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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas

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The origins of optics are shrouded in the darkness
of time. However, for the purposes of our survey, we
shall take our start in the fifth century B.C. with the
opinion of Empedocles concerning the nature of light;
he believed that light was produced by an effluvium
which emanated from bodies and impinged on the
organ of sight. The atomist Leucippus of Miletus, a
contemporary of Empedocles, expressed some more
definite ideas about sensations:

Every change produced by or impressed on things takes
place by virtue of a contact; all our perceptions are tactile,
and all our senses are varieties of touch. Consequently, since
our mind does not proceed from within us to sally forth
and touch external objects, it is necessary for these objects
to come and touch our mind by passing through our senses.
Now we do not see objects approaching us when we per-
ceive them; therefore, they must be sending to our mind
something which represents them, some shadow-like images
or material likenesses (simulacra) which cover these bodies;
these images move about on their surfaces, and can detach
themselves in order to bring to our mind the shapes, colors,
and all the other qualities of the bodies from which they

(Leucippus A, 29-31 Diels-Kranz).

Not all the philosophers of that time, however,
shared these same opinions. Thus, Democritus, accord-
ing to Theophrastus' (De sensibus 50; in Diels-Kranz,
A 135) report, maintained that “the air interposed
between the eye and the object receives a kind of
impression as a result of the compression exerted upon
it by the eye and by the object.” Archytas of Tarentum,
according to Apuleius, had a still more divergent idea:
he held that vision arises as the effect of an invisible
“fire” emitted from the eyes so that on encountering
objects it may reveal their shapes and colors.

This variety of opinion shows that in the fifth and
fourth centuries B.C. the problem of vision was at the
center of philosophical speculation; this sort of thinking
constituted the “optics” of that time. The word “op-
tics” is obviously of Greek origin, and really signifies
“science of vision.” It was not merely concerned with
an isolated problem, but entered into the great forum
of philosophical speculations of that period concerning
our “knowledge of the external world.” To the ques-
tion: How can the mind know that which surrounds
it?, the answer was quickly given that the sensory
mechanism served that function. The inquiry went
deeper, however, in order to explain the functioning
of each of the senses, and an exhaustive explanation
was offered for touch, taste, smell, and hearing. On
the other hand, the problem concerning sight presented
insurmountable difficulties. To explain how it is possible
to see simultaneously so many figures of diverse shapes
and colors and located in different places required the
investigations and researches of a score of centuries.

Putting aside the difficulty of “action at a distance,”
a problem which appears in the fragment of Leucippus
quoted above, the possible solutions of the problem
of vision were very limited; either something from the
object arrives at the eye, or something from the eye
goes out to the object, or else the intervening medium
serves as the connection between the object and the
eye. However, all of these solutions invited devastating
criticisms; discussion was both intense and violent
among the supporters of conflicting opinions. To de-
molish the ideas of opponents was easy, but no one
succeeded in constructing an acceptable theory.

As the result of extended studies speculation rallied
around two extreme conceptions: “visual rays” and

The theory of visual rays was maintained by mathe-
maticians, and it dominated the philosophical forum
for more than a thousand years. It was justified by
adopting an idea taken from a tactile experiment: a
blind man could know the shape, size, and position
of an object by exploring it with his hand; but he could
also explore it by means of a stick held in his hand,
that is, by an indirect “contact.” Since it was believed,
following Leucippus' dictum, that “all the senses are
varieties of touch,” it was not absurd to think that the
eye was supplied with something like sticks capable
of exploring the external world and of informing the
“sensorium,” i.e., the sensitive part of the eye, about
the world, as the blind man's stick does. It was there-
fore supposed that every eye emitted rectilinear and
slender emanations capable of exploring the external
world and of supplying the mind, by way of the eyes,


with the elements representing the external world, and
thus creating “the world of appearance.” This model
was very suitable for the study of perspective. A fol-
lower of this theory was none other than Euclid who
used it in his Optics and Catoptrics. Claudius Ptolemy,
when he wrote his Optics, also made use of visual rays.

The theory of “replicas” (also called simulacra, or
shadowy images) was the idea contained in the frag-
ment of Leucippus, quoted above; but one had to admit
that the replicas emitted from a body (in all directions)
had to contract along the way, while remaining similar
to themselves, until they became small enough to pass
through the pupil of an eye wherever it might be.

But the most important event of this period was the
contribution of Plato. He was deeply concerned with
the problem of the knowledge of the external world,
and particularly with that of the sense of sight. Un-
fortunately, he arrived at conclusions that had a dis-
astrous effect.

There was the very widespread and much discussed
opinion that the sensory apparatus generally does not
guarantee the information which it transmits to the
mind. On the other hand, the Epicurean school con-
sidered the senses infallible; all the others without
exception were convinced that the senses were more
or less deceptive. Still other thinkers found that not
all the senses were equally deceptive, and in the studies
of this subject came to the conclusion that touch is
the one sense in which we could place the greatest
confidence (although not completely, because touch
might also yield mistakes). Much more important,
however, was the conclusion that least deserving of
confidence was the sense of sight itself.

Plato's reasoning here was perfectly logical. The
external world comes to be known through the repre-
sentations that the mind makes of it, that is, by means
of the world of appearances. Now these mental repre-
sentations may be produced by the information coming
to the mind through the senses, but they may also be
spontaneous. Well then, Plato reasoned, those repre-
sentations which are created in the mind by means of
sensory information, especially when it comes by way
of the eyes, as a rule merit belief least of all; they do
not represent truth. On the other hand, those repre-
sentations made by the mind on its own initiative do
not show any trace of the deceptiveness of the senses,
and are therefore perfect, and therefore true.

These perfect and true representations are mathe-
matical; reasoning in this way Plato denied all value
to experience and assigned the entire value of specula-
tive thought to mathematical conceptions. In this re-
gard there is a very significant passage in the Phaedo,
one of the best known of Plato's dialogues:

And thought is best when the mind is gathered into herself
and none of these things trouble her—neither sounds, nor
sights nor pain nor any pleasure—but when she takes leave
of the body, and has as little as possible to do with it, when
she has no bodily sense or desire, but is aspiring after true

(Phaedo 65B; trans. Jowett).

The repercussions of Plato's philosophy were in-
calculably far-reaching. Given the authority of Plato,
his ideas practically paralyzed experimental activity
in the world of science. Sight in particular was con-
demned as a dangerous sense. A terrible sentence was
pronounced upon it: Non potest fieri scientia per visum
—“scientific knowledge cannot be achieved by
vision alone.” The rule was laid down that seeing is
believing only when sight conforms with touch. These
instructions entered the curriculum, and were taught
from one generation to another for more than twenty

The evidence on this matter is incredibly vast. It
is sufficient to consider the texts on optics in antiquity
and in the Middle Ages. In each of these texts a few
pages are devoted to the description of a few well-
known optical phenomena, but many more pages em-
phasize optical illusions. Even Lucretius, a convinced
Epicurean, in his poem On the Nature of Things (De
rerum natura
) did not doubt the deceptiveness of the
sense of sight, but instead of putting the blame on the
sensory apparatus, he attributed it to the inability of
the mind to interpret correctly the information coming
to it from the eyes. He concluded his treatment of
optics as follows:

Many other things of this sort we may observe with no less
wonder, phenomena which would lead us to distrust our
senses; all in vain, since most of them deceive us on account
of the mind's judgment which we interpolate ourselves, so
that we end up believing we have seen things never per-
ceived by the senses. In fact, there is nothing more difficult
than distinguishing plain facts from the delusions which the
mind straightway adds of itself

(Book IV, lines 462-68).

Considering the novelty of these ideas, we may
profitably examine other passages. One of them refers
to a well-known episode. The doubting apostle Saint
Thomas, was not present when Jesus, having risen from
the grave, entered the room where the apostles were
assembled. Thomas did not believe what the other
apostles told him, and he asserted that he would believe
only if he had “touched with his hand” the side of
the body of the Redeemer. And when Jesus reappeared,
he satisfied Thomas accordingly (John 20:24-27).

Another very interesting passage, fifteen centuries
later, is an excerpt from the Treatise on Painting (Trat-
tato della Pittura,
ca. 1550) of Leonardo da Vinci:


Masters do not rely on the judgment of the eye, because
it always deceives one, as is proven by anyone who wishes
to divide a line into two equal parts by judging with the
eye, and finds out how often the experiment fails. Wherefore
good judges always fear as suspicious similar reports of eye
witnesses, reports which ignorant persons accept...

graph 32).


It is well known that as a consequence of the politi-
cal events in the centuries following the advent of
Christianity, the center of gravity of the civilized world
was displaced from Greece to the Middle East. So far
as optics is concerned, an especially important contri-
bution was made by the school that flourished in
Bagdad around the ninth century. The famous philoso-
pher Abu-Yūsuf Ya'qūb ibn-Ishāq (813-80), called
Alkindi (or al-Kindi) in the West, asserted in the course
of his astrological studies that the action of the stars
on terrestrial things came about by means of rectilinear
rays emitted by every star in all directions. At another
time he advanced the idea that vision also came about
through the action on the “sensorium” of rectilinear
rays like those from the stars, but emitted by terrestrial

These ideas were taken up by Abu Ali Mohammed
ibn al-Hasan ibn al-Hythan, known in the West as
Alhazen. Previously, Lucretius had written in the
aforementioned work On the Nature of Things:

Moreover the eyes shun flaming objects and avoid looking
at them. Thus the Sun can blind you if you should continue
to look at it steadily, because its force is powerful and its
images, vibrating from the sky above across the clear at-
mosphere, disturb the tissues of the eyes. But any bright
splendor sears the eyes for the reason that it possesses seeds
of fire which penetrate the eyes and produce pain in them

(Book IV, lines 324-31).

Alhazen repeats these observations and adds another
of great interest: if anyone, after looking at the Sun
or any other intensely bright source, closes his eyes,
he continues to see its shape in “after-images” persist-
ing for an appreciable time. Today this phenomenon
is called “persistence of retinal images.” These phe-
nomena can be explained only by admitting that an
external agent acts on the sensorium, and therefore,
the theory of visual rays had to be regarded as de-

However, Alhazen did not limit himself to advancing
new arguments in order to demolish a theory which
many had already criticized. To be exact, his most
important contribution was to have offered reasons
which permitted him to explain how the replicas or
“skins” of a body as big as a mountain could pass
through the pupil into the eye without having to un-
dergo a contraction along the way. He regarded every
object as composed of so many elements, each of which
emitted its own tiny replicas in every direction; these
can enter the pupil of an eye wherever the eye happens
to be, and that can occur without any contraction
during their propagation. It is necessary to add that
these elemental replicas, while entering the eye, retain
their rectilinear path; and this was in agreement with
the ideas then current concerning the structure of the
eye and the path of refraction. In this way then the
eye comes to obtain an impression of shape similar to
that of the observed object. Although Alhazen did not
make the image reach as far as the retina (because he
wished to avoid the inversion of the image itself) and
made the hypothesis or simply assumed that the sensi-
tive area was the front surface of the eyeball, he gave
the initial ideas of the elements involved which later
led to the retinal image, thanks to the studies of
Maurolycos and especially to Kepler. This was a defin-
ite achievement, even if the optical mechanics on
which it was based was only to be perfected in due
time. But that is how what we today call the “retinal
image” arose.

Although the belief was strengthened that the sen-
sorium received an impression from an external agent,
still it was the general opinion that this impression had
to be received and elaborated by the mind, and that
to the latter belongs the final function of exhibiting
the impression in the world of appearances. But then
the problem of determining the nature of the external
agent assumed major proportions; and in the scientific
Latin vocabulary of that time this external agent was
designated by the term lumen while lux was used to
indicate its mental representation.

Alhazen's ideas (which were not limited to those
mentioned above) penetrated the Occident very slowly;
knowledge of these ideas was largely due to the work
of Vitellius or Witelo, who wrote an Optics in ten
books (Opticae libri decem). The work was in substance
actually a paraphrase of the works of Alhazen, even
though his name was not mentioned. Witelo's work
enjoyed a widespread diffusion and came to be re-
garded as a classic, known as Witelo's Optics, or simply

In order to understand the variety of contributions
that make the history of optics so rich and interesting,
it should be made clear that vision is a very complex
phenomenon, including as it does physical, physio-
logical, and also psychological elements. Because per-
sons of very diverse backgrounds and points of view
have occupied themselves with these elements in the


theory of vision, progress was made at different times
now in one branch of the subject and then in another.
Thus the theory of visual rays led to notable advances
in the geometrical treatment of the phenomenon, be-
cause mathematicians like Euclid and Ptolemy had
been interested in optics. The predominantly physico-
physiological bent of the Arabs had advanced the study
of the organ of vision. Then, around the thirteenth
century, the contribution of ecclesiastical dignitaries
consisted in giving special consideration to psychologi-
cal and philosophical as well as to theological aspects
of vision.

In the West the Greek term “optics” was replaced
by the word “perspective,” of Latin derivation, without
any change in content. Thus, the principal cultivators
of the science of perspectiva in the thirteenth century
were Robert Grosseteste, bishop of Lincoln, John
Peckham, archbishop of Canterbury, the Franciscan
friar Roger Bacon, Saint Bonaventura, and Saint
Thomas Aquinas. In their works perspectiva came fairly
close to being an article of theology, even if they took
into serious consideration the principles and contri-
butions of the Arabic school. Henceforth, no one was
to doubt any longer that vision was due to the action
of a lumen on the eye, but for them the central problem
was about the nature of the light (lux), which some
actually regarded as divine. At the same time, however,
the nature of the lumen was discussed in depth, espe-
cially the nature of the species, a name which in the
Middle Ages denoted a new conception of the replicas,
like their Greek prototypes, but much less materialistic.
There was a great deal of argument over the suitability
of “substance” or “accident” or “quality” to describe
the species of light, but the discussions, though subtle,
were inconclusive.

On the other hand, mathematicians continued to
make use of visual rays even if these rays now were
no longer needed to represent real entities. Nonetheless
they still constituted an excellent working instrument,
especially for studies of perspective (in the modern
sense of the word), which retained its essentially geo-
metrical content.

In summary, the closing centuries of the Middle Ages
witnessed a veritable decay among the theories in this
field of optics, in which it was barely possible to distin-
guish three principal tendencies: the mathematical one
of visual rays, the physico-physiological one of the
Arabic school, and the metaphysical one. Ideas con-
cerning vision may be summarized as follows: the
lumen, composed of “solar rays,” by illuminating bod-
ies produced an emission of “species” from the bodies;
these “species,” according to the process described by
Alhazen, entered the eyes and by stimulating the sen-
sorium produced a mental picture of the shapes and
colors of the world of appearances, which thus came
to be perceived as light (lux).

If in that manner one could explain vision when the
eye looked directly at an object, the problem became
entirely mysterious when the path of the “species” was
changed by an optical instrument, as in the case of
a plane mirror, and even worse in the case of a curved
mirror. There was as yet no idea at all about the true
nature of the optical image given by a plane or curved
mirror. Everyone was agreed in considering the image
an optical deception as the figures were seen where
the objects were certainly not to be found.

Some began to study the reflection of rays by con-
cave spherical mirrors, and since they began at first
with mirrors of wide angular opening (like those that
were entirely hemispherical), they began to construct
“caustic curves”—which are epicycloids, as is now well
known (Figure 1). Now, at night, by directing a con-
cave mirror towards a star in the sky, the mathe-
matician who had calculated the caustic saw a lumi-
nous point beyond the mirror itself. It was humanly
impossible to find a connection between the caustic
formed by the rays coming from the star and reflected
by the mirror, and the luminous point seen. It was
necessary to conceive two distinct entities; the rays
constituting the light (lumen) and the “species” capable
of producing vision.

Comparable reasoning had to be applied to the study
of rays passing through a glass sphere (pila crystallina).
Here too caustics like those of spherical mirrors were
found, complicated besides by the appearance of
colors. In this case, also, there was no way of con-
necting these caustics with the figures that were seen
by looking through the sphere.



A new development, that was bound to have far-
reaching consequences, occurred some time between
1280 and 1285 (the exact year cannot be determined).
Some artisans discovered that by placing in front of
the eyes of old persons transparent glass disks with
upcurved, clear surfaces, these persons saw things at
close quarters as well as they had when they were
young. These glass disks, having a shape similar to that
of a thick lentil, were called “lentils of glass” and also
“glass lentils” (later, “lenses”).

The proof that this discovery or invention was made
by artisans is based on several considerations. Assuming
that it was not known at that time what presbyopia
(farsightedness) was, and even less was known as to
how a lens really functioned (the law of refraction was
not formulated until more than three centuries later),
no possible reasoning could have led anyone to correct
farsightedness with a convergent lens; besides, the fact
that the glass disks were named after a vegetable surely
excludes the idea that they were fabricated or named
by a man of science. But the most convincing proof
that the glass lens was not a product of the science
of the thirteenth century is shown by the fact that when
the mathematicians became acquainted with the lens,
they examined it in the light of the science of the time,
and pronounced the inevitable verdict: “The glass
lenses are deceptive contrivances; don't look through
them if you don't wish to be fooled.”

This judgment may seem absurd today, but at the
time when it was pronounced it constituted the most
correct and logical application of the prevailing sci-
ence; since the figures seen through the lenses are never
verified by touch, they therefore are not true but
deceptive. For that reason glass lenses were not ad-
mitted to the field of science, and no man of science
took them seriously. If the lenses survived condem-
nation, it was owing to the “ignorance” (as Leonardo
da Vinci expressed it, in the passage quoted above) of
the artisans who had not faced the difficult problems
of man's knowledge of the external world.

The improvement of the lenses was likewise due to
the fact that the artisans gave the lenses' surfaces
different curvatures according to the age of the user;
and we also owe to the artisans the invention of con-
cave lenses for the correction of myopia (nearsighted-
ness). Historical search for the inventor of lenses, of
the kind to correct either presbyopia or myopia, shows
no hope of success; the makers of eyeglasses, who were
mostly illiterate, have written nothing about them; men
of scientific learning did not take the invention of
eyeglasses seriously; consequently, a discovery such as
the correction of nearsightedness, which today would
be rewarded with the richest international prizes, has
remained unhonored and unsung.

The banishment of lenses from science lasted for a
full three centuries. The history of lenses and especially
of the reversal of the situation, constitutes one of the
most significant and most interesting chapters in the
history of science. The protagonists in this great turning
point, which had repercussions of enormous conse-
quence on scientific progress in general, were Giambat-
tista della Porta, Johannes Kepler, and Galileo Galilei.

Della Porta (more commonly known as Porta) has
to be credited with having initiated this chapter of
history, but his contribution was not a truly scientific
one. Everything published about lenses, before Porta,
hardly fills an entire page, and while nearly everything
published was written in order to accuse the lenses
of deception, Porta in his magia naturalis (“Natural
Magic”) of 1589, devoted an entire chapter (Book XVII,
Ch. X) to the descriptions of the curious effects of
lenses. Besides, in the introduction to that chapter he
had the courage to write:

... (these wonders) are the same as the effect of lenses
(specillorum), which are absolutely necessary to the conduct
of human life. Nobody has as yet demonstrated either their
effects or the reasons [for these effects].

It is noteworthy that lenses were discussed here for
the first time in a printed book, and that it was not
a scientific book, but a collection of curiosities; also
it was not because the author was a man of science,
but an autodidact in search of wonders. It is to be noted
also that here lenses are called specilli, a respectable
name not reminiscent of any vegetable like lentils.

The passage quoted above had a remarkable histori-
cal importance for two reasons: in the first place be-
cause Porta's Magia naturalis had an enormous cir-
culation (it was translated into various languages
including the Arabic) and hence drew the attention
of a very large public to lenses; in the second place,
because in the quoted sentence there is implied a direct
accusation against science for not even having tried
to explain the operation or effects of lenses.

Porta himself thought of filling this serious scientific
lacuna by publishing his work on refraction (De refrac-
1593). It is a very pretentious work but of less
than modest content; nonetheless it is important be-
cause in Book VIII Porta makes the very first attempt
at a scientifically oriented study of lenses. There are
absurd arguments in it, even if Porta declared himself
satisfied with them, but they constitute a most impor-
tant testimonial of the optical knowledge of the time.
It is quite obvious to a reader today that it was impos-
sible for the ideas of medieval optics to explain the
functioning of lenses. Therefore, either medieval optics


or lenses had to disappear from the scientific scene.
Since lenses had already had three centuries of experi-
mental success, the fate of medieval optics was sealed.

As a matter of fact medieval optics was replaced
very soon by a new optics that is still valid today. The
birth of this new optics may be said to have occurred
in 1604, the year which saw the publication of
Johannes Kepler's work, Paralipomena ad Vitellionem.
Actually the abbot Francesco Maurolico in several
manuscripts, some bearing the date 1521, had already
advanced some new ideas such as the assumption that
every point of a body emits rectilinear rays in all
directions, rays that are neither visual nor solar but
simply geometrical; they are the rays of the geometrical
optics of today. However, since these manuscripts were
only first published in 1611, thirty-six years after their
author's death, Maurolico must be considered an iso-
lated pioneer who was not understood. Nevertheless,
Kepler carried out Maurolico's reasoning to conclusions
of fundamental importance.

There is a mine of new ideas in the aforementioned
volume of Kepler, but here we shall select two in
particular: the key to the mechanism of vision and the
conception of the optical image. We are in fact dealing
here with two fundamental and definitive achieve-

As for the mechanism of vision, we owe to Kepler
the proof of how “retinal images” (as they are called
today) are formed on the retina (Paralipomena ad
Ch. III, Pro. ix). He demonstrated that a
cone of rays emitted from a point source becomes
transformed, by refraction through the transparent
media of the eyes, into another cone that also has the
pupil for its base but has its vertex on the retina. And
so, if the object is formed of many points, we obtain
on the retina a stimulus arranged in an order corre-
sponding to that of the object (Figure 2).

He went further. He did not limit the process to
the formation of the retinal image, but pursued his
inquiry as far as the boundaries of the mind, even
facing the classical problem of how the mind utilizes
the elements of the retinal stimulus in order to create
therefrom its representation of the observed world. The
idea was clearly that this representation had to be a
figure created by the mind and located in front of the
eyes. The problem was to establish criteria for deter-
mining the shape and position of this figure.

Taking as his first object a point emitting rays, Kepler
quickly came to the conclusion that the stimulated area
of the retina defines the dimensions of the figure, so
that if this stimulated area is very tiny (as in the case
of a point-source of rays), the figure must be a “lumi-
nous point.” He also inferred that the “position” of
the stimulated point on the retina defines the “direc-
tion” in which the object-point is located and in which,
therefore, the luminous point is to be found (Figure 3).

At this juncture Kepler ran into the greatest difficulty
concerning the visual process, namely, how to deter-
mine the distance from the object-point to the eye.
The solution of this problem was enormously impor-
tant. Kepler started from the idea that to measure a
distance by means of optical data, it is necessary to
triangulate, and he showed that this is precisely what
happens in binocular vision by virtue of the conver-
gence on the object of the visual rays of both eyes.
But he noted further that vision can be accomplished
also by one eye alone, and that also under these condi-
tions the mind must have the elements needed to de-
termine the distance from the object to the eye. More-
over, in this case, too, a triangulation is required, and
Kepler found the triangle formed by the point-object
as its vertex and the diameter of the eye's pupil as
its base. He assumed that the observer's mind is able
to evaluate the elements of this (telemetric) triangle,
and he called the latter “the triangle which measures
distance” (triangulum distantiae mensorium).

In conclusion, the mechanics of vision, as Kepler
conceived it, emerges as follows: the object-point emits
rays in straight lines in all directions; from these rays
a small cone is formed as they enter the eye of the
observer; the cone is refracted and transformed into
another cone having its vertex on the retina, which
becomes stimulated at a point. From this point signals
start along the optic nerve reaching the brain and


mind, which thus is informed that the object is a point
lying in a certain direction at a certain distance. The
mind therefore creates a very tiny figure, a “luminous
point”; which it locates at the vertex of the telemetric
triangle, where the object-point should be found. The
observer then asserts that he is “seeing the object.”

Although Kepler did not concern himself with other
characteristics of the “luminous point” such as its color
and brightness, his achievement is a masterpiece that
will never be sufficiently admired. He soon drew from
this theory about luminous points consequences that
are fundamental for modern optics. The reasoning,
outlined above, requires that light rays proceed in
straight lines, but that does not always happen; in
particular they can be bent by reflection at a mirror
or by refraction through one or more surfaces. Kepler
first considered the simplest case, that of a plane mir-
ror. The rays coming from an object-point are reflected
by the mirror so that their lines of prolongation back
of the mirror meet in a point behind the reflecting
surface. Therefore they impinge upon the eye of the
observer as if they proceeded from that point. Pene-
trating the eye, the rays stimulate the retina, and
consequently by applying the mechanical procedure
described above, the observer's mind is bound to locate
the luminous point at the vertex of the telemetric
triangle. For this reason the observer cannot locate the
point on the object but has to locate it at the point
symmetrically opposite, behind the mirror. Therefore,
a figure can be also seen where the object actually is
not situated. Hence the observer cannot say that he
“sees the object,” but should say he “sees its image.”

That is how the current idea of an optical image
originated. However, we no longer talk about a tele-
metric triangle, because since Kepler's time new ideas
about optics have arisen which we shall discuss shortly.
But before proceeding, we must point out that Kepler
himself asserted that his theory did not always corre-
spond to experience. To be precise, things went well
when the images fell on a screen, but did not always
turn out so well when the eye looked directly at a
mirror or other optical device. Kepler understood that
in these two sets of conditions there was something
clearly different, and he expressed this conviction by
the use of two different names for the figures seen;
those seen on the screen he called “pictures” (picturae),
and the others he called the “images of things” (imag-
ines rerum
). He advised his scientific readers to con-
centrate their attention on the pictures.

The fact remains that Kepler was the first to explain
in a satisfactory manner why we see the figures of
objects placed in front of a mirror as though they were
behind it (op. cit., Ch. V, Pro. xviii, Definition).

Among the numerous new and important ideas con-
tained in Kepler's Paralipomena ad Vitellionem it is
interesting to note an omission, namely, that there are
no studies of lenses (op. cit., Ch. III, passim). Despite
his competence in optics, even Kepler did not believe
in lenses. He did devote one page to explaining the
correction of farsightedness by means of convex lenses,
and of nearsightedness by means of concave lenses. But
he makes a point of writing that he made this inquiry
as a result of the insistent pressure, over a three-year
period, of a high authority in Prague. It is obvious that
Kepler wished to excuse himself before the mathe-
maticians of his day for giving to lenses any consid-
eration at all (op. cit., Ch. V, Pro. xxviii).

Kepler's book did not produce any reaction when
it appeared; it was too new and too difficult to under-
stand. The fact that Kepler's work was soon forgotten
may be attributed to the extremely conservative tend-
ency of the science of the time, shared by all in that


cultural environment. It is incredible that such a rich
harvest of new ideas and great accomplishments should
have been so neglected that even towards the end of
the seventeenth century nearly all scientific men were
still talking the language of medieval optics.

However, the arrival on the scene of Galileo Galilei
brought about in a much more effective manner the
collapse of ancient optics and the renewal of the scien-
tific mentality. It may seem odd that a result of this
sort should have been produced by a scientist who had
such a very modest competence in optics, a science
which was then entirely limited to medieval optics.
Galileo was a professor of mechanics and astronomy
at the University of Padua.

Galileo's contribution came about in 1604 when
some artisans of Middleburg, Holland put into circula-
tion some spyglasses with a diverging eyepiece. These
spyglasses were made by copying a model that came
from Italy and bore the date 1590. These spyglasses
met with no approval. Strange as it may seem today,
the fact is that no scientist was interested in the new
instrument. But this negative response could not have
been different for any instrument that used lenses.

Even though the general public was not imbued with
philosophical prejudices, it did not appreciate the new
instrument because people considered it useless. This
reaction was due to the fact that the spyglasses from
Holland were made with the lenses of ordinary eye-
glasses and, as today's technical optics can easily ex-
plain, such lenses cannot make a worthwhile spyglass.
The result, in fact, was that the Dutch did not succeed
in getting a magnification of more than three times,
and it is known that an instrument magnifying only
three times is a poor instrument and serves no
useful purpose. This was precisely the conclusion
reached by the layman to whom the spectacle-makers
of the time tried to sell the new “spyglasses” (occhiali).
Despite this fact, in 1608 spyglasses were found in the
shops of the opticians in Paris, but the situation may
be summarized by saying that the spyglass was made
badly by the opticians; it was despised by the public
and condemned by the scientists.

The situation changed radically with Galileo's com-
ing on the scene. He had learned of the existence of
the spyglass in the spring of 1609, but paid no attention
to it; however, during the first week of July he had
the new idea that the spyglass could be a valuable
instrument (C. De Waard, Jr., De Uitivinding der Ver-
The Hague [1906], pp. vi, 340). He began
to build it with his own hands for he realized that he
needed to make the lenses better than the opticians
had made the eyeglasses. He devoted himself intensely
to this task of improving the power of the eyeglass,
and in a short time he achieved extraordinary results;
his telescopes within three months attained a power
of magnification of thirty times. To the public “Gali-
leo's telescope” was a new instrument which left the
spyglass of the spectacle-makers far behind. In reality,
it was the same spyglass with a diverging eyepiece,
except that Galileo's lenses were much better made.

With this new instrument Galileo made amazing
astronomical discoveries, among which the most revo-
lutionary was his discovery of the satellites of Jupiter.
When Galileo announced in his Sidereal Messenger
(Sidereus nuncius, March 1610), the discovery of four
additional “moving bodies” in the sky, besides the
mountains of the moon, and the stars of the Milky Way,
the learned world launched a campaign of unprece-
dented violence against him. His discoveries struck a
deadly blow at traditional philosophy, astrology, and
even medicine, which was then closely linked to as-
trology. The scientists denied absolutely that these
discoveries had any value, seeing that they had been
made only by means of the telescope, an instrument
notoriously unworthy of confidence.

There ensued a tremendous polemic between the
whole scientific world (without any exception) on the
one hand, and Galileo all alone, on the other; yet he
was firmly convinced that he was right in believing
what he saw in his telescope, even though it was not
confirmed by the sense of touch.

As we have said, Galileo's competence in optics was
very modest. Still his adversaries hurled against him
the learning of all the philosophers and astronomers
of the twenty preceding centuries. He never chose to
fight back on technical grounds, and instead resorted
to totally extra-academic tactics by availing himself
of the collaboration of the Grand Duke of Tuscany,
Cosimo de' Medici. With this purpose in mind, Galileo
named the satellites of Jupiter “the Medicean Planets.”

Conducting his campaign with superlative skill,
Galileo succeeded in overcoming the hostility of the
scientists, and in making his “faith” in the observations
he had made with his telescope (cannocchiale) prevail.
Today this Galilean faith has become so universally
accepted that we have even forgotten about the pre-
Galilean lack of confidence in the sense of sight. Actu-
ally the fact that this diffidence dominated the scientific
world for twenty centuries has only recently been
discovered, and not everyone is as yet convinced about
it. It must also be pointed out that a very long time
elapsed before the old skepticism yielded to the Gali-
lean faith in lenses; it took several generations to
achieve this transition. The same was true in the case
of Kepler's new ideas in astronomy.

Kepler's own conduct during the anti-Galilean po-
lemic over Galileo's telescope was very interesting. For
some years Kepler himself showed a lack of confidence


in the discoveries made with Galileo's telescope.
Kepler did not treat them in his Paralipomena ad
or in his Dissertatio cum nuncio siderio.
His initial lack of confidence, in common with the
general skepticism of his time, was also evident from
the way in which he subjected to very severe tests the
telescope built by Galileo, given to him by the Elector
of Cologne, as though it was expected that its failings
would then appear, as others were trying to show. But
after two weeks of all these testings by himself and
others, Kepler was thoroughly convinced that Galileo
was right, so he became a convert to the new faith
about the end of August 1610, and wrote the Narratio
(published in September 1610).

Now that he was converted, Kepler again took up
the optical theory expounded in his Paralipomena ad
and in a few weeks wrote the Dioptrice
(published in January 1611). It was a wonderful little
book which for the first time propounded the theory
of lenses, and explained the operation of the telescope
with a diverging lens as eyepiece, and also laid down
the theoretical basis for the telescope with a converg-
ing eyepiece as well as for the telephoto lens.


Even if the great majority of scientific men remained
faithful to the principles of classical philosophy, in
particular to Platonic ideas, and deeply distrusted any-
thing experimental in character and hence based on
the senses, the number of converts to the new faith
increased every day. They formed a new class of per-
sons who preferred the direct observation of natural
phenomena to the reading of classical texts.

The philosophical line adopted in the behavior of
these persons is very interesting. They knew no argu-
ment capable of destroying the impeccable reasoning
of the classical philosophers and therefore never en-
gaged in debates that would surely end in favor of their
opponents. Instead, they simply closed their ears to
the classical teachings and ignored the old doubts about
the workings of the senses. They forgot the judgment:
“Science cannot be achieved by vision alone” (Non
potest fieri scientia per visum solum
) and employed the
optical instruments with complete confidence and en-

In summary, the contribution made by Galileo to
this sector of the subject was both technical and philo-
sophical. From the technical point of view he greatly
improved upon the spyglass and made it a usable
telescope; from the philosophical point of view he
restored confidence in the sense of sight both by direct
observation and by means of optical instruments, thus
restoring the value of sense experience. Having given
mankind a new and powerful instrument and the faith
to use and appreciate it, Galileo may be considered
the true and principal founder of modern science. The
birth date of modern science may be taken as August
24, 1609, the date of Galileo's letter to the Doge of
Venice. That letter was the first written document in
which a scientist had the courage to declare solemnly
that the telescope was capable of rendering services
of “inestimable aid.”

A confirmation, that may be called brilliant, of much
that has been expounded above is to be found in the
new history of the microscope. Many historians of
science have studied the history of the compound
microscope, believing that the history of the micro-
scope must be based on it. But the facts have to be
considered otherwise.

The compound microscope has its own history as
an instrument, because it has become a truly scientific
instrument after nearly two centuries of efforts by
persistent technicians. In reality it had its actual influ-
ence on scientific progress after 1840, the time when
Giovan Battista Amici placed a hemispherical lens in
front of the objective, and put forward “the technique
of immersion” (placing the object under scrutiny in
a drop of oil, between the front lens and the cover
glass). Until that time microscopy was done with the
simple (single-lens) microscope which gave better
service than the compound microscope did before the
above-mentioned innovations. All the great discoveries
in the microscopic field of research were made with
the simple microscope until the middle of the nine-
teenth century.

The “father of microscopy” is, by unanimous con-
sensus, Anthony van Leeuwenhoek; during his long life
he built hundreds of microscopes, but they were all
simple ones, not even one being compound. And with
the former simple type he made some stupendous
discoveries. His simple microscopes were converging
lenses, placed in a small metal mounting with a pair
of screws for bringing the object into focus.

Thus the history of microscopy is not that of the
compound microscope, which came upon the scene
only at a later date. Yet one may wonder whether the
simple microscope, consisting optically of a single
convergent lens, might not have been put to use before
the end of the thirteenth century. Why was it not

But that is not all. A concave mirror is also a micro-
scope, and, as we have already emphasized, the con-
cave mirror had been studied from the time of the
Greeks. Euclid in particular dealt with it in his
Catoptrics, and it was studied intensively in the Optics
of Claudius Ptolemy; hence, by that time it might have
been possible to make microscopic observations. The
fact then that as early as 1524 Giovanni Rucellai pub-


lished a short poem (L'Ape, lines 963-95) in which he
described the anatomy of a bee as seen in a concave
mirror, draws our attention to the behavior of his
contemporaries, not a single one of whom followed
Rucellai or used his technique of observation. Why?

The answer to this question is very simple; science
and philosophy regarded lenses and concave mirrors
as being deceptive, because they made one see figures
that were false to the sense of touch. The new Galilean
faith was needed to overcome this mode of reasoning,
and equally needed were new men. It is not without
significance that Antony van Leeuwenhoek's profession
was that of a sheriff's bailiff in the States-General of
Holland, and not that of a college professor. He had
learned to use lenses, while a child, for the purpose
of counting threads in a textile business.

However, alongside the new men, the numerous and
tenacious band of robed philosophers insisted on main-
taining the positions formulated in the classical texts.
The laws of nature rather than ratiocination and study
provided for the liquidation of these texts, but that
would take many decades. Only at the end of the
seventeenth century was medieval optics practically
displaced from the scientific field. Lenses had entered
the field of research with flying colors. They constituted
a subject of fertile study at the hands of first-rate
mathematicians and experimenters. Astronomy espe-
cially profited from them in a most conspicuous way.

Optical studies settled down on new sites. The
mathematicians who had once been occupied with
studying the geometrical behavior of visual rays and
then with that of solar rays, now devoted themselves
to studying the new geometrical rays. Kepler had
demonstrated the utility of these rays as a repre-
sentative model of lumen whether in reflection, refrac-
tion, the functioning of lenses, or the mechanism of

Scientists of an experimental and physical orienta-
tion came face to face with the great subject of the
nature of lumen and color, a subject which was of
interest not only from the scientific but also from the
philosophical point of view. The technical problem
finally assumed more importance and interest every
day, especially because men doing research were al-
ways asking for more powerful instruments free of any
defects. Some particulars about the development of
research along these new lines will bring us to consid-
erations of noteworthy interest.

The “new men,” as we have designated them, were
full of enthusiasm for the study of nature, and were
inspired by a great faith in observation and experiment,
having decided not to take too seriously the prepara-
tion and philosophical criticism of their work. Instead
of limiting themselves, under the classical rule, to
“describing” natural phenomena, they substituted the
claim to “explaining” phenomena by means of “mech-
anisms.” This new way of proceeding produced, on the
one hand, an unprecedented progress of science, but,
on the other hand, it failed to provide research with
a secure and thoroughly scrutinized foundation.

Generally speaking, though an exaggerated and un-
controlled positivism installed itself, it was nonetheless
enjoying an illusory position despite its usefulness. The
classical and basic distinction between the “world of
appearance” and the “world of reality” was forgotten,
and the result was to take as true, that is, as physically
and objectively real, what was indisputably a subjective
creation of the mind of the observer. Thus they suc-
ceeded in not realizing, or in taking least into account,
the role of the observer in the observation of phe-
nomena; they minimized everything that in classical
science had a psychical character, and they ended up
by attributing a physical nature to everything, what-
ever the cost.

An excellent example of the methodology just de-
scribed is furnished by the evolution of the concept
of “optical image.” There is no doubt that the images
seen with the use of optical instruments—whether it
is the simplest plane mirror, the magnifying lens, or
the more complex instruments for aiding vision—are
psychical entities, as Kepler had so well demonstrated.
The importance of the works of this learned scientist
can be better appreciated if we take due account of
the fact that observations made by different persons
have very subtle subjective characteristics, and are
therefore as diverse as there are different observers.
So long as this difficulty was not overcome, it was not
possible to square the optical observations with optical
theory. Kepler himself avoided concerning himself too
much with the images of things (imagines rerum). On
the other hand, the “pictures” (picturae) corresponded
fairly well with the rule of the (telemetric) triangle,
and that fact unified the functioning of the eyes of
different observers, and permitted the mathematization
of the theory of images. This method was a victory
of incalculable value, because it made possible the
development of geometrical optics.

However, in the new philosophical climate those
pursuing mathematical studies forgot that it was nec-
essary to intercept the picturae on a screen in order
to conform to the rule of the telemetric triangle, and
also forgot that the image is actually something “seen,”
that is, created by the observer's mind. Besides, their
thinking became distorted when it followed a line of
reasoning of the following sort: according to the rule
of the telemetric triangle, the observer “must” see the
image at the vertex of the cone of rays emerging from
the optical system and entering the eye; it is useless


to repeat this every time that an image is studied. Thus
the vertex of the cone of rays (Figure 4) emerging from
the optical system, was considered and called the
image, and one ceased to talk about the eye and the
telemetric triangle.

Thereupon the optical image lost its mental charac-
ter and assumed a purely objective and physical char-
acter independent of the observer. And that is why
Kepler was ignored or forgotten, and without any
genuine open discussion or deliberation a geometrical
optics was spontaneously installed, based on the hy-
pothesis that the rule of the telemetric triangle is
always and exactly verified. This was a clandestine
hypothesis that no one was conscious of as such, and
that is why it was never discussed and criticized. In
fact, the above-mentioned rule was also forgotten, and
very rarely it was fleetingly asserted that the image
of an object-point is seen at the vertex of the cone of
rays that reach the cornea of the observer's eye, as
if this were a self-evident truth.

Only recently have Kepler and the rule of the tele-
metric triangle been exhumed, and the function of the
human eye been discussed in the light of modern scien-
tific knowledge of optics. The result has been dis-
astrous: the rule itself is hardly ever verified; it really
plays the role of a wonderful “working hypothesis.”
For that reason geometrical optics is not the general
study of images, but is valid only for “pictures”
(Kepler's picturae), even if this label has been forgotten
and replaced by “images.” When this criticism was
enunciated, it remained surprising to observe how the
experimental test of geometrical laws was system-
atically avoided in the study of optics. The really
disturbing fact was that when optical images are ob-
served without projecting them on screens (especially
so-called “virtual” images which cannot be assembled
on screens), there is an enormous discrepancy between
the conclusions of geometrical theory and the experi-
mental data. The fact that the discrepancy was not
mentioned by anyone until a much later date shows
to what extent a well attested mathematical theory was
able to convince and blind so many experimenters.

It is thus evident that in the geometrical treatment
of optical images a definition of their nature was
avoided. When anyone tried to offer one, the many
conceptual difficulties which had been successfully
minimized by silence reappeared; and so the mathe-
matical treatment lost much of the value that had been
previously attributed to it.

Nowadays the definition of “images” has been thor-
oughly discussed, with the result that various types of
images must be distinguished; some are physical, some
mathematical, some mental, some chemical, and some
electronic. It has become clear that the images con-
sidered in geometrical optics are mathematical ab-
stractions with the aid of which we try to represent ex-
perimental images, but they are really very far from
doing so.

In the field of research on the nature of lumen and
of color, positivistic philosophy has exerted an influ-
ence analogous to the one just described with respect
to optical images. Dismissing the clear distinction be-
tween the world of reality and the world of appear-
ances, one has to cease also accepting as clear that
the lumen (radiation) is in the world of reality and the
lux (light) in the world of appearances. Just as was done
for picturae and imagines rerum, the distinction be-
tween lumen and lux was eliminated, and the use of
a single word light (luce) was inaugurated; it was this
term also that represented the mental entity. However,
though people ceased calling attention to the differ-
ence in “nature” between the external agent and the
mental representation, they spoke instead of the “na-
ture of light” (luce), of the “velocity of light,” and of
the “action of light” on the eyes. Thus they absolutely
avoided making it clear whether they were talking
about a physical object or the image that an observer
sees. In that way light became a physical entity. The
same course was run by the concept of color, a concept
which has always followed closely the fortunes of light.
Color also ended up by being considered a physical,
objective entity, and therefore independent of the

The most salient consequence of the philosophy of


physicists from the eighteenth to the twentieth century
was the emergence of two new sciences; photometry
and colorimetry, both arising with the evident purpose
of measuring light first and color afterward. An aim
of this kind could be conceived and pursued only by
persons convinced that light and color were physical
entities, since mental entities still cannot be measured.

It is of some interest to point out that this unfortu-
nate influence of philosophy on the distortion of the
fundamental concepts of optics was exerted despite the
fact that the great masters to whom we owe the most
important researches concerning the nature of lumen
and color, like René Descartes, Father Francesco Maria
Grimaldi, Isaac Newton, and Christiaan Huygens, and
so many others, had made it very clear that light and
color were clearly only entities of the mind.

In the seventeenth century the nature of lumen was
the subject of very animated discussions, which also
had repercussions in theological circles. For example,
Father F. Grimaldi wrote an impressive work on the
nature of lumen, color, and the rainbow (Physico-
mathesis de lumine, coloribus, et iride
), published in
1665, two years after his death. Most of the professors
were opposed to considering lumen as a substance, not
only because they were Aristotelians but also because
of the hostility in their circle towards atomism. The
opinion that prevailed among them was that lumen
was an “accident of the genus quality” (lumen accidens
de genere qualitatum
) or a motion, necessarily of an
undulatory nature.

However, for some time there had arisen a minority
who were convinced that lumen was of a material
or corpuscular nature, because only thus could one
explain its rectilinear propagation (which no one
doubted), for no one had succeeded in explaining how
such rectilinear propagation could result from wave
motion. On this point René Descartes was particularly
explicit in his Dioptrique of 1638; even while proposing
various models to explain light phenomena, he insisted
above all on the corpuscular model, regarding lumen
as a swarm of spherical corpuscles (Figure 5) endowed
with two motions: a very rapid translatory motion and
a rotational motion around the center of each corpus-
cle, which today would be called a “spin.” Descartes'
opinion was that this rotary motion was the physical
cause of the vision of colors in the sense that an ob-
server would see various colors according to the spin
with which particles impinged upon the retina. Still
using this corpuscular model, Descartes states in his
Dioptrique the law of refraction, which Willebrord
Snell had already formulated but not published. The
finding of an exact and definitive law of refraction, after
so many centuries of fruitless efforts, gave a fresh
impetus to the progress of optics.

Even Father Grimaldi was on the side of the fol-
lowers of the material conception of lumen, but he
also insisted on the subjective nature of light and color.
He has been considered a forerunner of the wave
theory of color because he attributed vision of the
various colors to the innumerably diverse frequencies
that the vibration of matter might have along the path
that the light-ray followed (Figure 6). He was driven
to the point of writing that he suffered an “irritation
of the bile” because of the irrational insistence of most
philosophers of his time that color was something
inherent in bodies while he himself maintained that
colors were the subjective effect of the action of rays
of lumen of diverse frequencies on the retina. And then
it should also be remembered that in Father Grimaldi's
volume, mentioned above, there was described for the
first time a group of phenomena known as “diffrac-
tion,” and that he coined the term (Pro. XLV, No. 41;
Pro. I, passim).

Isaac Newton's contribution profoundly influenced
the development of optical theories, especially those
concerning color, since for the nature of the lumen
he simply embraced the corpuscular theory, already
followed by many others. Newton began his research
activities in this domain when Father Grimaldi's work
appeared. Newton's theory was hailed as a great suc-
cess because he gave an explanation of the phenome-
non of refraction whereas no one in so many centuries
of studies had succeeded in giving a mechanistic ex-
planation of refraction. Newton's new idea was to
explain the deviation of the rays in refraction by means
of the force of attraction exerted by the matter of the
refractory body on the material corpuscles composing
the lumen. Admiration for Newton rose to great height
when he drew from his theory of universal attraction
the explanation of optical dispersion already observed
and studied by Marcus Marci of Kronland, who wrote


about it in his Thaumantias... (1648; Theorem XVIII,
p. 99; XXI and XXII, p. 101). Newton explained disper-
sion by imagining that the particles constituting lumen
possessed diverse masses, and consequently, refraction
made them undergo different amounts of deviation,
according to their mass. With that idea in mind, he
correlated colors with the deviations experienced in
refraction and consequently with the mass of the parti-
cles. However, in the most explicit and determined
manner, he insisted on asserting that colors are subjec-
tive phenomena, and that for this reason the rays, or
corpuscles of lumen, should be called “ruby-like” (pro-
ducing red) and not red. Newton declared that in his
own writings he had used the term “red,” not because
it was strictly and philosophically correct, but only
because “the vulgar” would not have been able other-
wise to understand the experiments he was prepared
to describe (Opticks, Book I, Part II, Pro. ii, Definition).

Unfortunately, Newton himself had to remark that
his idea of explaining optical phenomena by means of
the force of attraction between matter and corpuscles
led to conclusions that conflicted irremediably with
experience. In fact, he abandoned that idea, explicitly
admitting that corpuscles were endowed with natural
“dispositions” of the medieval type and that only these
“dispositions” and not the material forces of attraction
allowed one to explain the new optical phenomena
discovered in his time—the coloration of thin sheets
(by interference), the phenomenon of diffraction (dis-
covered by Father Grimaldi), and the double refraction
of Icelandic spar (discovered in 1669 by Erasmus
Bartolinus). In this situation Newton abandoned the
universality of the law of material attraction.

The conception of lumen as a swarm of colored
particles became untenable at the beginning of the
nineteenth century, through the works especially of
Thomas Young and Augustin Fresnel, when the cor-
puscular theory, which Isaac Newton had valued so highly and made so famous, collapsed quickly and was
replaced by the wave theory of Young and Fresnel.

Besides, by attributing to light an ethereal motion
of various frequencies, there was left no way of attrib-
uting luminosity to this motion which possessed neither
brightness nor color; the reason for color, finally, was
found in the frequency of the motion. This way of
thinking is still widespread on a vast scale among
physicists failing to consider how grotesque and absurd
are its logical consequences.

Subsequent researches in this domain formed a
branch of the science called “Physical Optics.” The
name was well justified so long as it was a matter of
physical research into the nature of an entity, lumen,
observable only by the use of the eyes, and hence, a
part of optics. But in the early years of the nineteenth
century Frederick W. Herschel discovered the infra-red
rays; Johann W. Ritter and William H. Wollaston
discovered the ultra-violet rays. Then other discoveries,
even more sensational, followed, leading to the mag-
nificent synthesis of James Clerk Maxwell; in his theory
the waves constituting light were made part of the
great series of electromagnetic waves.

As a result the study of the nature of the waves,
which had been a typical subject of optics, began to
lose its significance insofar as it was absorbed in the
study of electromagnetic waves in general. One could
deduce from this that optics would become a branch
of the science called electromagnetism and thus lose
its status as an autonomous science. The situation be-
came all the more complicated and precarious when,
in the meantime, new “detectors” were invented,
namely, instruments capable of revealing those waves
which until the beginning of the nineteenth century
had been observable only by means of the eye; specifi-
cally, these inventions were the photosensitive emul-
sions, used in photography, the thermoelectric pile, the
bolometer, the radiometer, and still others. To these
instruments radio receivers and photoelectric cells can
be added even if the latter are not all suited to reveal
electromagnetic waves capable of stimulating the
human eye also. The net result is that the eye lost its
exclusive function of revealing lumen, and descended
to the modest level of a very selective detector of
electromagnetic waves in competition with the others
listed above.

Such was the outcome of the extreme positivism that
had dominated optics in the eighteenth and nineteenth
centuries. As soon as most of the interest and attention
became concentrated on the physical agency capable
of stimulating the eye, and prevailed over research
sufficiently to disregard the contribution of the eye in
visual phenomena, it was inevitable that optics should
lose its significance as an autonomous science and


become absorbed in a more general branch of the
science of physics.

In order to avoid such a catastrophic conclusion it
was necessary to return to the origins of optics. Instead
of considering it as the study of a gamut of electro-
magnetic waves, limited to frequencies included in the
range capable of stimulating the human eye (limits
which nobody has as yet succeeded in defining in a
way accepted by or acceptable to the civilized world),
optics has been regarded as the “science of vision.”
Accordingly, optics has regained all of its unique and
indestructible character as an autonomous science. As
such, it is more complex in its constituents: partly
physical through the study of the external factor capa-
ble of stimulating the human eye; partly physiological
through the study of the response of the organ of vision
to the external stimulus; and finally, the decisive psy-
chological role played by the mind which is concerned
with the representation of the world of appearances
resulting from the external stimulation of the eye.

Before concluding this article, we must indicate the
importance of the development taken by “technical
optics” as a result of the establishment of the telescope
and microscope as scientific instruments of extremely
great value. Today we witness an extraordinarily deli-
cate and precise technique with scientific foundations
of a very distinctive nature. Galileo's initiative in de-
voting himself to working on lenses as the objectives
of telescopes, with a much greater care than that given
to the lenses of eyeglasses, was appreciated and fol-
lowed by several “masters.” With admirable persist-
ence and skill they obtained results which made them
famous. It suffices to recall the names of Ippolito
Mariani (the righthand assistant of Galileo), Francesco
Fontana and Eustachio Divini, and also Evangelista
Torricelli, successor of Galileo in the high office of
Mathematician of the Grand Duke of Tuscany, who
worked on objective lenses which are extraordinary for
their excellence, approximating the better ones we
have today.

Towards the middle of the eighteenth century, S.
Klingenstierna, in Sweden, and John Dollond, in Eng-
land, constructed the first achromatic objectives by
combining lenses made of different kinds of glass, thus
improving the performance of optical instruments.
However, optical technique has become very compli-
cated and could not remain exclusively in the hands
of even the most skillful artisans. Hence, it was neces-
sary to have recourse to the collaboration of expert
mathematicians to develop the “optical calculus,” a
new branch of applied mathematics, indispensable for
research on the design of systems most suited to pro-
vide the best performance. At the same time, it was
also necessary to generate the production of new types
of glass, called “optical glass,” endowed with the par-
ticular characteristics of refraction and dispersion
without which the designs prepared by the optical
calculators cannot be realized.

However, optical systems attained a rational basis
only after the wave-theory allowed the precise defini-
tion of tolerance in the characteristics of the materials
employed in working on them. These tolerances are
measured exactly in fractions of an optical wavelength,
which, as is well known, is of the order of magnitude
of half a micron (a thousandth of a millimeter).

The cooperation of mathematicians specializing in
geometrical optics with physicists specializing in
wave-theory has brought technical optics to the limits
of theoretical possibilities. Today there are optical
systems that are called “optically perfect,” in the sense
that even if they were made with finer tolerances they
would not perform any better. The limit of perform-
ance is determined by the structure of the radiation
employed and not by the excellence of the workman-


Thus optics has returned to having the significance
assigned to it by the ancient Greek philosophers when
they coined the name which exactly stands for the
“science of vision,” as we indicated in the beginning.
The same definition was adopted by Denis Diderot in
the great Encyclopédie of the French Academy. After
a long detour, the science of vision has returned to
the forefront of studies, bringing back order and clarity
in a field in which as a result of the great expansion
of research, due to the influence of the study of radia-
tion, there has occurred an unprecedented and enor-
mous upheaval. Refusing henceforth to talk about
“physical optics” and returning to its awareness of the
indisputably mental character of light, colors, and
images, “optics, the science of vision” resumes its
march towards a bright future.


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Theory of Vision
(London, 1709). René Descartes, La Di-
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ad Vitellionem
(Frankfurt, 1604); idem, Dioptrice (Augusta
[Augsburg], 1611). Marcus Marci de Kronland, Thaumantias
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ortu et causis
(Prague, 1648). Francesco Maurolico, Photismi
de lumine et umbra, Diaphaneon
(Naples, 1611). Isaac
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(London and Cambridge, Mass., 1970); idem,
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(Florence, 1967); idem, New Optics (Florence, 1971). E. Ro-
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Sizi, Dianoia astronomica, ottica, physica (Venice, 1611),
trans. C. Pighetti (Florence, 1964).


[See also Astrology; Atomism; Experimental Science; New-
ton on Method; Idea; Platonism; Positivism.]