Visual Illusions: Their Causes, Characteristics and Applications

by Matthew Luckiesh

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 altitudes on occasions when the sky was much darker than when viewed from the earth’s surface. Dember and Uibe assumed the apparent shape as a part of a sphere (justifying this assumption 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 altitude 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 cumulus clouds are present. The bases of these vary in height, but are found at altitudes 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 altitudes. 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-glasses 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 association 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 space 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 altitudes 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 altitude. 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.

Fig. 78.—An accurate tracing from a photograph (continual exposure) of the moon rising.