Optical Illusions

Optical illusions reveal the complexity of visual perception; a kinetic illusion is included here

Philosophers have suggested that our awareness was an exact, innate representation of the world around us, and psychologists that there was a self-aware consciousness within us responding in a unique and predictable way to sense impressions. Physicists and physiologists consider their job done when the material and objective relations have been fully described and understood. At first, they studied the refraction of the eye and the vibrations of the inner ear, then the structure of the nervous system, and now the electrical signals of the nervous system. There is a wide river of ignorance still to be crossed before perception is understood, and until it is, we can only observe its mysterious behaviour.

Optical illusions are badly named, since they are not unreal perceptions, but just misjudgments or ambiguous ones. The visual sense does the best it can to interpret the scene around us, but sometimes it fails. Two of the most striking failures are the stereoscopic perception of solid form on viewing a stereopair, and the appearance of continuous motion in the jerky image sequences of cinema. Both are pleasurable and desirable failures. Let us consider some more subtle ones in this article.

I recall with nostalgia and pleasure the many times I have watched a full autumn moon rise into the hazy evening sky over a wide eastern horizon. Its face is tawny, because the frequent inversions of autumn evenings hold the smoke of burning leaves close to the ground. She looks large, gigantic, larger than the trees and bluffs, or the houses and the highways. I think I should be able to see craters and mountains easily on the magnified disc, but I cannot. Sometimes even the familiar maria are hard to make out. The disc is round and seems perfectly circular, though I know it must be slightly flattened because of atmospheric refraction. As she rises, the haze is slowly left behind, and she becomes whiter and brighter, and the maria now look sharper. An hour or two later when I look, the moon is hard and bright and sharp, again in her normal celestial haunts after a visit to ours.

What I have seen is called the horizon illusion, known and remarked from antiquity. The rising moon seemed four times as large as the moon in the zenith. At first it seemed close, almost an earthly thing, but later its celestial nature took hold. Ptolemy explained that this was only apparent; the objective size of the moon was no different on the horizon than in the zenith. He said that although the celestial sphere was, indeed, a sphere, it appeared farther from the observer at the horizon, and bodies subtending the same angle appeared larger when presumed to be at a greater distance. A man at 1000 yards subtending the same angle as a man at 100 yards, would indeed appear to be a giant. It was the misjudgment of distance that caused the illusion. I feel that this explanation, though incomplete and unsatisfying, is still rather close to the best that can be said given our state of knowledge.

There have been very many explanations and analyses of the horizon illusion, many which accept Ptolemy's foundation, and seek to understand why distances to the horizon are misjudged, and others that look for some different cause. In fact, there is a book on the horizon illusion, and it has been the subject of more scientific papers than any other optical illusion. I will direct the reader to this voluminous literature for a deeper study, and only make some comments on the basis of my own observations.

When I see the moon near the horizon, it is clearly behind any objects I see there, clouds as well as houses and trees. Any object behind another is farther away and the moon is generally larger than anything else in sight in the distance. I do not know how strong the illusion is if, for example, the moon rises behind a uniform wall relatively close to me. I usually see it rising over vegetation and buildings. It looked remarkably large once when it rose behind a large office tower about a mile away, and was wider than that structure. The haze and creamy light help to make the moon seem a terrestrial thing, not the celestial body I know it is at a vast distance. The moon is, in fact, perceived as an earthly object, and in this guise can only seem gigantic. Constellations near the horizon share this expansion.

I seldom have seen the moon setting in the west in the dawn, since I usually sleep until well after the sun is up. I have done so, however, and my memory is that the moon appears pale in the cool, clear air. It seems a celestial body, and its size may be a little expanded, but nothing like in the autumn evenings. The red setting sun appears quite large and flattened, larger than the dawn moon, and sunspots are not visible, just as lunar detail is not visible in the haze. In the clear air of Wyoming, the sun sets into the Laramie Range as a brilliant ball I do not look at. My impression from glances is that it seems hard and bright. I conclude that the illusion is variable in strength, strongest in hazy air with subdued illumination, weakest in limpid air with bright light, and is mainly due to an unconscious assumption that the disc is a terrestrial object.

Some illusions are caused by ambiguity in the scene. In 1860, Sinsteden noticed a remarkable thing about a windmill seen in silhouette towards the darkening evening sky of the west. This view is represented to the left. It is unclear whether the axis of the sails is directed away from you or towards you. The direction of rotation of the sails depends on which is the case. Sinsteden and I can, by a conscious effort, imagine the scene in whichever way we choose, and if we switch views, the direction of rotation reverses! This remarkable illusion can be shown here through the magic of GIF animation. The absolutely exciting message of this illusion to me is that conscious thought can change the perception, reinforcing my view that mental processing plays the essential role in vision; everything else is auxiliary.

A couple of years earlier, Schroeder had published a static ambiguous figure, shown in the middle below. This is a very famous illusion, still often shown. The red surface can either be to the front of the figure, or to the back. In one case a flight of stairs is shown, in the other something less common, perhaps stairs seen from below. As in the case of the Sinsteden illusion, one can go from one interpretation to the other by an effort of will. There are many other such ambiguous figures, including the intaglio faces that can be seen as faces in relief. The drawing procedure called isometric projection is very subject to ambiguity, since perspective gives no aid.

The figure on the left, due to Zöllner, shows the effects of contrast with the diagonal teeth on the parallel vertical bars. The bars seem anything but parallel! The method of drawing this figure affects the strength of the illusion, and the form shown is one of the strongest. However, the illusion occurs to some degree however the short diagonal elements are drawn. This illusion shows an error in estimation. The lines tend to become more parallel if you concentrate on a pair of them, but there is always some tension. When I look at the figure with both eyes, I also get a stereoscopic effect, as if it were corrugated. A related illusion is shown at the left below, where it should be noted that there are no inclined lines at all. These patterns should certainly be avoided in decoration!

One of the most frequently mentioned illusions, called Poggendorff's illusion, is shown above at the right. His name was probably chosen either to honour him, or because he suggested it at one time or another to an investigator. It is fairly strong in the case on the left. The diagonal lines meet at the point where the left-hand side of the vertical bar is crossed, but the right-hand lines seem too low. It is usually presented as shown at the right, where the diagonal lines do not seem to be in the same straight line. The one on the right seems too low. This tendency has been taken into account in the Union Flag of the United Kingdom, where the red saltire of St Patrick is displaced so that it seems to be continuous on both sides of the cross of St George. This gives the flag a definite top and bottom, which those unfamiliar with it usually reverse. There are many variants of Poggendorff's illusion.

Another illusion of the same kind as Zöllner's was constructed by Hering, and is shown above in two forms. The horizontal parallels are seen bowed outwards in the top figure, and bowed inwards in the bottom figure.

Below are two more geometrical-optical illusions which came along later. In Bourdon's, the horizontal line seems bowed upwards. I do not perceive this illusion distinctly, but you may. Different people do not have the same responses to these illusions, again showing the intervention of the mind. In Loeb's illusion, the bottom of the two parallel lines on the right seems a bit higher than the top of the two parallel lines on the left, whereas in fact the two are in the same straight line.

On the left below are two forms of the celebrated Müller-Lyer illusion, in which two lines of equal length seem unequal because of their surroundings. In both cases, the line ab is the same length as the line a'b', which seems a little longer.

On the right is an illusion due to Baldwin. The small cross is midway between the two discs, but the large disc seems to attract it a little towards itself. I do not find this a strong illusion.

In the figure on the right, the vertical line is the same length as the horizontal line. You may find this difficult to believe, since the illusion is so strong, but measurement should convince you. This is called the top hat illusion, because it is often illustrated by a top hat, in which the crown is as high as the brim is broad, but looks much higher. This illusion gives clear evidence of the tendency to over-estimate vertical distances that makes hills ahead of us seem steeper, and valleys deeper, than they actually are. It is, of course, completely distinct from the horizon illusion with which this paper began, and the two are not related. Helmholz suggests sketching squares freehand and then measuring them to see how strong the illusion is. My squares tend to be rather square, but there seems to be an overestimation of about 1 part in 20.

The figure at the left, called the Kanisza square, shows that the impression of a square in front of the four circles is one way the mind interprets the picture, which is really just four circles, each with a quadrant removed. The square is not strongly or irresistibly perceived, the mind only offering it as a probable explanation for the figure. You may notice that the mind may supply ghostly edges to the square to separate it from the background. This figure was used in recent research with infants (Science, around November 2000) to find out the age at which different elements are combined to form a recognizable object. The age was determined as about 7 months after birth, on the basis of brain activity recorded electrically. This demonstrates yet again that perception is learned, not innate.

Other classes of illusions are concerned with contrasts in illumination, irradiation, and very frequently, with colour. Some of these have physical explanations, but most still involve mental processing.

A practical reason for studying optical illusions is to understand how to counteract their unwanted effects. In classical Greek temple architecture, columns were expected to look evenly tapered, and architraves straight and level, to an observer standing before the building. However, columns appear slightly concave, and the architraves appear to sag. Therefore, columns were deliberately made slightly convex, an effect called entasis, and architraves slightly bowed, to counteract this tendency. The displacement of the saltire of St Patrick in the Union Flag is another example.

There are illustrations of more illusions, and a more general discussion of the nature of illusion, in the related paper Illusions.


  1. M. Hershenson (editor), The Moon Illusion (Hillsdale, NJ: Lawrence Erlbaum Associates, 1989) shows that the horizon illusion has not lost its fascination. Note the title, which may lead the unwary to assume that it deals only with the moon.
  2. For a bibliography of work on optical illusions up to 1924, and especially the horizon illusion, see H. v. Helmholtz, Handbuch der Physiologischen Optik (New York: Dover, 1962) vol. III, p. 364-369.
  3. M. Luckeish, Visual Illusions (New York: Dover, 1965). A reissue of the original of 1915. A good survey, and widely available.
  4. S. Tolansky, Optical Illusions (Oxford: Pergamon Press, 1964)
  5. C. H. Paraquin, The World's Best Optical Illusions (New York: Sterling Publ. Co., 1987)
  6. M. Fineman, The Nature of Visual Illusion (Mineola, NY: Dover Publ., 1981)

Return to Optics Index

Composed by J. B. Calvert
Created 5 April 2000
Last revised 23 November 2000