In the drawing 9 the wheel is intersected by perpendicular sections on its axes: vertical and horizontal. This gives an illusion, that the circle is concave at the intersection of the sections.
In the drawing 10 a the height of an isosceles triangle was divided into two equal parts. Part of the height of this triangle, being closer to its top, it appears smaller than the part at its base. In the drawing 10 b the upper trapezoid seems larger than the lower trapezoid, which has been slightly shifted from the top, but in fact both are the same.
Two squares with the same dimensions have been divided into four equal parts: first – vertical lines, second – horizontal. Seems, that the first square is wider than the second (fig.11). The same illusion will appear when hatching two squares of equal size with vertical and horizontal lines (fig.12).
Let us now turn to the explanation of the so-called. Delboef's delusions (Joseph Delboef – philosopher, Belgian mathematician and psychologist, he dealt mainly with psychophysics and studied the differences between visual impressions).
In the drawing 13 two circles with the same radii R are shown: inside -1 and external – 2. With funds 0 wheels, two more circles were drawn: Outside 3 with a larger radius and internal 4 with a radius smaller than the radius R.. Seems, that the inner circle 1 is greater than the outside, marked with a number 2. We can explain this phenomenon as follows: looking at those wheels, we do not see them separately, but we perceive the circular rings.
In the drawing 14 both inner wheels 1 i 2 have R radii of equal length, while the outer circles are drawn with radii of different lengths. When we look at the drawing it seems to us, that the inner circle 1 is greater than the inner circle 2.
A similar phenomenon of visual illusions occurs in the drawings 15 i 16 and is due to the size contrast of the fields surrounding the inner circles. These drawings show the same arrangement of wheels in contour and silhouette. By comparing them we find, that the phenomenon of visual illusions appears more clearly in the figure 16.
Yet another example of the interpretation of some visual illusions is shown in the figure 17: two squares, the first of which is hatched with lines at an angle 45 degrees, and others – the same size – it is bright and surrounded by a larger square, hatched at the same angle. The bright square plane, as active, appears larger than the dark plane.
We can see the same phenomenon in the picture 18, which has four squares of equal size, and inside them circles and squares of the same diameters and sides. By coloring individual planes black and white, we get an impression, that white apparently magnifies, and black reduces the area of the circle and square. This phenomenon is used, for example, in clothing.
By drawing a square and a circle with a diameter equal to the length of the side of the square (rys. 19 a) we perceive, that the diameter of the circle is apparently smaller than the side of the square. On the other hand, by drawing a circle with a diameter slightly larger than the side of the square, we get the impression of equal dimensions (rys. 19 b).
In the drawing 20 a and b show two planes at the same angle. This drawing can be read in two ways: as two pages (or walls) seen from the outside or inside.
The given examples do not exhaust all the phenomena of optical illusions, but they show only the simplest and most typical, with whom we will be meeting in reading various drawings. They signal, how easy it is to make mistakes by looking briefly at the drawings, without analyzing them.
In everyday life we come across various examples of visual illusions, for example about the size of the sun's disc at sunrise, at noon and at sunset, the size of the full moon at sunrise, so near the horizon of the earth. We also perceive visual illusions when looking at objects closer to us or distant, at the confluence of the road line going deep and the line of the tops of roadside trees, bases of telegraph poles etc.. Perspective phenomena will be discussed in more detail in this chapter 5.
The cited examples of optical illusions are related to a well-known eye defect, which, despite its precise structure, causes mistakes when perceiving images. This defect can also be explained by certain psychological and physiological properties. Among the commonly held theories about the formation of visual illusions, this one deserves attention in the first place, which points, that the viewer's attention when perceiving different visual impressions is diverted from the main goal by additional elements in the form of lines or planes with a different arrangement. We also know, that light and color provide many optical illusions. These issues will be discussed in later chapters.