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VISUAL ILLUSIONS
_THEIR CAUSES, CHARACTERISTICS AND APPLICATIONS_
BY M. LUCKIESH
DIRECTOR OF APPLIED SCIENCE, NELA RESEARCH LABORATORIES,
NATIONAL LAMP WORKS OF GENERAL ELECTRIC CO.
AUTHOR OF "COLOR AND ITS APPLICATIONS," "LIGHT AND SHADE
AND THEIR APPLICATIONS," "THE LIGHTING ART," "THE
LANGUAGE OF COLOR," "ARTIFICIAL LIGHT--ITS
INFLUENCE UPON CIVILIZATION,"
"LIGHTING THE HOME," ETC.
100 ILLUSTRATIONS
NEW YORK
D. VAN NOSTRAND COMPANY
EIGHT WARREN STREET
1922
COPYRIGHT, 1922, BY
D. VAN NOSTRAND COMPANY
PREFACE
Eventually one of the results of application to the analysis and
measurement of the phenomena of light, color, lighting, and vision is a
firmly entrenched conviction of the inadequacy of physical measurements as
a means for representing what is perceived. Physical measurements have
supplied much of the foundation of knowledge and it is not a reflection
upon their great usefulness to state that often they differ from the
results of intellectual appraisal through the visual sense. In other
words, there are numberless so-called visual illusions which must be taken
into account. All are of interest; many can be utilized; and some must be
suppressed.
Scientific literature yields a great many valuable discussions from
theoretical and experimental viewpoints but much of the material is
controversial. The practical aspects of visual illusions have been quite
generally passed by and, inasmuch as there does not appear to be a volume
available which treats the subject in a condensed manner but with a broad
scope, this small volume is contributed toward filling the gap.
The extreme complexity of the subject is recognized, but an attempt toward
simplicity of treatment has been made by confining the discussion chiefly
to static visual illusions, by suppressing minor details, and by
subordinating theory. In other words, the intent has been to emphasize
experimental facts. Even these are so numerous that only the merest
glimpses of various aspects can be given in order to limit the text to a
small volume. Some theoretical aspects of the subject are still extremely
controversial, so they are introduced only occasionally and then chiefly
for the purpose of illustrating the complexities and the trends of
attempted explanations. Space does not even admit many qualifications
which may be necessary in order to escape criticism entirely.
The visual illusions discussed are chiefly of the static type, although a
few others have been introduced. Some of the latter border upon motion,
others upon hallucinations, and still others produced by external optical
media are illusions only by extension of the term. These exceptions are
included for the purpose of providing glimpses into the borderlands.
It is hoped that this condensed discussion, which is ambitious only in
scope, will be of interest to the general reader, to painters, decorators,
and architects, to lighting experts, and to all interested in light,
color, and vision. It is an essential supplement to certain previous
works.
M. LUCKIESH
November, 1920.
CONTENTS
CHAPTER PAGE
I. Introduction 1
II. The eye 13
III. Vision 29
IV. Some types of geometrical illusions 44
V. Equivocal figures 64
VI. The influence of angles 76
VII. Illusions of depth and of distance 102
VIII. Irradiation and brightness-contrast 114
IX. Color 124
X. Lighting 144
XI. Nature 164
XII. Painting and decoration 179
XIII. Architecture 195
XIV. Mirror Magic 205
XV. Camouflage 210
LIST OF ILLUSTRATIONS
FIGURE PAGE
1. Principal parts of the eye 14
2. Stereoscopic pictures for combining by converging or
diverging the optical axes 41
3. Stereoscopic pictures 41
4. The vertical line appears longer than the equal horizontal
line in each case 46
5. The vertical dimension is equal to the horizontal one, but
the former appears greater 47
6. The divided or filled space on the left appears longer
than the equal space on the right 49
7. The three lines are of equal length 50
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 50
9. Three squares of equal dimensions which appear different
in area and dimension 51
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 52
11. Two equal semi-circles 53
12. Arcs of the same circle 53
13. Three incomplete but equal squares 53
14. Middle sections of the two lines are equal 54
15. An effect of contrasting areas (Baldwin's figure) 54
16. An illusion of contrast 55
17. Equal circles which appear unequal due to contrast
(Ebbinghaus' figure) 56
18. Equal circles appearing unequal owing to contrasting
concentric circles 56
19. Circles influenced by position within an angle 57
20. Contrasting angles 57
21. Owing to perspective the right angles appear oblique and
vice versa 58
22. Two equal diagonals which appear unequal 58
23. Apparent variations in the distance between two parallel
lines 59
24. A striking illusion of perspective 60
25. Distortion of a square due to superposed lines 61
26. Distortion of a circle due to superposed lines 62
27. Illustrating fluctuation of attention 65
28. The grouping of the circles fluctuates 66
29. Crossed lines which may be interpreted in two ways 67
30. Reversible cubes 68
31. The reversible "open book" (after Mach) 69
32. A reversible tetrahedron 69
33. Reversible perspective of a group of rings or of a tube 70
34. Schroeder's reversible staircase 70
35. Thiery's figure 71
36. Illustrating certain influences upon the apparent
direction of vision.
By covering all but the eyes the latter appear to be
drawn alike in both sketches 73
37. Zoellner's illusion of direction 77
38. Parallel lines which do not appear so 79
39. Wundt's illusion of direction 79
40. Hering's illusion of direction 80
41. Simple effect of angles 81
42. The effect of two angles in tilting the horizontal lines 83
43. The effect of crossed lines upon their respective
apparent directions 83
44. Another step toward the Zoellner illusion 84
45. The two diagonals would meet on the left vertical line 85
46. Poggendorff's illusion. Which oblique line on the right
is the prolongation of the oblique line on the left? 85
47. A straight line appears to sag 86
48. Distortions of contour due to contact with other contours 87
49. An illusion of direction 88
50. "Twisted-cord" illusion. These are straight cords 89
51. "Twisted-cord" illusion. These are concentric circles 89
52. A spiral when rotated appears to expand or contract,
depending upon direction of rotation 90
53. Angles affect the apparent length of lines 91
54. The horizontal line appears to tilt downward toward the
ends 92
55. The horizontal line appears to sag in the middle 92
56. The Mueller-Lyer illusion 93
57. Combined influence of angles and contrasting lengths 95
58. Two equal oblique lines appear unequal because of their
different positions 95
59. An illusion of area 96
60. Five equal areas showing the influence of contour upon
judgment of area 97
61. Showing the effect of directing the attention 98
62. Simple apparatus for demonstrating the remarkable effects
of contrasts in brightness and color 115
63. Illustrating brightness-contrast 117
64. An effect of brightness-contrast. Note the darkening of
the intersections of the white strips 118
65. The phenomenon of irradiation 121
66. An excellent pattern for demonstrating color-contrast 126
67. By rotating this Mason (black and white) disk
color-sensations are produced 133
68. For demonstrating retiring and advancing colors 137
69. By combining these stereoscopically the effect of
metallic lustre (similar to graphite in this case) is
obtained 141
70. A bas-relief lighted from above 146
71. An intaglio lighted from above 147
72. A bas-relief lighted from the left 148
73. An intaglio lighted from the left 149
74a. A disk (above) and a sphere (below) lighted from overhead 145
b. A disk and a sphere lighted by perfectly diffused light 145
75. A concave hemispherical cup on the left and a convex
hemisphere on the right lighted by a light-source of
large angle such as a window 150
76. The same as Fig. 75, but lighted by a very small
light-source 151
77. Apparent ending of a searchlight beam 161
78. An accurate tracing from a photograph (continual
exposure) of the moon rising 171
79. Accurate tracings from a photograph (short exposures at
intervals) of the sun setting 172
80. Explanation offered by Smith of the apparent enlargement
of heavenly bodies near the horizon 174
81. Explanation of a common mirage 176
82. Illustrating the apparent distortion of a picture frame
in which the grain of the wood is visible 190
83. Another example similar to Fig. 82 191
84. From actual photographs of the end-grain of a board 192
85. Exaggerated illusions in architecture 198
86. Illustrating the influence of visual angle upon apparent
vertical height 199
87. Irradiation in architecture 200
88. Some simple geometrical-optical illusions in architecture 201
89. By decreasing the exposed length of shingles toward the
top a greater apparent expanse is obtained 202
90. An example of a mirror "illusion" 207
91. Another example of "mirror magic" 208
92. A primary stage in the evolution of the use of
geometrical-optical illusions on ships 226
93 and 94. Attempts at distortion of outline which preceded
the adoption of geometrical-optical illusions 228
95 and 96. Illustrating the use of models by the Navy
Department in developing the geometrical-optical illusion
for ships 229
97 and 98. Examples of the geometrical-optical illusion as
finally applied 231
99. Representative earth backgrounds for an airplane
(uncamouflaged) as viewed from above 235
100. Illustrating the study of pattern for airplanes. The
photograph was taken from an altitude of 10,000 feet.
The insert shows the relative lengths (vertical scale)
of an airplane of 50-foot spread at various distances
below the observer 239
VISUAL ILLUSIONS
I
INTRODUCTION
Seeing is deceiving. Thus a familiar epigram may be challenged in order to
indicate the trend of this book which aims to treat certain phases of
visual illusions. In general, we do not see things as they are or as they
are related to each other; that is, the intellect does not correctly
interpret the deliverances of the visual sense, although sometimes the
optical mechanism of the eyes is directly responsible for the illusion. In
other words, none of our conceptions and perceptions are quite adequate,
but fortunately most of them are satisfactory for practical purposes. Only
a part of what is perceived comes through the senses from the object; the
remainder always comes from within. In fact, it is the visual sense or the
intellect which is responsible for illusions of the various types to be
discussed in the following chapters. Our past experiences, associations,
desires, demands, imaginings, and other more or less obscure influences
create illusions.
An illusion does not generally exist physically but it is difficult in
some cases to explain the cause. Certainly there are many cases of errors
of judgment. A mistaken estimate of the distance of a mountain is due to
an error of judgment but the perception of a piece of white paper as pink
on a green background is an error of sense. It is realized that the
foregoing comparison leads directly to one of the most controversial
questions in psychology, but there is no intention on the author's part to
cling dogmatically to the opinions expressed. In fact, discussions of the
psychological judgment involved in the presentations of the visual sense
are not introduced with the hope of stating the final word but to give the
reader an idea of the inner process of perception. The final word will be
left to the psychologists but it appears possible that it may never be
formulated.
In general, a tree appears of greater length when standing than when lying
upon the ground. Lines, areas, and masses are not perceived in their
actual physical relations. The appearance of a colored object varies
considerably with its environment. The sky is not perceived as infinite
space nor as a hemispherical dome, but as a flattened vault. The moon
apparently diminishes in size as it rises toward the zenith. A bright
object appears larger than a dark object of the same physical dimensions.
Flat areas may appear to have a third dimension of depth. And so on.
Illusions are so numerous and varied that they have long challenged the
interest of the scientist. They may be so useful or even so disastrous
that they have been utilized or counteracted by the skilled artist or
artisan. The architect and painter have used or avoided them. The
stage-artist employs them to carry the audience in its imagination to
other environments or to far countries. The magician has employed them in
his entertainments and the camoufleur used them to advantage in the
practice of deception during the recent war. They are vastly entertaining,
useful, deceiving, or disastrous, depending upon the viewpoint.
Incidentally, a few so-called illusions will be discussed which are not
due strictly to errors of the visual sense or of the intellect. Examples
of these are the mirage and certain optical effects employed by the
magician. In such cases neither the visual sense nor the intellect errs.
In the case of the mirage rays of light coming from the object to the eye
are bent from their usual straight-line course and the object appears to
be where it really is not. However, with these few exceptions, which are
introduced for their specific interest and for the emphasis they give to
the "true" illusion, it will be understood that illusions in general as
hereinafter discussed will mean those due to the visual mechanism or to
errors of judgment or intellect. For the sake of brevity we might say that
they are those due to errors of visual perception. Furthermore, only those
of a "static" type will be considered; that is, the vast complexities due
to motion are not of interest from the viewpoint of the aims of this book.
There are two well-known types of misleading perceptions, namely illusions
and hallucinations. If, for example, two lines appear of equal length and
are not, the error in judgment is responsible for what is termed an
"illusion." If the perceptual consciousness of an object appears although
the object is not present, the result is termed an "hallucination." For
example, if something is seen which does not exist, the essential factors
are supplied by the imagination. Shadows are often wrought by the
imagination into animals and even human beings bent upon evil purpose.
Ghosts are created in this manner. Hallucinations depend largely upon the
recency, frequency, and vividness of past experience. A consideration of
this type of misleading perception does not advance the aims of this book
and therefore will be omitted.
The connection between the material and mental in vision is
incomprehensible and apparently must ever remain so. Objects emit or
reflect light and the optical mechanism known as the eye focuses images of
the objects upon the retina. Messages are then carried to the brain where
certain molecular vibrations take place. The physiologist records certain
physical and chemical effects in the muscles, nerves, and brain and
behold! there appears consciousness, sensations, thoughts, desires, and
volitions. How? and, Why? are questions which may never be answered.
It is dangerous to use the word _never_, but the ultimate answers to those
questions appear to be so remote that it discourages one from proceeding
far over the hazy course which leads toward them. In fact, it does not
appreciably further the aims of this book to devote much space to efforts
toward explanation. In covering this vast and complex field there are
multitudes of facts, many hypotheses, and numerous theories from which to
choose. Judgment dictates that of the limited space most of it be given
to the presentation of representative facts. This is the reasoning which
led to the formulation of the outline of chapters.
Owing to the vast complex beyond the physical phenomena, physical
measurements upon objects and space which have done so much toward
building a solid foundation for scientific knowledge fail ultimately to
provide an exact mathematical picture of that which is perceived. Much of
the author's previous work has been devoted to the physical realities but
the ever-present differences between physical and perceptive realities
have emphasized the need for considering the latter as well.
Illusions are legion. They greet the careful observer on every hand. They
play a prominent part in our appreciation of the physical world. Sometimes
they must be avoided, but often they may be put to work in various arts.
Their widespread existence and their forcefulness make visual perception
the final judge in decoration, in painting, in architecture, in
landscaping, in lighting, and in other activities. The ultimate limitation
of measurements with physical instruments leaves this responsibility to
the intellect. The mental being is impressed with things as perceived, not
with things as they are. It is believed that this intellectual or
judiciary phase which plays such a part in visual perception will be best
brought out by examples of various types of static illusions coupled with
certain facts pertaining to the eye and to the visual process as a whole.
In special simple cases it is not difficult to determine when or how
nearly a perception is true but in general, agreement among normal
persons is necessary owing to the absence of any definite measuring device
which will span the gap between the perception and the objective reality.
Illusions are sometimes called "errors of sense" and some of them are
such, but often they are errors of the intellect. The senses may deliver
correctly but error may arise from imagination, inexperience, false
assumptions, and incorrect associations, and the recency, frequency, and
vividness of past experience. The gifts of sight are augmented by the mind
with judgments based upon experience with these gifts.
The direct data delivered by the visual sense are light, intensity, color,
direction. These may be considered as simple or elemental sensations
because they cannot be further simplified or analyzed. At this point it is
hoped that no controversy with the psychologist will be provoked. In the
space available it appears unfruitful to introduce the many qualifications
necessary to satisfy the, as yet uncertain or at least conflicting,
definitions and theories underlying the science of psychology. If it is
necessary to add darkness to the foregoing group of elemental visual
sensations, this will gladly be agreed to.
The perceptions of outline-form and surface-contents perhaps rank next in
simplicity; however, they may be analyzed into directions. The perception
of these is so direct and so certain that it may be considered to be
immediate. A ring of points is apparently very simple and it might be
considered a direct sense-perception, but it consists of a number of
elemental directions.
The perception of solid-form is far more complex than outline-form and
therefore more liable to error. It is judged partially by binocular vision
or perspective and partly by the distribution of light and shade. Colors
may help to mold form and even to give depth to flat surfaces. For
example, it is well known that some colors are "advancing" and others are
"retiring."
Perhaps of still greater complexity are the judgments of size and of
distance. Many comparisons enter such judgments. The unconscious acts of
the muscles of the eye and various external conditions such as the
clearness of the atmosphere play prominent parts in influencing judgment.
Upon these are superposed the numerous psycho-physiological phenomena of
color, irradiation, etc.
In vision judgments are quickly made and the process apparently is largely
outside of consciousness. Higher and more complex visual judgments pass
into still higher and more complex intellectual judgments. All these may
appear to be primary, immediate, innate, or instinctive and therefore,
certain, but the fruits of studies of the psychology of vision have shown
that these visual judgments may be analyzed into simpler elements.
Therefore, they are liable to error.
That the ancients sensed the existence or possibility of illusions is
evidenced by the fact that they tried to draw and to paint although their
inability to observe carefully is indicated by the absence of true
shading. The architecture of ancient Greece reveals a knowledge of certain
illusions in the efforts to overcome them. However, the study of illusions
did not engage the attention of scientists until a comparatively recent
period. Notwithstanding this belated attention there is a vast scientific
literature pertaining to the multitudinous phases of the subject; however,
most of it is fragmentary and much of it is controversial. Some of it
deals with theory for a particular and often a very simple case. In life
complex illusions are met but at present it would be futile to attempt to
explain them in detail. Furthermore, there have been few attempts to
generalize and to group examples of typical phenomena in such a manner as
to enable a general reader to see the complex fabric as a whole. Finally,
the occurrence and application of illusions in various arts and the
prominence of illusions on every hand have not been especially treated. It
is the hope that this will be realized in the following chapters in so far
as brevity of treatment makes this possible.
Doubtless thoughtful observers ages ago noticed visual illusions,
especially those found in nature and in architecture. When it is
considered that geometrical figures are very commonly of an illusory
character it appears improbable that optical illusions could have escaped
the keenness of Euclid. The apparent enlargement of the moon near the
horizon and the apparent flattened vault of the sky were noticed at least
a thousand years ago and literature yields several hundred memoirs on
these subjects. One of the oldest dissertations upon the apparent form of
the sky was published by Alhazen, an Arab astronomer of the tenth century.
Kepler in 1618 wrote upon the subject.
Philosophers of the past centuries prepared the way toward an
understanding of many complexities of today. They molded thought into
correct form and established fundamental concepts and principles. Their
chief tool was philosophy, the experimental attack being left to the
scientists of the modern age. However, they established philosophically
such principles as "space and time are not realities of the phenomenal
world but the modes under which we see things apart." As science became
organized during the present experimental era, measurements were applied
and there began to appear analytical discussions of various subjects
including optical illusions. One of the earliest investigations of the
modern type was made by Oppel, an account of which appeared in 1854. Since
that time scientific literature has received thousands of worthy
contributions dealing with visual illusions.
There are many facts affecting vision regarding which no theory is
necessary. They speak for themselves. There are many equally obvious facts
which are not satisfactorily explained but the lack of explanation does
not prevent their recognition. In fact, only the scientist needs to worry
over systematic explanations and theoretical generalizations. He needs
these in order to invade and to explore the other unknowns where he will
add to his storehouse of knowledge. A long step toward understanding is
made by becoming acquainted with certain physical, physiological, and
psychological facts of light, color, and lighting. Furthermore,
acquaintance with the visual process and with the structure of the eye
aids materially. For this reason the next two chapters have been added
even at the risk of discouraging some readers.
In a broad sense, any visual perception which does not harmonize with
physical measurements may be termed an "illusion." Therefore, the term
could include those physical illusions obtained by means of prisms,
lenses, and mirrors and such illusions as the mirage. It could also
include the physiological illusions of light and color such as
after-images, irradiation, and contrast, and the psycho-physiological
illusions of space and the character of objects. In fact, the scope of the
following chapters is arbitrarily extended to include all these aspects,
but confines consideration only to "static" illusions.
In a more common sense attention is usually restricted to the last group;
that is, to the psycho-physiological illusions attending the perception of
space and the character of objects although motion is often included. It
should be obvious that no simple or even single theory can cover the vast
range of illusions considered in the broad sense because there are so many
different kinds of factors involved. For this reason explanations will be
presented wherever feasible in connection with specific illusions.
However, in closing this chapter it appears of interest to touch upon the
more generally exploited theories of illusions of the type considered in
the foregoing restricted sense. Hypotheses pertaining to illusions are
generally lacking in agreement, but for the special case of what might be
more safely termed "geometrical-optical illusions" two different theories,
by Lipps and by Wundt respectively, are conspicuous. In fact, most
theories are variants of these two systematic "explanations" of illusions
(in the restricted sense).
Lipps proposed the principle of mechanical-esthetic unity, according to
which we unconsciously give to every space-form a living personality and
unconsciously consider certain mechanical forces acting. Our judgments are
therefore modified by this anthropomorphic attitude. For example, we
regard the circle as being the result of the action of tangential and
radial forces in which the latter appear to triumph. According to Lipps'
theory the circle has a centripetal character and these radial forces
toward the center, which apparently have overcome the tangential forces
during the process of creating the circle, lead to underestimation of its
size as compared with a square of the same height and breadth. By drawing
a circle and square side by side, with the diameter of the former equal to
the length of a side of the latter, this illusion is readily demonstrated.
Of course, the square has a greater area than the circle and it is
difficult to determine the effect of this disparity in area. Figure 60
where the areas of the circle and square are equal and consequently the
height of the former is considerably greater than the latter, is of
interest in this connection. By experimenting with a series of pairs
consisting of a circle and a square, varying in dimensions from equal
heights to equal areas, an idea of the "shrinking" character of the circle
becomes quite apparent.
Wundt does not attribute the illusion to a deception or error of judgment
but to direct perception. According to his explanation, the laws of
retinal image (fixation) and eye-movement are responsible. For example,
vertical distances appear greater than horizontal ones because the effort
or expenditure of energy is greater in raising the eyes than in turning
them through an equal angle in a horizontal plane. Unconscious or
involuntary eye-movements also appear to play a part in many linear or
more accurately, angular illusions, but certainly Wundt's explanation does
not suffice for all illusions although it may explain many geometrical
illusions. It may be said to be of the "perceptive" class and Lipps'
theory to be of the "judgment" or "higher-process" class. As already
stated, most of the other proposed explanations of geometrical illusions
may be regarded as being related to one of these two theories. There is
the "indistinct vision" theory of Einthoven; the "perspective" theory of
Hering, Guye, Thiery, and others; the "contrast" theory of Helmholtz,
Loeb, and Heyman; and the "contrast-_confluxion_" theory of Mueller-Lyer.
In order not to discourage the reader at the outset, theories as such will
be passed by with this brief glimpse. However, more or less qualified
explanations are presented occasionally in some of the chapters which
follow in order to indicate or to suggest a train of thought should the
reader desire to attempt to understand some of the numerous interesting
illusions.
II
THE EYE
Helmholtz, who contributed so much toward our knowledge of the visual
process, in referring to the eye, once stated that he could make a much
better optical instrument but not a better eye. In other words, the eye is
far from an ideal optical instrument but as an eye it is wonderful. Its
range of sensitiveness and its adaptability to the extreme variety of
demands upon it are truly marvelous when compared with instruments devised
by mankind. Obviously, the eye is the connecting link between objective
reality and visual perception and, therefore, it plays an important part
in illusions. In fact, sometimes it is solely responsible for the
illusion. The process of vision may be divided into several steps such as
(1) the lighting, color, character, and disposition of objects; (2) the
mechanism by which the image is formed upon the retina; (3) various
optical defects of this mechanism; (4) the sensitiveness of the parts of
the retina to light and color; (5) the structure of the retina; (6) the
parts played by monocular and binocular vision; and (7) the various events
which follow the formation of the image upon the retina.
The mechanism of the eye makes it possible to see not only light but
objects. Elementary eyes of the lowest animals perceive light but cannot
see objects. These eyes are merely specialized nerves. In the human eye
the optic nerve spreads to form the retina and the latter is a specialized
nerve. Nature has accompanied this evolution by developing an instrument
the--eye--for intensifying and defining and the whole is the visual
sense-organ. The latter contains the most highly specialized nerve and the
most refined physiological mechanism, the result being the highest
sense-organ.
[Illustration: Fig. 1.--Principal parts of the eye.
A, Conjunctiva; B, Retina; C, Choroid; D, Sclera; E, Fovea; F, Blind Spot;
G, Optic Nerve; H, Ciliary Muscle; I, Iris; J, Cornea; K, Ligament.]
The eye is approximately a spherical shell transparent at the front
portion and opaque (or nearly so) over the remaining eighty per cent of
its surface. The optical path consists of a series of transparent liquids
and solids. The chief details of the structure of the eye are represented
in Fig. 1. Beginning with the exterior and proceeding toward the retina we
find in succession the cornea, the anterior chamber containing the aqueous
humor, the iris, the lens, the large chamber containing the vitreous
humor, and finally the retina. Certain muscles alter the position of the
eye and consequently the optical axis, and focusing (accommodation) is
accomplished by altering the thickness and shape, and consequently the
focal length, of the lens.
The iris is a shutter which automatically controls to some degree the
amount of light reaching the retina, thereby tending to protect the latter
from too much light. It also has some influence upon the definition of the
image; that is, upon what is termed "visual acuity" or the ability to
distinguish fine detail. It is interesting to compare the eye with the
camera. In the case of the camera and the photographic process, we have
(1) an inverted light-image, a facsimile of the object usually diminished
in size; (2) an invisible image in the photographic emulsion consisting of
molecular changes due to light; and (3) a visible image developed on the
plate. In the case of the eye and the visual process we have (1) an
inverted light-image, a facsimile of the object diminished in size; (2)
the invisible image in the retinal substances probably consisting of
molecular changes due to light; and (3) an _external_ visible image. It
will be noted that in the case of vision the final image is projected
outward--it is external. The more we think of this outward projection the
more interesting and marvelous vision becomes. For example, it appears
certain that if a photographic plate could see or feel, it would see or
feel the silver image upon itself but not out in space. However, this
point is discussed further in the next chapter.
In the camera and photographic process we trace mechanism, physics, and
chemistry throughout. In the eye and visual process we are able to trace
these factors only to a certain point, where we encounter the
super-physical and super-chemical. Here molecular change is replaced by
sensation, perception, thought, and emotion. Our exploration takes us from
the physical world into another, wholly different, where there reigns
another order of phenomena. We have passed from the material into the
mental world.
The eye as an optical mechanism is reducible to a single lens and
therefore the image focused upon the retina is inverted. However, there is
no way for the observer to be conscious of this and therefore the inverted
image causes no difficulty in seeing. The images of objects in the right
half of the field of view are focused upon the left half of the retina.
Similarly, the left half of the field of view corresponds to the right
half of the retina; the upper half of the former to the lower half of the
latter; and so on. When a ray of light from an object strikes the retina
the impression is referred back along the ray-line into the original place
in space. This is interestingly demonstrated in a simple manner. Punch a
pin-hole in a card and hold it about four inches from the eye and at the
same time hold a pin-head as close to the cornea as possible. The
background for the pin-hole should be the sky or other bright surface.
After a brief trial an inverted image of the pin-head is seen _in the
hole_. Punch several holes in the card and in each will be seen an
inverted image of the pin-head.
The explanation of the foregoing is not difficult. The pin-head is so
close to the eye that the image cannot be focused upon the retina;
however, it is in a very favorable position to cast a shadow upon the
retina, the light-source being the pin-hole with a bright background.
Light streaming through the pin-hole into the eye casts an erect shadow of
the pin-head upon the retina, and this erect image is projected into space
and inverted in the process by the effect of the lens. The latter is not
operative during the casting of the shadow because the pin-head is too
close to the lens, as already stated. It is further proved to be outward
projection of the retinal image (the shadow) because by multiplying the
number of pin-holes (the light-sources) there are also a corresponding
number of shadows.
The foregoing not only illustrates the inversion of the image but again
emphasizes the fact that we do not see retinal images. Even the "stars"
which we see on pressing the eye-lid or on receiving a blow on the eye are
projected into space. The "motes" which we see in the visual field while
gazing at the sky are defects in the eye-media, and these images are
projected into space. We do not see anything in the eye. The retinal image
impresses the retina in some definite manner and the impression is carried
to the brain by the optic nerve. The intellect then refers or projects
this impression outward into space as an external image. The latter would
be a facsimile of the physical object if there were no illusions but the
fact that there are illusions indicates that errors are introduced
somewhere along the path from and to the object.
It is interesting to speculate whether the first visual impression of a
new-born babe is "projected outward" or is perceived as in the eye. It is
equally futile to conjecture in this manner because there is no
indication that the time will come when the baby can answer us
immediately upon experiencing its first visual impression. The period of
infancy increases with progress up the scale of animal life and this
lengthening is doubtless responsible and perhaps necessary for the
development of highly specialized sense-organs. Incidentally, suppose a
blind person to be absolutely uneducated by transferred experience and
that he suddenly became a normal adult and able to see. What would he say
about his first visual impression? Apparently such a subject is
unobtainable. The nearest that such a case had been approached is the case
of a person born blind, whose sight has been restored. This person has
acquired much experience with the external world through other senses. It
has been recorded that such a person, after sight was restored, appeared
to think that external objects "touched" the eyes. Only through visual
experience is this error in judgment rectified.
Man studies his kind too much apart from other animals and perhaps either
underestimates or overestimates the amount of inherited, innate,
instinctive qualities. A new-born chick in a few minutes will walk
straight to an object and seize it. Apparently this implies perception of
distance and direction and a cooerdination of muscles for walking and
moving the eyes. It appears reasonable to conclude that a certain amount
of the wealth of capacities possessed by the individual is partly
inherited, and in man the acquired predominates. But all capacities are
acquired, for even the inherited was acquired in ancestral experience.
Even instinct (whatever that may be) must involve inherited experience.
These glimpses of the depths to which one must dig if he is to unearth the
complete explanations of visual perception--and consequently of
illusions--indicate the futility of treating the theories in the available
space without encroaching unduly upon the aims of this volume.
Certain defects of the optical system of the eye must contribute toward
causing illusions. Any perfect lens of homogeneous material has at least
two defects, known as spherical and chromatic aberration. The former
manifests itself by the bending of straight lines and is usually
demonstrated by forming an image of an object such as a wire mesh or
checkerboard; the outer lines of the image are found to be very much bent.
This defect in the eye-lens is somewhat counteracted by a variable optical
density, increasing from the outer to the central portion. This results in
an increase in refractive-index as the center of the lens is approached
and tends to diminish its spherical aberration. The eye commonly possesses
abnormalities such as astigmatism and eccentricity of the optical
elements. All these contribute toward the creation of illusions.
White light consists of rays of light of various colors and these are
separated by means of a prism because the refractive-index of the prism
differs for lights of different color or wave-length. This causes the blue
rays, for example, to be bent more than the red rays when traversing a
prism. It is in this manner that the spectrum of light may be obtained. A
lens may be considered to be a prism of revolution and it thus becomes
evident that the blue rays will be brought to a focus at a lesser
distance than the red rays; that is, the former are bent more from their
original path than the latter. This defect of lenses is known as chromatic
aberration and is quite obvious in the eye. It may be demonstrated by any
simple lens, for the image of the sun, for example, will appear to have a
colored fringe. A purple filter which transmits only the violet and red
rays is useful for this demonstration. By looking at a lamp-filament or
candle-flame some distance away the object will appear to have a violet
halo, but the color of the fringe will vary with accommodation. On looking
through a pin-hole at the edge of an object silhouetted against the bright
sky the edge will appear red if the light from the pin-hole enters the
pupil near its periphery. This optical defect of the eye makes objects
appear more sharply defined when viewed in monochromatic light. In fact,
this is quite obvious when using yellow glasses. The defect is also
demonstrated by viewing a line-spectrum focused on a ground glass. The
blue and red lines cannot be seen distinctly at the same distance. The
blue lines can be focused at a much less distance than the red lines.
Chromatic aberration can account for such an illusion as the familiar
"advancing" and "retiring" colors and doubtless it plays a part in many
illusions.
The structure of the retina plays a very important part in vision and
accounts for various illusions and many interesting visual phenomena. The
optic nerve spreads out to form the retina which constitutes the inner
portion of the spherical shell of the eye with the exception of the front
part. Referring again to Fig. 1, the outer coating of the shell is called
the sclerotic. This consists of dense fibrous tissue known as the "white
of the eye." Inside this coating is a layer of black pigment cells termed
the choroid. Next is the bacillary layer which lines about five-sixths of
the interior surface of the eye. This is formed by closely packed "rods"
and "cones," which play a dominant role in the visual process. A
light-sensitive liquid (visual purple) and cellular and fibrous layers
complete the retinal structure.
The place where the optic nerve enters the eye-ball and begins to spread
out is blind. Objects whose images fall on this spot are invisible. This
blind-spot is not particularly of interest here, but it may be of interest
to note its effect. This is easily done by closing one eye and looking
directly at one of two small black circles about two inches apart on white
paper at a distance of about a foot from the eye. By moving the objects
about until the image of the circle not directly looked at falls upon the
blind-spot, this circle will disappear. A three-foot circle at a distance
of 36 feet will completely disappear if its image falls directly upon the
blind-spot. At a distance of 42 inches the invisible area is about 12
inches from the point of sight and about 3 to 4 inches in diameter. At 300
feet the area is about 8 feet in diameter. The actual size of the retinal
blind-spot is about 0.05 inch in diameter or nearly 5 degrees. Binocular
vision overcomes any annoyance due to the blind-spots because they do not
overlap in the visual field. A one-eyed person is really totally blind for
this portion of the retina or of the visual field.
The bacillary layer consists of so-called rods and cones. Only the rods
function under very low intensities of illumination of the order of
moonlight. The cones are sensitive to color and function only at
intensities greater than what may be termed twilight intensities. These
elements are very small but the fact that they appear to be connecting
links between the retinal image and visual perception, acuity or
discrimination of fine detail is limited inasmuch as the elements are of
finite dimensions. The smallest image which will produce a visual
impression is the size of the end of a cone. The smallest distance between
two points which is visible at five inches is about 0.001 inch. Two cones
must be stimulated in such a case. Fine lines may appear crooked because
of the irregular disposition of these elemental light-sensitive points.
This apparent crookedness of lines is an illusion which is directly due to
the limitations of retinal elements of finite size.
The distribution of rods and cones over the retina is very important. In
the fovea centralis--the point of the retina on the optical axis of the
eye--is a slight depression much thinner than the remainder of the retina
and this is inhabited chiefly by cones. It is this spot which provides
visual acuteness. It is easily demonstrated that fine detail cannot be
seen well defined outside this central portion of the visual field. When
we desire to see an object distinctly we habitually turn the head so that
the image of the object falls upon the fovea of each eye. Helmholtz has
compared the foveal and lateral images with a finished drawing and a rough
sketch respectively.
The fovea also contains a yellow pigmentation which makes this area of the
retina selective as to color-vision. On viewing certain colors a
difference in color of this central portion of the field is often very
evident. In the outlying regions of the retina, rods predominate and in
the intermediate zone both rods and cones are found. Inasmuch as rods are
not sensitive to color and cones do not function at low intensities of
illumination it is obvious that visual impressions should vary, depending
upon the area of the retina stimulated. In fact, many interesting
illusions are accounted for in this manner, some of which are discussed
later.
It is well known that a faint star is seen best by averted vision. It may
be quite invisible when the eye is directed toward it, that is, when its
image falls upon the rod-free fovea. However, by averting the line of
sight slightly, the image is caused to fall on a retinal area containing
rods (sensitive to feeble light) and the star may be readily recognized.
The fovea is the point of distinct focus. It is necessary for fixed
thoughtful attention. It exists in the retina of man and of higher monkeys
but it quickly disappears as we pass down the scale of animal life. It may
be necessary for the safety of the lower animals that they see equally
well over a large field; however, it appears advantageous that man give
fixed and undivided attention to the object looked at. Man does not need
to trust solely to his senses to protect himself from dangers. He uses his
intellect to invent and to construct artificial defenses. Without the
highly specialized fovea we might see equally well over the whole retina
but could not look attentively at anything, and therefore could not
observe thoughtfully.
When an image of a bright object exists upon the retina for a time there
results a partial exhaustion or fatigue of the retinal processes with a
result that an after-image is seen. This after-image may be bright for a
time owing to the fact that it takes time for the retinal process to die
out. Then there comes a reaction which is apparent when the eye is
directed toward illuminated surfaces. The part of the retina which has
been fatigued does not respond as fully as the fresher areas, with the
result that the fatigued area contributes a darker area in the visual
field. This is known as an after-image and there are many interesting
variations.