Visual Illusions Part 9

The angle at which the beam must diverge to appear parallel to an observer depends upon the distance of the observer from the searchlight. A beam which seems parallel to a person close to it will not appear so at a distance. This fact probably accounts for the difficulties encountered during "searchlight drill" in the army in getting a beam which satisfied both the private operating the lamp and the officer down the field as to its parallelity.

To summarize, the apparent abrupt ending of a searchlight beam is purely an optical illusion. It really has no ending; it extends to infinity.

XI

NATURE

Visual illusions abound everywhere, and there are a number of special interest in nature. Inasmuch as these are representative of a wide range of conditions and are usually within the possible experience of nearly everyone daily, they appear worthy of special consideration. Some of these have been casually mentioned in other chapters but further data may be of interest. No agreement has been reached in some cases in the many suggested explanations and little or no attempt of this character will be made in the following paragraphs. Many illusions which may be seen in nature will be pa.s.sed by because their existence should be obvious after reading the preceding chapters. For example, a tree appears longer when standing than after it has been felled for the same reason that we overestimate vertical lines in comparison with horizontal ones. The apparent movement of the sun, moon, and stars, when clouds are floating past, is a powerful, though commonplace, illusion but we are more specifically interested in static illusions. However, it is of interest to recall the effect of involuntary eye-movements or of fluctuation in fixation because this factor in vision is important in many illusions. It is demonstrated by lying face upward on a starlit night and fixing the gaze upon a star. The latter appears to move more or less jerkily over its dark background. The magnitude and involuntary nature of these eye-movements is demonstrated in this manner very effectively.

The effect sometimes known as aerial perspective has been mentioned heretofore. The atmosphere is not perfectly transparent or colorless and is not h.o.m.ogeneous from an optical standpoint. It scatters rays of the shorter wave-lengths more than those of the longer wave-lengths. Hence it appears of a bluish tint and anything seen through great distances of it tends toward a reddish color. The blue sky and the redness of the setting sun are results of this cause. Distant signal-lights are reddened, due to the decrease in the rays of shorter wave-length by scattering. Apparently we have come to estimate distance to some extent through the amount of blurring and tinting superposed upon the distant scene.

In the high Rockies where the atmosphere is unusually clear, stretches of fifty miles of atmosphere lying between the observer and the distant peaks will show very little haze. A person inexperienced in the region is likely to construe this absence of haze as a shorter distance than the reality and many amusing incidents and ludicrous mistakes are charged against the tenderfoot in the Rockies. After misjudging distance so often to his own discomfiture a tourist is said to have been found disrobing preparatory to swimming across an irrigation ditch. He had lost confidence in his judgment of distance and was going to a.s.sume the risk of jumping across what appeared to be a ditch but what might be a broad river. Of course, this story might not be true but it serves as well as any to emphasize the illusion which arises when the familiar haze is not present in strange territory.

It is a common experience that things "loom in a fog," that is, that they appear larger than they really are. An explanation which has been offered is that of an "excess of aerial perspective" which causes us to overestimate distance and therefore to overestimate size. If this explanation is correct, it is quite in the same manner that in clear atmosphere in the mountains we underestimate distance and, consequently, size. However, another factor may enter in the latter case, for the illusion is confined chiefly to newcomers; that is, in time one learns to judge correctly. On entering a region of real mountains the first time, the newcomer's previous experience with these formations is confined to hills relatively much smaller. Even allowing considerably for a greater size when viewing the majestic peaks for the first time, he cannot be expected to think in terms of peaks many times larger than his familiar hills. Thus underestimating the size of the great peaks, he underestimates the distance. The rarity of the atmospheric haze aids him in making this mistake. This is not offered as a subst.i.tute for aerial perspective as the primary cause of the illusion but it appears to the author that it is a cause which must be taken into account.

The apparent form of the sky has attracted the attention of many scientific investigators for centuries. There are many conflicting opinions as to the causes of this appearance of form, but there is general agreement that the sky appears usually as a flattened vault. The sky is bright, due to scattering of light by actual particles of solid matter and moisture and possibly by molecules of gas. Lack of optical h.o.m.ogeneity due to varying refractive index is likely to be partially responsible. Usually a prominent layer of haze about a mile in thickness (although this varies considerably) lies next to the earth's surface. The top of this haze is fairly well defined as aerial travelers know, but the sky above is still far from black, indicating scattered light and illuminated particles still higher. As one continues to ascend, thereby leaving more and more of the luminous haze behind, the sky becomes darker and darker. Often at alt.i.tudes of four or five miles the sky is very dark and the sun is piercingly bright. Usually there is little or no bright haze adjacent to the sun at these high alt.i.tudes as is commonly seen from the earth's surface. At these high alt.i.tudes the author is not conscious of a flattened vault as at the earth's surface but the illusion of a hemispherical dome still persists.

There is some agreement that the dome of the sky appears less depressed at the zenith by night than by day. This is in accord with the author's observation at very high alt.i.tudes on occasions when the sky was much darker than when viewed from the earth's surface. Dember and Uibe a.s.sumed the apparent shape as a part of a sphere (justifying this a.s.sumption to their satisfaction) and obtained estimates of the apparent depression at the zenith. They estimated the middle point of the arc from the zenith to the horizon and then measured the angular alt.i.tude of that point. They found that the degree of clearness of the sky has considerable influence upon the apparent height and they state that the sky appears higher in the sub-tropics than in Germany. On very clear moonless nights they found that the shape of the sky-dome differs little from that of a hemisphere. They concluded that the phenomenon is apparently due to optical conditions of the atmosphere which have not been determined.

It is of interest to note the appearance of the sky when c.u.mulus clouds are present. The bases of these vary in height, but are found at alt.i.tudes from three to five thousand feet. They appear to form a flat roof of clouds bending downward at the horizon, thus giving the appearance of a vaulted but flattened dome. This apparent shape does not differ much in clear weather, perhaps due largely to the accustomedness of the eye and to the degradation of color from blue to gray toward the horizon. Furthermore the lower sky is usually much brighter than the zenith and the latter being darker appears to hang lower. It is of interest to note how persistent is the illusion of a flattened dome, for when one rises rapidly in the air and, within a few minutes, is on the level with the clouds or the dense low-lying haze, he is mildly surprised to find these are levels and not vaulted roofs. Despite the fact that by many previous experiences he has learned what to expect, the feeling of mild surprise is born each time on ascending rapidly.

The appearance of the flattened vault of the sky is held by some to account for the apparent enlargement of the sun, moon, and the constellations at the horizon. That is, they appear more distant at the horizon and we instinctively appraise them as being larger than when they are at higher alt.i.tudes. It is certain that these heavenly bodies do appear much larger when they are rising or setting than when they are nearer the zenith. In fact, this is one of the most remarkable and surprising illusions which exist. Furthermore this apparent enlargement has been noted universally, still many persons have attributed it to an actual optical magnification. Although we are more familiar with this enlargement in connection with the sun and moon, it still persists with the constellations. For example, Orion is apparently very large; in fact, this is the origin of the name. That this enlargement is an illusion can be shown in several ways but that it is solely due to the influence of the apparent flattened form of the sky may be doubted. Certainly the moon appears greatly enlarged while near the horizon, even when there is doubt as to an appreciable appearance of flattening of the sky-dome.

Many peculiar conditions and prejudices must be taken into account. For example, if various persons are asked to give an idea of how large is the disk of the sun or moon, their answers would vary usually with the head of a barrel as the maximum. However, the size of a tree at a distant sky-line might unhesitatingly be given as thirty feet. At the horizon we instinctively compare the size of the sun, moon, and constellations with hills, trees, houses, and other objects, but when the former are high toward the zenith in the empty sky we may judge them in their isolated position to be nearer, hence smaller.

Normally the retinal image grows larger as the object approaches, but this same sensation also arises when an object grows in size without altering its distance. If the moon be viewed through field-gla.s.ses the image is larger than in the case of the unaided eyes, but it is quite common for observers to state that it appears smaller. The enlargement may be interpreted as approach and inasmuch as we, through habit, allow for enlargement as an object approaches, we also must reduce it in our imagination to its natural size. Perhaps in this case we overdo this reduction.

James states that the increased apparent size of the moon near the horizon "is a result of a.s.sociation and probability. It is seen through vaporous air and looks dimmer and duskier than when it rides on high; and it is seen over fields, trees, hedges, streams, and the like, which break up the intervening s.p.a.ce and makes us the better realize the latter's extent."

Both these causes may make the moon seem more distant when it is at low alt.i.tudes and as its visual angle grows less, we may think that it must be a larger body and we so perceive it. Certainly it looks particularly large when a well-known object is silhouetted against its disk.

Before proceeding further with explanations, it may be of interest to turn to Fig. 78 which is an accurate tracing of the path of the moon's image across a photographic plate. The camera was placed in a fixed position and the image of the moon's disk on rising was accurately focused on a panchromatic plate. A dense red filter was maintained over the lens throughout in order to eliminate the effect of selective absorption of the atmosphere. But the slightest enlargement was detected in the width of the path near the horizon as compared with that at the highest alt.i.tude. This copy was made because it was thought better for reproduction than the photograph which would require a half-tone. This is positive evidence that the phenomenon is an illusion.

[Ill.u.s.tration: Fig. 78.--An accurate tracing from a photograph (continual exposure) of the moon rising.]

Similarly Fig. 79 is a copy of a negative of several exposures of the sun.

Owing to the greater brightness, continuous exposure was not considered feasible. A panchromatic plate and red filter was used as in the case of the moon. The various exposures were made without otherwise adjusting the camera. Again no enlargement at the horizon was found.

[Ill.u.s.tration: Fig. 79.--Accurate tracings from a photograph (short exposures at intervals) of the sun setting.]

Although the foregoing is conclusive evidence of the illusory character of the enlargement there are other ways of making measurements. On viewing the sun at the horizon a bright after-image is obtained. This may now be projected upon the sky as a background at any desired alt.i.tude. It will appear much smaller at the zenith than the sun appears at the horizon.

Certainly this is a simple and conclusive demonstration of the illusion.

In this case the after-image of the sun or the sun itself will usually appear at least twice as large as the after-image at the zenith.

If the variation in the position of the eyes is held to account for the illusion, this explanation may be supported by using a horizontal telescope with adjustable cross-hairs, and a mirror. By varying the position of the latter the disk of the sun may be measured at any alt.i.tude without varying the position of the eye. When everything is eliminated from the field but the moon's disk, it is found to be constant in size.

However, this is not conclusive evidence that the variation in the position of the line of sight accounts for the illusion.

As a demonstration of the absence of enlargement of the size of the moon near the horizon some have brought forward measurements of the lunar circles and similar phenomena. These are said to be unaffected by the alt.i.tude of the moon except for refraction. But even this does not change the horizontal diameter and actually diminishes the vertical one. The moon is further away when near the horizon than when at the zenith, the maximum increase in distance being one-half the diameter of the earth. This would make the moon appear about one-sixtieth, or one-half minute of arc smaller at the horizon than at the zenith. This is not only in the wrong direction to aid in accounting for the apparent enlargement, but it is so slight as to be imperceptible to the unaided eye.

Nearly two centuries ago Robert Smith and his colleagues concluded that the sky appears about three times as far away at the horizon as at the zenith. They found that the relative apparent diameters of the sun and of the moon varied with alt.i.tude as follows:

Alt.i.tude Relative apparent diameter

0 deg. (horizon) 100 15 " 68 30 " 50 45 " 40 60 " 34 75 " 31 90 " (zenith) 30

[Ill.u.s.tration: Fig. 80.--Explanation offered by Smith of the apparent enlargement of heavenly bodies near the horizon.]

They also found a similar relation between the alt.i.tude and the apparent size of constellations. Fig. 80 is a reproduction of a diagram which Smith submitted as ill.u.s.trating the cause of the illusion of apparent enlargement of heavenly bodies near the horizon. If the sky seems to be a flattened vault, the reason for the apparent decrease in the size of the sun, the moon, or the constellations, as they approach the zenith, is suggested by the diagram.

It has also been suggested that such illusions as those shown in Figs. 10 and 19 are a.s.sociated with that of apparent enlargement of heavenly bodies near the horizon. It will be left to the reader to decide whether or not there is any similarity or relation.

Zoth appears to have proved, to his own satisfaction at least, that the chief factors are not aerial perspective, the apparent curvature or form of the sky, and the comparison of the sun or moon with objects of known size. He maintained that the illusion of apparent decrease in size as these bodies increase in alt.i.tude is due to the necessary elevation of the eye. No available experimental evidence seems to refute his statement. In fact, Guttman's experiments seem to confirm it to some extent. The latter found that there was an apparent diminution in the size of objects of several per cent, in objects slightly more than a foot distant from the eyes, as they were raised so that the line of vision changed from horizontal to an angle of forty degrees. The magnitude of this diminution is not sufficient to promote the acceptance of elevation of the eyes as a primary cause of the illusion in respect to the heavenly bodies.

Notwithstanding arguments to the contrary, it is difficult to eliminate aerial perspective and the apparent form of the sky as important factors.

That no explanation of this illusion has been generally accepted indicates the complexity of the causes. Certainly the reddish coloration of the sun and moon near the horizon and the contrast with the misty atmosphere combined with the general vague aspect of the atmosphere contribute something if no more than a deepening of the mystery. Variations in the transparency and brightness of the air must play some part.

In discussing the great illusions of nature, it appears appropriate to introduce the mirage. This is not due to an error of sense of judgment.

The eye sees what is presented but the inversions and other peculiar effects are due to variations in the refractive index of the atmosphere.

These variations account for the appearance of "lakes" in arid deserts, of the inverted images of ships and icebergs on the sea and of "pools of water" on pavements. The refractive index of the atmosphere is continually changing, but the changes are chiefly of two types: (1) those due to irregular heating and (2) those due to normal variation with alt.i.tude. The former type are particularly responsible for mirages.

[Ill.u.s.tration: Fig. 81.--Explanation of a common mirage.]

A common type of mirage is ill.u.s.trated in Fig. 81. This is often visible on deserts where the hot sand causes the adjacent layer of air to expand and therefore, the refractive index to increase. This layer of air then may be considered to operate like an inverted prism. The rays of light close to the earth are bent convex to the earth and the curvature of those higher up may be reversed. The reason that an object may appear double, or as if mirrored by the surface of a nearby pond, is clearly shown in the ill.u.s.tration.

Similar atmospheric conditions are found sometimes over pavements and over bodies of water. As one rides along in an automobile ascending an incline, if he closely observes at the moment the line of sight is just on the level of the pavement, he will often be rewarded by the sight of a mirage.

An approaching pedestrian may have no feet (they are replaced by a bit of sky) and the distant pavement will appear to contain pools of water on its surface.

Sometimes on deserts, over ice fields, or on northern seas, mirages are of the inverted type. A horseman or ship may appear suspended in the air in an inverted position. When the density of the air is great enough so that only the upper rays reach the eye, the object will be seen inverted and far above the surface upon which nothing is seen. Many modifications of these types are possible through variations in the refractive indices of various strata of air. Sometimes the air is stratified horizontally and even vertically, which results in magnification as well as other peculiar effects.

As one rides over the desert in a rapidly moving train or automobile these vagaries of nature are sometimes very striking, because the speed of motion will make the effects of the varying refractive indices more marked. A distant foothill may appear to float in the air or to change its shape very rapidly. An island surrounded by quiet air and water may appear like a huge mushroom barely supported by a stem.

Arctic mirages are no less wonderful than those of the hot barren deserts.

While traveling along over the ice and snow distant white peaks may a.s.sume the most fantastic shapes. At first they may appear flattened like a table-land and then suddenly they may stretch upward like spires. They may shrink then spread like huge mushrooms supported by the stalk-like bases and stretching out laterally. Suddenly they may shoot upward into another series of pinnacles as if another range had suddenly arisen. Such antics may go on for hours as one travels along a frozen valley. Even a change of position of the eyes accompanying a change from erect to lying down may cause remarkable contortions of the distant mountains and one is reminded of the psalmist's query, "Why hop ye so, ye hills?"

Although not an illusion but a physical reality, it is of interest in pa.s.sing to note the colored halo or aureole surrounding the shadows of objects cast by the sun against a cloud, fog, or jet of steam. The most wonderful effects are seen by the aerial traveler over a bank of clouds when the upper sky is clear. For example, the shadow of the aircraft cast by the sun upon a dense layer of clouds is surrounded by a halo or aureole of the colors of the rainbow. The phenomenon is purely optical, involving diffraction of light. A well-known example of this is the "Spectre of the Brocken."

XII

PAINTING AND DECORATION

In the arts where colors, brightnesses, contrasts, lines, forms, and perspectives mean so much, it is obvious that visual illusions are important. Sometimes they are evils which must be suppressed; in some cases they are boons to the artist if he is equal to the task of harnessing them. Ofttimes they appear unheralded and unexpected. The existence of visual illusions is sufficient to justify the artist's pride in his "eye" and his dependence upon his visual judgment rather than upon what he knows to be true. However true this may be, knowledge is as useful to the artist as to anyone else. The artist, if he is to produce art, is confronted with the tremendous task of perfecting an imperfect nature and he is handicapped with tools inferior to those which nature has at her disposal. He must deal with reflected lights from earthly materials.