Leonardo's Optics

These enthusiastic words show what Leonardo thinks of the eye — the main instrument both of a painter and a scientist. Three features of “the window of the soul” and related problems appear to be of particular significance for Leonardo da Vinci: (a) anatomy of the eye and the mechanism of seeing; (b) optical effects in the nature perceived through this “window”; and the more special problem — (c) how to express in the best way all the diversity of a real world in a flat picture.

Today we present a brief description of Leonardo’s activities in various aspects of optics, which is regarded as the “most reliable” science on various effects in nature perceived by the eye. Undoubtedly, it will be interesting and instructive for the reader to trace how the unsurpassed genius in the history proceeded from the formulation of problems to fundamental conclusions.

On mechanisms of seeing

In half an inch from the discovery

Trying to understand the mechanism of seeing, Leonardo rejected Plato’s ideas that “the visual power is extended from the eye by rays as far as the surfaces of nontransparent bodies.” He found a simple and convincing argument contra the emission theory: the rays from your eyes cannot embrace in the star-lit night sky all this abundance of stars at a quick glance.

Further research, however, turned out to be difficult and long. As always, Leonardo started his work from studying the structure of the object he was examining: “Describe in your “Anatomy” what proportion there is between the diameters of all the images in the eye and the distance from them of the crystalline lens.” As the eye content leaks away from the eye with an undercut shell, Leonardo devised an original method to overcome this difficulty: “In the anatomy of the eye, in order to be able to see the inside well without spilling its watery humour, you should place the whole eye in white of egg and make it boil and become solid; and then cut the egg and the eye transversally so that no part of the middle portion be poured out.”

Unfortunately, the author’s ingenuity led him wrong in this case. Because of the difference in the structure of different parts of the eye, the crystalline lens, which is a biconvex lens in the human eye, acquires an almost spherical shape when heated. Moreover, it moves off the cornea and is shifted toward the eye center.

This erroneous study had favored the concept that the eye is a double lens optical system which forms an erect image, but not an inverted one, which takes place in reality.

Therefore, according to the scheme of vision proposed by Leonardo, it forms a direct image rather than a turned image, as it should be done by a collecting lens.

To check his scheme of image construction in the eye, Leonardo also intended to make a large glass model of the eye with a helmet for the observer’s head. In addition, he invented for this purpose an original experiment with a needle located between the eye and a screen with an orifice.

I recommend you to repeat this simple and beautiful experiment, but with a tailor’s pin with a shackle instead of a sharp needle. What happens there? The light passing through a small hole in the screen produces a shadow of the pin in the eye (not just an “image”!), which can be easily verified by gluing a piece of tracing paper half-covered with ink onto the hole in the pin. The shadow can also be seen on a sheet of paper placed where the eye was located, and the shadow is not turned upside down! What conclusions can be drawn from this test? The light passing through the orifice generates a shadow on the rear surface of the eye, and the shadow is aligned straight, but the “sensitive organ” (in today’s terms, the visual apparatus in the brain) habitually turns this image upside down!

Proposing a test with an object moving in front of a small hole in a screen placed ahead of the eye, Leonardo da Vinci was actually half an inch from discovering the mechanism of seeing. Unfortunately, he was not able to find the correct explanation to his observations, and the discovery was made by one of the founding fathers of celestial mechanics, J.Kepler, at the beginning of the 17th century.

Gioconda’s mystery: 2 in 1

Apparently, Leonardo was the first to pay attention to the effect associated with the perception of rapid changes in an object: persistence of the image for a certain time:

“The radiance of the sun or other luminous body will remain in the eye for some time after it has been seen; and the motion of a single firebrand whirled rapidly in a circle causes this circle to seem an continuous and uniform flame; the drops of rain water seem continuous threads descending from their clouds.”

Leonardo found empirically how converging and diverging lenses should be used to correct defects of vision. He fabricated both solid lenses and lenses consisting of two thin layers of glass with water between them. Spectacles were chosen to suit the age of a person rather than the focal distance

The essence of this phenomenon, which involves changes in the active element of photoreceptors under the action of light, was discovered comparatively recently. The delay in image perception is the basis of cinema and TV, which we are so accustomed to. It is the delay in image perception that explains one of Leonardo’s secrets — charming Gioconda’s smile that has fascinated people for five centuries.

Thus, what is the reason for Gioconda’s mystery? The answer was found by analyzing consecutive frames in the movie about a man looking attentively at the painting: the first glance was directed to the right side of the mouth, then it moved upward to the nose, eyes, and forehead, and finally arrived at the left side of the mouth. The left side of Gioconda’s mouth smiles, whereas the right side expresses concentrated attention. As the observer’s sight does not capture the entire picture simultaneously but runs over it consecutively, the observer is in a paradoxical situation because of the delay in visual perception: the eye sees different states of mind simultaneously.

This interpretation of the mysterious half-smile of Gioconda is supported by the results of a recent computer-aided study performed by Dutch and American researchers. A special program was used to analyze the main facial features, including bending of the lips, and the location and depth of eye wrinkles. Then the program estimated the expression of Gioconda’s face in terms of six principal groups of emotions. According to these estimates, Gioconda’s face is happy by 83 %, expresses disgust by 9 %, is full of fear by 6 % and angry by 2 %.

Another sensational discovery in the history of arts was made in 1987. L. Swartz, an art historian and a specialist in computer graphics, demonstrated that turning Leonardo’s self-portrait by 90 ° ensures a rather accurate coincidence of the typical parameters of the painter’s and Gioconda’s faces. Probably, this was a trick used by Leonardo to obtain a portrait of a Renaissance person with a sophisticated inner world: he used features of his own face in different emotional states to draw different parts of Gioconda’s face.

On photometry

Light and shadow

Leonardo da Vinci can be considered the founder of photometry — the part of optics dealing with illumination. There are more than a hundred notes on the issues of light and shadow in Leonardo’s notebooks. He studied optical effects arising from one or several sources and depending on the position of these sources with respect to the object and the eye, the effects of direct and scattered light, color reflexes, etc.

“All the things seen come to the eye by pyramidal lines and the point of the aforesaid pyramid makes its termination and end in the middle of the pupil…”

Leonardo also discovered the basic laws of photometry. First, the illumination intensity of a body depends on the angle of light incidence: “The light which falls on a shaded body at the acutest angle receives the highest light, and the darkest portion is that which receives it at an obtuse angle and both the light and the shadow form pyramids…”

Second, the light intensity depends on the distance from the source of light. Leonardo deduced the so-called “pyramidal law,” which implies that the light intensity decreases in an inverse proportion to the squared distance between the source of light and the object. It should be noted that Leonardo applied the pyramidal law in considering many other processes, in particular, in the description of perspective, analysis of sound attenuation with distance, and emission of heat by a hot body.

On light emission, absorption, and scattering

Heat is the essence of rays

“The Sun warms by its natural heat” — Leonardo came to this conclusion by analyzing experiments on the thermal effect of light. “The concave mirror although cold when it receives the rays of the fire reflects them hotter than the fire. A ball of glass filled with cold water sends out from itself rays caught from the fire which are even hotter than the fire. From the two experiments referred to, it follows, as regards this warmth of rays that issue from the mirror or from the ball of cold water, that they are warm of their own essence, and not because the mirror or ball are hot.”

This reasoning implies the fundamental character of the issue of the source of heat induced by the Sun. They say that the problem formulated is half-solved, but the final answer may require much time and effort. The real mechanism of solar energy as a source of heat was elucidated only at the beginning of the 20th century, when the nuclear reactions of matter in the Sun were discovered.

The sky is so blue...

Amazingly, it was 500 years ago that Leonardo da Vinci formulated the problem of origin of the sky color and from merely admiring this phenomenon he came to an almost correct understanding of its nature.

“I say that the blue which is seen in the atmosphere is not its own color, but is caused by the heated moisture having evaporated into most minute, imperceptible particles, which the beams of solar rays attract and cause to seem luminous against the deep intense darkness of the region of fire that forms a covering against them. And this may be seen, as I myself saw it, by anyone who ascends Mon Boso, a peak of Alps... If the atmosphere had this transparent blue as its natural color, it would follow that wherever a greater quantity of atmosphere came between the eye and the fiery element, it would appear of a deeper shade of blue, as is seen with blue glass and sapphires, which appear darker in proportion as they are thicker. And the atmosphere, under these conditions, acts in exactly the opposite way, since where a greater quantity of it comes between the eye and the sphere of fire, there it is seen much whiter, and this happens toward the horizon... It follows therefore, from what I say, that the atmosphere acquires its blueness from the particles which catch the luminous rays of the sun. We may also observe the difference between atoms of dust and those of smoke seen in sun’s rays as they pass through the chinks of the walls in dark rooms, that the one seems the color of ashes, and the other — the thin smoke — seems of a most beautiful blue.”

The key points of Leonardo’s model are very similar to the current concepts which imply that the blue color of the sky results from scattering of the solar light consisting of electromagnetic waves on density fluctuations of air. The short-wave (blue) range of the spectrum is scattered to a much greater extent.

Red alarm

Studying the features of perception of distant objects, Leonardo found, in addition to the geometric perspective, two more aspects of the problem and even gave them special names: the perspective of color (the way in which visible colors vary as they recede from the eye) and the perspective of disappearance (how objects should appear less distinct in proportion as they are more remote).

Here is one of his observations important for a landscape painter: “Of various colors which are none of them blue that which at a great distance will look bluest is the nearest to black; and so, conversely, the color which is least like black will at a great distance best preserve its own color. Hence the green of fields will assume a bluer hue than yellow or white will, and conversely yellow or white will change less than green, and red still less.”

Do you know, that the minimal scattering of red rays of the spectrum is the physical base for the use of this color for emergency signals and in traffic lights? Thus, it is the most widely used scientific result of Leonardo da Vinci, which seems to be able to compete only with the bicycle, also invented by Leonardo da Vinci.

As for the perspective of disappearance, these studies represent the scientific base of sfumato (which means “smoky” in Italian), a famous artistic invention of Leonardo da Vinci.

On the wave nature of light

“The wave in the grain is seen to travel over the field, and the stalks of grain do not move from their place”

This is a brief (only one line) note from Leonardo’s “Atlantic Code”, but it contains the key word “waves”. Then there followed a long-time and extremely careful study of the essence of wave motion in experiments with water. This was consistent with the joky recommendation given later by Kozma Prutkov: “Throwing stones into water, watch the circles formed; otherwise, this will be an idle entertainment.”

The phenomenon of dispersion — decomposition of solar light into a spectrum — was described by Leonardo 200 years before the famous Newton’s experiments with a glass prism

Leonardo found that perturbations induced on water by thrown stones can easily penetrate each other without any noticeable consequences. This effect, however, is not observed at the collisions of solids or water and air flows! Leonardo concluded that the effect detected is actually a characteristic feature of the phenomenon of wave motion.

He formulated a conclusion on the wave nature of sound and light: “Although the voices which penetrate the air proceed from their sources in circular motion, nevertheless the circles which are propelled from their different centers meet without any hindrance and penetrate and pass across one other...”

Three centuries before the phenomenon of interference was discovered, Leonardo da Vinci pointed to the common nature of various phenomena, such as versicoloured bird’s feathers, iridescent colors on the surface of old glasses, and oil films on the water surface.

Further he wrote: “Just as a stone flung into the water becomes the centre and cause of many circles, and as sound diffuses itself in circles in the air: so any object, placed in the luminous atmosphere, diffuses itself in circles, and fills the surrounding air with infinite images of itself, and the every image appears in its entirety and in all its parts. The air is full of infinity of straight lines and rays which cut each other without displacing each other and which reproduce on whatever they encounter the true form of their cause.”

It should be recalled that the concept of the wave nature of light was accepted by physicists only in the 18th century after 100-year-long discussions. The dramatic evolution of physical optics is the result of complicated specific features of the interaction between light and matter, depending on the ratio between the light wavelength and the reference size of the object.

Leonardo was the first to notice and describe in detail another wonderful optical effect:
“An eye looking at a luminous body will seem to see a circle brighter than the rest of the air around it. The reason for this is that the said brightness is in the eye, and not outside and around the source of light, as it seems to be... And the said circle will appear to have steps of various colors, like the rainbow…”
This phenomenon called diffraction in scientific literature is used for further improvement of advanced optical systems.

Leonardo, who strived to find “infinite reasons and infinite connections in any phenomenon,” could not even think that geometric optics was incompatible with the concepts of the wave nature of light. Considering a phenomenon as a whole was one of the most important points of his scientific method.

“Peruse me O Reader, if you find delight in my work, since this profession very seldom returns to this world, and the perseverance to pursue it and to invent such things anew is found in few people. And come men, to see the wonders which may be discovered in Nature by such studies.”

*All italicized texts belong to Leonardo da Vinci