image does not quite cover the under one: this may take place in various ways.
Let a playing-card be held before a mirror. We shall at first see’ the distinct image of the card, but the edge of the whole card, as well as that of every spot upon it, will be bounded on one side with a border, which is the beginning of the second reflection. This effect varies in different mirrors, according to the different thickness of the glass, and the accidents of polishing. If a person wearing a white waistcoat, with the remaining part of his dress dark, stands before certain mirrors, the border appears very distinctly, and in like manner the metal buttons on dark cloth exhibit the double reflection very evidently.
224
The reader who has made himself acquainted with our former descriptions of experiments (80) will the more readily follow the present statement. The window-bars reflected by plates of glass appear double, and by increased thickness of the glass, and a due adaptation of the angle of reflection, the two reflections may be entirely separated from each other. So a vase full of water, with a plane mirror-like bottom, reflects any object twice, the two reflections being more or less separated under the same conditions. In these cases it is to be observed that, where the two reflections cover each other, the perfect vivid image is reflected, but where they are separated’ they exhibit only weak, transparent, and shadowy images.
225
If we wish to know which is the under and which the upper image, we have only to take a coloured medium, for then a light object reflected from the under surface is of the colour of the medium, while that reflected from the upper surface presents the complemental colour. With dark objects it is the reverse; hence black and white surfaces may be here also conveniently employed. How easily the double images assume and evoke colours will here again be striking.
226
Thirdly, the primary images may be considered as principal images, while the secondary can be, as it were, annexed to these as accessory images. Such an accessory image produces a sort of double form; except that it does not separate itself from the principal object, although it may be said to be always endeavouring to do to. It is with secondary images of this last description that we have to do in prismatic appearances.