Optical Illusions

errors in the evaluation and comparison of lengths of segments, magnitudes of angles, and distances between objects, as well as in the perception of the shapes of objects, that are committed by observers under certain conditions. Such errors are extremely numerous, varied, and difficult to classify. With few exceptions, there are no satisfactory explanations of the specific reasons for optical illusions. Examples of optical illusions that arise as a result of the eye’s tendency to overestimate the length of vertical lines in comparison with horizontal lines are shown in Figure 1. The height of the drawing in (a) seems to be greater than its width; they are actually equal.

There are various optical illusions relating to the perception of the direction of lines. Examples of such illusions are given in (b) and (c). The long, diagonal straight lines in (b) seem to diverge. The optical illusions shown in (c) are of the same type. In this figure, straight parallel lines seem to be curved. A number of optical illusions are due to certain objects or parts of objects being perceived not separately, in isolation, but rather in connection with objects or parts of objects that surround them (the

Figure 1. Optical illusions: (a) the height of the drawing seems greater than its width, although they are equal; (b) the long diagonal lines are parallel to each other, although they seem to diverge; (c) the two middle lines going from right to left are parallel straight lines, although they seem to be arcs with their concavities facing one another; (d) the deck of the ship on the right seems shorter than the one on the left, but they are represented by equal straight lines; (e) both drawings are absolutely identical, although the upper one seems shorter and wider than the lower one; (f) the lower arc seems more convex and shorter than the upper one, but they are identical; (g) the letters of the sign are actually straight; (h) this drawing can be imagined in three ways: in the form of a stairway, as a stepped recess, and as a strip of paper folded like an accordion and extended diagonally.

psychological law of contrasts). This type of optical illusion is shown in (d), in which equal segments of a straight line (the deck of a ship) in the two figures seem to be of different length.

The illusions illustrated in (e) and (f) belong to special types of optical illusions. Both drawings in (e) are identical, but the upper drawing seems narrower and taller than the lower drawing. Two identical arcs in (f) seem different in both length and curvature. In (g) the observer sees letters made up of black and white stripes on a special background. The letters are placed absolutely straight, which may be shown with a ruler, but they appear to be turned in various directions. Optical illusions associated with the perception of relief, such as those shown in (h), are often encountered. Upon long observation of the drawing, the spatial perception may change, both voluntarily (as a result of some effort of the imagination) and involuntarily, and even contrary to the will. Optical illusions caused by the phenomenon of irradiation also exist.

Optical illusions are important in the graphic arts and in architecture, where their skillful use broadens the possibilities of the artist or architect. The significance of optical illusions in painting was pointed out as early as 1774 by L. Euler.