Chapter 4 - Types of Geometrical Optical Illusions:
Illusions of Interrupted Extent

Illusions of Interrupted Extent. - Distance and area appear to vary in extent, depending upon whether they are filled or empty or are only partially filled. For example, a series of dots will generally appear longer overall than an equal distance between two points. This may be easily demonstrated by arranging three dots in a straight line on paper, the two intervening spaces being of equal extent, say about one or two inches long. If a series of about twelve dots is placed in one of the spaces, the empty space will then appear shorter. However, if only one dot is placed in the middle of one of the empty spaces, this space now is likely to appear of less extent than the empty space. (See Fig. 7.) A specific example of this type of optical illusion is shown in Fig. 6. The filled or divided space generally appears greater than the empty or undivided space, but certain qualifications of this statement are necessary. In a the divided space unquestionably appears greater than the empty space.

Fig. 6. - The divided or filled space on the left appears longer than the equal space on the right.

Apparently the filled or empty space is more important than the amount of light which is received from the clear spaces, for a black line on white paper appears longer than a white space between two points separated a distance equal to the length of the black line. Furthermore, apparently the spacing which is the most obtrusive is most influential in causing the divided space to appear greater for a than for b. The optical illusion still persists in c.

An idea of the magnitude may be gained from certain experiments by Aubert. He used a figure similar to a Fig. 6 containing a total of five short lines. Four of them were equally spaced over a distance of 100 mm. corresponding to the left half of a, Fig. 6. The remaining line was placed at the extreme right and defined the limit of an empty space also 100 mm. long. In all cases, the length of the empty space appeared about ten per cent less than that of the space occupied by the four lines equally spaced. Various experimenters obtain different results, and it seems reasonable that the differences may be accounted for, partially at least, by different degrees of unconscious correction of the optical illusion. This emphasizes the desirability of using subjects for such experiments who have no knowledge pertaining to the optical illusion.

As already stated there are apparent exceptions to any simple rule, for, as in the case of dots cited in a preceding paragraph, the optical illusion depends upon the manner in which the division is made. For example, in Fig. 7, a and c are as likely to appear shorter than b as equal to it. It has been concluded by certain investigators that when subdivision of a line causes it to appear longer, the parts into which it is divided or some of them are likely to appear shorter than isolated lines of the same length. The reverse of this statement also appears to hold. For example in Fig. 7, a appears shorter than b and the central part appears lengthened, although the total line appears shortened. This optical illusion is intensified by leaving the central section blank.

Fig. 7. - The three lines are of equal length.

A figure of this sort can be readily drawn by the reader by using short straight lines in place of the circles in Fig. 8. In this figure the space between the inside edges of the two circles on the left appears larger than the overall distance between the outside edges of the two circles on the right, despite the fact that these distances are equal. It appears that mere intensity of retinal stimulation does not account for these optical illusions, but rather the figures which we see.

Fig. 8. - The distance between the two circles on the left is equal to the distance between the outside edges of the two circles on the right.

In Fig. 9 the three squares are equal in dimensions but the different characters of the divisions cause them to appear not only unequal, but no longer squares.

Fig. 9. - Three squares of equal dimensions which appear different in area and dimension.

In Fig. 10 the distance between the outside edges of the three circles arranged horizontally appears greater than the empty space between the upper circle and the left- hand circle of the group.

Fig. 10. - The vertical distance between the upper circle and the left-hand one of the group is equal to the overall length of the group of three circles.

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