A smooth surface always glows only. Reflection of light by a surface

Rays falling on a surface can be reflected from it, passed through or absorbed. Depending on this, surfaces are distinguished between shiny and matte, transparent and opaque, black and white. A surface that absorbs significantly more light rays than it reflects and “transmits” is perceived as black, and one that reflects most of the light incident on it appears white to us. If the majority of light rays pass through the layer of a substance unhindered, then it will be transparent.

The reflection of light rays from a surface obeys the well-known law discovered by I. Newton - the angle of incidence of the ray is equal to the angle of reflection, regardless of the nature of the material and the length of the light wave. If a luminous flux consisting of parallel rays falls on a smooth surface, then the reflected flux will also consist of parallel rays and appear as if emerging from this surface. A surface that reflects light in this way is called shiny. If a stream of such light enters the observer’s eye, then the surface that reflects it turns out to be invisible. In such cases they say: “she shines.” We constantly encounter this phenomenon in museums and at exhibitions, when a glazed picture shines or shines from many points of view, and it can be difficult to find a point of view from which it becomes clearly visible.

Bodies with a rough surface reflect light according to the same law as shiny ones. However, due to the fact that the surface of such bodies consists of microscopic surfaces located at different angles, light is reflected from it in different directions, diffuse reflection or scattering of light occurs. Such surfaces from different points of view appear the same in lightness, have no glare and are called matte. But you need to keep in mind that different materials reflect light differently. For example, glass, plastics, water have a so-called specular reflection, and metals give a softer reflection, even when polished.

Some surfaces do not reflect or transmit light, but emit it - such as the surface of a hot metal. Such surfaces will always be brighter than surfaces that reflect light. The individual characteristics of the combination of scattering and direct reflection of light by a given surface determine its character, “texture,” and make it possible to distinguish plaster from marble, oil white from gouache. We even distinguish objects with vision alone by the nature of their surface, by the combination of highlights and shadows that form a matte, semi-matte or glossy surface. We distinguish shine on the surface of an object and talk about metallic, diamond, glass, porcelain shine; we make this distinction based on some subtle signs that cannot be defined verbally. In painting, conveying the surface qualities of an object along with their color, lighting, shape and position in space is one of the most important tasks.

#1: The bottom of a body of water always appears to be closer to the surface of the water to an observer in a boat. Explain this phenomenon.
ANSWER: The image of the lake bottom is formed on the retina of the eye from rays reflected from the bottom. When rays reflected from the bottom from water into air pass, the angle of incidence of the rays at the interface is less than the angle of refraction. Therefore, rays hitting the retina intersect “closer” to their exit point. This phenomenon can be verified by constructing an image of any point on the bottom.

No. 2: Why does the image of an object in water always look less bright than the object itself in the air?
ANSWER: Reflected rays from an object in water always lose part of their energy at the interface between these media (the result of reflection) and when they travel a certain distance in this medium. As a result, the intensity (energy) of the rays entering the observer’s eye decreases.

No. 3: Is it possible to transition from one medium to another without refraction? Indicate two possible options.
ANSWER: A) A ray of light falls perpendicular to the interface between two media.
B) The absolute refractive indices of the media are the same, for example glycerin and turpentine.

No. 4: In the center of a hollow, thick-walled glass ball there is a point source of light. Are rays of light passing through the walls of this sphere refracted?
ANSWER: Refraction does not occur, since the rays fall perpendicular to the element of the surface of the ball, i.e. along the radius, which is perpendicular to this element of the surface of the ball.

No. 5: Why is the bottom of the river located near a bridge visible to an observer on the bridge, but for an observer on the shore the same area may not be visible?
ANSWER: The eyes of an observer located on the bridge receive rays reflected from the bottom at an angle less than the maximum. For an observer located on the river bank, rays reflected from the bottom can fall on the interface at an angle greater than the limiting one. As a result, the river bottom may not be visible.

No. 6: In what cases does a glass prism deflect a ray incident on it not towards the base of the prism, but towards the refractive angle (the angle at the top of the prism)?
ANSWER: The absolute refractive index of the surrounding medium must be greater than the absolute index of the material from which the prism is made.

No. 7: Why is the foam formed in water (due to strong pressure) opaque, although it consists of water bubbles filled with air?
ANSWER: The opacity of an inhomogeneous medium is due to the fact that at each transition from one medium to another, in addition to refraction, reflection from the bubbles is also observed. As a result, the intensity of the rays entering the eye from the many bubbles is minimal and they appear opaque.

No. 8: Why does a diamond shine more than its glass imitation of the same shape?
ANSWER: The energy of reflected light, in addition to the angle of incidence, also depends on the absolute refractive index (the higher the refractive index, the greater the proportion of reflected energy). Different angles of incidence on the face of a diamond create images on the retina of the eye that change over time, which causes brilliance.

No. 9: Why do objects at the bottom of a reservoir seem to sway when there is gusts of wind?
ANSWER: The angle of incidence of rays on the surface of the water (due to vibrations) is constantly changing. Therefore, the angle of refraction also changes, and the angle of reflection from an object located at the bottom of the reservoir also changes accordingly. As a result, images of objects appear to be moving.

No. 10: Why does the apparent position of a star not coincide with its true position?
ANSWER: At different altitudes, the refractive index of air in the Earth's atmosphere is different. As a result, the trajectory of the beam is bent, so a beam hits the eye, the continuation of which is not the given star. This phenomenon is called atmospheric refraction.

No. 11: Why does a ball thickly covered with soot seem shiny when lowered into water and illuminated with light?
ANSWER: At the soot-water boundary, air is absorbed, resulting in complete reflection from this layer, which leads to the maximum intensity of the flux of rays entering the eye of the observer.

No. 12: Under what conditions does a transparent and colorless object become invisible in the rays of transmitted light?
ANSWER: This is only possible if the absolute refractive index of the surrounding medium is equal to the absolute refractive index of the observed object.

No. 13: Why do objects viewed through thick glass display cases sometimes appear distorted?
ANSWER: The optical density and thickness of the glass in different places of the display case can be different (due to its large size), which creates some mixing of parts of the item in question.

No. 14: Crushed glass is opaque, but when in water it becomes transparent again. Explain this phenomenon.
ANSWER: The energy of the reflected beam depends on the relative refractive index of the media, since glass and water have almost the same absolute refractive indices, the proportion of reflected energy from crushed glass sharply decreases, which leads to an increase in the energy of the transmitted beam.

No. 15: During the day, a mirage is sometimes observed in deserts - the observer sees the surface of a reservoir in the distance. Explain this phenomenon.
ANSWER: The heated layer of air directly adjacent to the asphalt has a lower density, and therefore a lower absolute refractive index, than that of the layers lying above. As a result, sand appears to reflect light just as well as the surface of water.

No. 16: How does the reflection of light from a transparent medium differ from total internal reflection, at the same angle of incidence in the same medium? Please indicate at least two differences.
ANSWER: A) Because in the case of total internal reflection, a refracted ray is also observed.
B) The intensity of the reflected beam, in the case of total internal reflection, is always less than when reflected from a transparent medium

No. 17: A scuba diver (who is far enough from the shore) can always see an object located on the shore. A person on the shore can only rarely see a scuba diver? Explain this fact.
ANSWER: All the rays reflected from an object on the shore fall into the scuba diver’s eye. The light rays reflected from the scuba diver mainly (due to the large distance) fall at angles greater than the maximum, as a result of which the human eye on the shore perceives minimal light energy.

No. 18: Why does a sharp bend in the light guide (light guide) lead to a sharp weakening of the energy of the light flux coming out of it?
ANSWER: At the point of bending, the angle of incidence becomes small and the light no longer undergoes complete reflection, but partially comes out of this system.

No. 19: Why is it that you can see much better when swimming underwater if you wear a mask?
ANSWER: The eye refracts light rays. If water touches the eye, then the light rays are refracted quite weakly, because The refractive index of water is close in value to the refractive index of the eye lens. While wearing a mask, there is air between the eye and the glass and the rays entering the eye are refracted as usual.

No. 20: Why are car headlight glasses made corrugated, i.e., consisting of small triangular prisms?
ANSWER: This set of prisms, the refractive angle of which is at the top, deflects the rays from the light source and deflects them down onto the road.

No. 21: Why does water that forms a fog or cloud appear opaque to an observer on the surface of the Earth, although the water is transparent to light rays?
ANSWER: Opacity is caused by the scattering of light in an inhomogeneous medium. With each transition from one medium to another, light is reflected, and the “fraction” of the reflected energy depends on the absolute refractive index of the medium and the angle of incidence. Due to the fact that the cloud is located quite high, the angles of incidence are small, and therefore the proportion of reflected energy is small. In the case of fog, which is located at a low altitude due to the high concentration of water molecules, the incident rays of light experience multiple reflections and despite the large angles of incidence, the absolute refractive index plays a significant role here.

No. 22: Why does the water appear darker to a passenger looking down from an airplane flying over the sea than in the distance?
ANSWER: If the observer looks down, then the angles of incidence of the rays are small, and therefore the angles of reflection are also small. As a result, a low-energy beam of rays hits the passenger's eye. Rays entering the observer's eye from more distant areas of the sea naturally strike at larger angles and therefore have greater energy.

No. 23: Why do drivers driving on the highway see puddles of water on the highway on sunny days?
ANSWER: The heated layer of air directly adjacent to the asphalt has a refractive index lower than that of the layers of air above. The result is total reflection and asphalt (which has a refractive index close to that of water) appears to reflect light just as well as water.

No. 24: Why do car headlight glasses have a corrugated surface on the inside?
ANSWER: The corrugated surface of the headlight glasses is a set of small prisms that collect the rays in the desired direction.

No. 25: Why do some fabrics shine and others don’t?
ANSWER: The fabric shines if the threads in it are arranged in the correct order parallel to each other and, as it were, form grooves on the surface of the fabric. At certain angles, such fabric reflects the light falling on it quite strongly. At other angles this reflection is weak. Therefore, when the fabric is turned in the rays of light, it reflects either better or worse - it shines.

#26: Why are the clouds mostly white? Why are thunderclouds black?
ANSWER: The water droplets in the cloud are quite large, and light is reflected from their outer surface. With this reflection, the light does not decompose into its component colors, but remains white. Very dense clouds appear black because they allow little sunlight to pass through - it is either absorbed by water droplets in the cloud or reflected upward.

No. 27: Why do the colors of wet objects, after rain, seem deeper, more saturated than dry ones?
ANSWER: A thin film of water covering a wet object reflects incident white light in one specific direction. The surface of an object no longer scatters white light in all directions, and its own color becomes dominant. Diffused light does not overlap with that reflected from the subject, and therefore the color appears more saturated.

#28: Point out the difference in lighting using a spotlight and using a car headlight.
ANSWER: The spotlight emits parallel beams, so it illuminates a small area, and the headlight has a diffuser that expands the light beam to illuminate the entire width of the road.

No. 29: Why soil, cardboard, wood, etc. do they appear darker when wetted?
ANSWER: Dry material has a rough surface, so the reflected light is scattered. If the material is wetted, then the light will be reflected specularly from the water film. In addition, having passed through this film, the light is partially absorbed and partially again diffusely reflected from the cardboard. But some of the rays will experience complete reflection and will not come out.

No. 30: Is it possible to glue two pieces of glass so that the glued area is invisible?
ANSWER: It is possible if the refractive index of the dried glue is equal to the refractive index of glass.

No. 31: Why is soot black, although rays from the entire solar spectrum fall on it?
ANSWER: Soot absorbs all rays.

No. 32: Some cars have additional yellow fog lights. For what?
ANSWER: Water droplets (fog) scatter red, orange and yellow light the least.

No. 33: Which lamps are preferable to install in stores where they sell fabrics: incandescent or fluorescent lamps?
ANSWER: Fluorescent lamps, because... Their radiation is closer in spectral composition to that of the sun.

No. 34: When making artificial mother-of-pearl buttons, minute shading is done on their surface. Why do they then acquire a rainbow color?
ANSWER: Hatching plays the role of a diffraction grating, giving a spectrum in reflected rays.

Achromatic colors

From a physics point of view, white light is a luminous flux consisting of waves of different lengths. Different surfaces greet the rays of light falling on them with different “hospitality”: some

surfaces, for example, absorb short-wave rays and reflect long-wave rays, while others do the opposite. With such selective absorption of light rays, the surface, as we say, receives a certain color, color. But there are surfaces that more or less uniformly absorb and reflect rays of all wavelengths. This indiscriminate absorption creates so-called gray surfaces. The more the surface is non-selective, that is, indifferent to the wavelength, reflects light rays, the whiter it will be, and, conversely, the smaller, the blacker it will be. Surfaces that uniformly reflect rays of all wavelengths are called achromatic. Achromatic colors have only one characteristic - lightness, which is mainly determined by the amount of light reflected from the surface.

Depending on the lighting and the ability of the surface to reflect light in one quantity or another, a gradual series of achromatic tones can be created, starting from white and ending with black. The paradoxical nature of the very name “achromatic color”, that is, “colorless color”, once again indicates the inseparable connection between light and color. And indeed, on the one hand, black, white, gray can be considered as something opposite to color, to everything colored, and on the other hand, we place black and white paints among other colors and, therefore, there is no reason not to consider them as color, just like other. For a painter, white, gray, black are the same colors as yellow, blue, etc., because they are used in a group of other colors as equal elements of color harmony and color. With all this, the division of colors into chromatic and achromatic is practically necessary. Arranged in order of decreasing lightness, achromatic colors form a series in which five main relatively specific steps can be distinguished: black, dark gray, gray, light gray and white. For scientific purposes, the achromatic series is taken to be much more differentiated. In Ostwald's color atlas it consists, for example, of 16 gradations, in Mansell's - 29, in Teplov's - 24. The degree of lightness of an achromatic tone is difficult to express absolutely. We can quite easily choose a lighter or darker one from two objects, but we cannot note how much darker it is. Therefore, lightness is measured using units that indicate the equality or inequality of two brightnesses.

The range of lightness from white to black in nature is thousands of times greater than the range of lightness between black and white paints under studio lighting conditions. This clearly shows that the ratios of brightness in nature cannot be transferred to the canvas in their absolute values, but require a kind of translation, which has long been noticed by artists. In a number of classic works of world painting we see amazing lighting effects that are striking in their truthfulness. The ways of this translation are diverse and do not yet fit into any formulas, even in the work of those artists whose slogan was the greatest closeness to nature.

Brightness and lightness

In everyday understanding, the difference between brightness and lightness is usually not noticed, and both concepts are considered almost equivalent. However, one can notice some difference in the use of these words, which also reflects the difference between these two phenomena. As a rule, the word “brightness” is used to characterize particularly light surfaces that are highly illuminated and reflect a large amount of light. So, for example, a sheet of paper or snow illuminated by the sun is spoken of as bright surfaces, and the walls of a room are spoken of as light. The word “brightness” is also often used to describe color, meaning such qualities of the latter as saturation or purity. Finally, the word "brightness" is primarily used to evaluate light sources.

In the natural science theory of color, the difference between the terms “brightness” and “lightness” is quite clear. Brightness is a physical concept, the value of which is characterized by the amount of light entering the eye of the average observer from a surface emitting or reflecting light. Lightness is a feeling of brightness, in which specific conditions of individual perception play an important role; This is a concept that primarily falls under the purview of psychology. The same physical, objective brightness can cause different sensations of lightness, and, conversely, the same lightness can correspond to different degrees of brightness.

The painter most likely deals directly with lightness, and not with brightness. In the work of both a painter and a draftsman, the ability to convincingly and artistically express light and color relationships largely depends on the sensitivity of the eye, which is fickle and can change under the influence of external and internal stimuli. The eye does not react to any irritation, but only to one that has reached a certain magnitude. Psychologists call this minimum difference between two degrees of brightness that the eye can notice the sensitivity threshold. In order to notice in nature and then express in the material the subtlest nuances of light and color, the artist’s eye must have a sufficiently high sensitivity, which is given by nature and develops in the learning process.

Threshold sensitivity changes when moving from one lighting condition to another. With a sharp change in lighting conditions, it decreases significantly for some time, and then, as the eye adapts to the new conditions, it begins to increase. Everyone knows well that if on a bright sunny day you enter a dimly lit room from the street, then for some time the eye is unable to discern almost anything in it and only gradually begins to see objects in the room. When working en plein air on a bright sunny day, it is easy to make the mistake of overly brightening or whitening the sketch, because in the process of working the eye gets used to the increased brightness. And, conversely, you can get very confused in lightness and color relationships in low light. It should be borne in mind here that in low light, in addition to the fact that the eye adapts to the reduced illumination, color tones and their saturation also change: blues in natural evening light seem brighter, reds, yellows - less saturated, more whitish, and at high brightnesses - yellowish.

A decrease in the sensitivity of the eye, on the contrary, noticeably affects its adaptation to a strongly illuminated picture plane. Adapting to bright light, the eye perceives all colors as significantly washed out, and in an effort to make them more saturated, the artist invariably ends up with falsehood, inconsistency and variegation. Only experience allows an artist to avoid such mistakes.

White

In scientific color science, the term “whiteness” is also used to assess the lightness qualities of a surface, which, in our opinion, is of particular importance for the practice and theory of painting. The term “whiteness” in its content is close to the concepts of “brightness” and “lightness”, however, unlike the latter, it contains a connotation of a qualitative characteristic and even, to some extent, aesthetic.

What is whiteness? R. Ivens explains this concept as follows: “If lightness characterizes the perception of brightness, then whiteness characterizes the perception of reflectivity.” The more a surface reflects the light falling on it, the whiter it will be, and theoretically, an ideal white surface should be considered a surface that reflects all rays falling on it; however, in practice such surfaces do not exist, just as there are no surfaces that would completely absorb the light incident on them. In practice, we call surfaces that reflect different amounts of light white. For example, we rate chalk soil as white soil, but as soon as you paint a square on it with zinc white, it will lose its whiteness. If we then paint the inside of the square with white that has even greater reflectivity, for example barite, then the first square will also partially lose its whiteness, although we will practically consider all three surfaces to be white. It turns out that the concept of “whiteness” is relative, but at the same time there is some kind of boundary from which we begin to consider the perceived surface to be no longer white.

The concept of whiteness can be expressed mathematically. The ratio of the light flux reflected by a surface to the flux incident on it (in percentage) is called “albedo” (from Latin albus - white). This relationship for a given surface is generally maintained under different lighting conditions, and therefore whiteness is a more constant quality of a surface than lightness. For white surfaces, the albedo will be 80-95%. The whiteness of various white substances can thus be expressed in terms of their reflectivity. V. Ostwald gives the following table of the whiteness of various white materials:

Barium sulfate (barite white) – 99%

Zinc white – 94%

Lead white – 93%

Gypsum – 90%

Fresh snow – 90%

Paper – 86%

A body that does not reflect light at all is called an absolute black body in physics. But the blackest surface we see will not be completely black from a physical point of view. Since it is visible, it reflects at least some amount of light and thus contains at least a negligible percentage of whiteness - just as a surface approaching ideal white can be said to contain at least a negligible percentage of blackness. We consider a surface to be practically black, in the perception of which details are indistinguishable due to the lack of physical stimulus. White and gray in nature have superficial qualities, and gray, the darker it is, to a lesser extent. Black is devoid of these qualities. Ivens defines the difference between white, gray and black as follows: “White is a phenomenon related entirely to the perception of surface; gray is the perception of the relative lightness of the surface, and black is the positive perception of the insufficiency of the stimulus to provide the proper level of vision.”

In the practice of painting, the concept of black is also very relative. The blackest spot in a painting has some whiteness and color tone. Various black colors, which can be mistaken for extreme blackness, turn out to be so only when perceived in isolation; when compared with each other, they, in addition, always reveal different color shades. Van Gogh, for example, counted up to 27 different black colors from Frans Hals. We almost never encounter purely achromatic black. The color of black paint is the standard of black for the artist, and the experience he has acquired in perception makes it possible to correlate all other tones with this blackness.

Constancy of whiteness

The concept of whiteness is related to the problem of the so-called constancy of perception, which is generally of exceptional importance for the theory of fine arts, and artistic and pedagogical practice in particular. The phenomenon of constancy, speaking schematically, boils down to the fact that, despite the inconstancy and variability of the light signals received by the retina, in perception we receive a more or less constant image corresponding to a real object. We will perceive a sheet of white paper as white both in a dimly lit room, and in sunlight, and under electric lighting, despite the fact that in fact it will have different degrees of lightness. The same is true for black surfaces. White paper in a darkened room reflects less light than black paper in bright sunlight; but we don't confuse black paper with white paper.

For the artist, therefore, the question comes down to the division in the perception of lightness or whiteness of the surface and its illumination at a given moment. If you offer a beginner to write on a sheet of white paper located in the shade, he will write it with pure white, just as he would write on a black surface with black paint. But let’s assume that the artist is faced with the task of conveying the whiteness of the surface as it appears to him in reality. This is only possible if he conveys its apparent lightness. For a white surface in the shadow and a black surface in the light, the artist uses gray tones, but in the painting they will be perceived as white and black surfaces. Here, the so-called relationships play a decisive role, that is, the entire context of the image, contrasts and a number of other points, which will be discussed below. Thus, seeing unconstantly, the painter gives the viewer the possibility of a constant perception of whiteness.

The degree of constancy of the perception of whiteness for white and black surfaces is not the same. The constancy of the perception of white surfaces is more pronounced; it decreases for gray tones - in other words, the higher the reflectivity of the surface, the more noticeable the constancy of its whiteness will be; The lower the reflectivity, the less effective this constancy is. The effect of constant lightness is most noticeable in familiar perceptual conditions. We do not notice a change in the whiteness of a sheet of paper in a room with normal lighting. The appearance of the effect of constancy of whiteness is also greatly influenced by our practical experience. For example, snow, which is well known to us from experience as white, will be perceived as white in a wide variety of lighting conditions. Blue shadows on the snow do not appear to us as blue snow, but as white snow in the shadows, colored by blue light. There is some analogy between the constancy of the perception of whiteness and the constancy of the perception of the size of an object - we do not notice, for example, perspective changes in the apparent sizes of objects when they are far from us, and clearly see their decrease at large distances.

The visual assessment of the whiteness of a surface depends, therefore, on the amount of light reflected by the surface and on the perceptual setting. We will return to this issue in connection with the perception of color and when considering light and color relationships in the image system.

Light and object shape

It is well known how significant the role of light is in the perception of the shape of an object. Surface and volume are factors independent of lighting in the only sense that we perceive them in any lighting. The appearance of an object can be characterized by a number of features that are variable and dependent on lighting conditions. These characteristics include lightness, color tone and its saturation, texture, and shape. It is interesting that a change in one of these characteristics leads to a change in others - for example, a change in illumination entails a change in the lightness of the surface, and with it its color also changes. Thus, none of these characteristics will be, in essence, independent, which is of particular importance for the problem of the integrity of perception and the integrity of the image.

Perception is always primarily aimed at the form, and not at the lighting. This predominance is so strong that it is, as a rule, not noticed by an untrained observer, and a certain effort is required in order to perceive the change in the intensity of illumination on the surface before the shape itself.

Natural chiaroscuro can be imagined as consisting of two layers: the lightness inherent in a given surface, and the light that “layers” on it. We have already said above that this has been the tradition of understanding light in painting for quite a long time. This long-standing tradition of understanding chiaroscuro as something external in relation to the object’s own lightness and color corresponds in artistic practice to understanding the lightness of an object as consisting of local color and chiaroscuro that arises during illumination. This is exactly how mesh was understood in the early Renaissance. Another feature is connected with this - the perception of lightness as transparency. Under natural conditions, a situation is possible in which objects or surfaces are viewed through some other object and between the eye and the observed surface, thereby creating some kind of environment that weakens the lightness of the surface in question - for example, if you look at an object through a tulle curtain or at a landscape through a veil of fog. In these cases, we clearly imagine that the lightness of the objects in question is weakened due to the influence of the layer lying on top of them. In painting, this layer corresponds to glaze, which can be considered as a kind of transparent medium superimposed on the local color of the object.

However, in reality, we just have a gray spot, which will be practically no different from a spot of paint obtained as a result of mechanical mixing, and when we perceive such a spot, no separation or stratification occurs if we localize attention only on it itself. Let's take the simplest image as an example: a dark vertical stripe, which is crossed by a lighter and relatively transparent horizontal stripe, so that the vertical stripe is visible through it. Such an image can be perceived in different ways: either as two stripes, differently oriented and placed on top of each other, or as five squares located in the same plane. Of course, the eye will perceive this situation as two stripes, and thus the chiaroscuro will be split into two spatial layers.

Rice. 6. Transparency effect is achieved by difference in tone

R. Arnheim explains this with his universal principle of simplicity, to which visual perception always strives: the perception of two intersecting stripes placed on top of each other is simpler and clearer than a combination of several elements in one plane. But there is another possible explanation for this phenomenon: visual perception strives for a certain completeness, tries to find an organic connection between the individual elements of the image.

In a painting, this effect of transparency, as we will call it, arises only thanks to the found color and lightness relationships. If we look only at the veil, then we will see nothing but the gray surface, but if we look at the same time at the veil and the area of the body not covered by the veil, then we clearly perceive the transparency of the fabric and the surface behind it.

Chiaroscuro and perspective

Leonardo da Vinci spoke of the presence of “three perspectives, that is, the reduction of the figures of bodies, the reduction of their sizes and the reduction of their colors. Further,” he says, “of these three perspectives, the first comes from the eye, and the other two are produced by the air located between the eye and the object seen by that eye.”

According to modern terminology, we are talking here about linear, aerial and color perspectives, between which there is the same connection as between the shape of an object, its color and light and shade, for each of them explains the patterns of spatial changes in these basic features of the object form. We will talk about color perspective below, but here we will only note the relationship between linear and aerial perspectives. The basic law of this connection boils down to the fact that as we move away from us, objects lose the sharpness of their outlines and change their lightness. In this case, dark objects become lighter as they move away, and light objects, on the contrary, become darker.

Aerial perspective played a particularly prominent role in landscapes, where it serves as a very important means of expressing spatial depth. But not in all eras she enjoyed respect from artists and theorists. Schelling, for example, wrote about aerial perspective: “...a picture where aerial perspective is observed will remind us less that what we are contemplating is a work of art than one where this is not the case; but if this principle were made universal, there would be no art at all, and since it cannot be universal, then illusion, that is, the identification of truth with appearance up to sensory truth, cannot be the goal of art at all. Likewise, the ancients - according to everything we know about them - did not observe aerial perspective. In the same way, artists of the 14th and 15th centuries did not observe it, for example Pietro Perugino, Raphael’s teacher (paintings in Dresden). And in Raphael’s paintings, aerial perspective is only partially observed.”

Reading these lines, you need to keep in mind that before the Renaissance, painting did not, in essence, use chiaroscuro and linear perspective, and perhaps not only because it did not correspond to the aesthetic concepts of that time, but also because artists they were not known.

From the point of view of the development of the method of depiction itself, the discovery of the laws of perspective and, in particular, aerial perspective was progress that did not in the least hinder, as some modern theorists sometimes try to claim, the development of art. During the late Renaissance and beyond, many outstanding works were created in which central perspective, aerial perspective, and chiaroscuro are integral elements of the artistic form.

All living things strive for color.

I.V. Goethe. The doctrine of flowers.

Spectral colors

If for an artist, as we have already said, white and black are colors, then from a physical point of view this is not entirely true. Leonardo da Vinci to some extent anticipated the later discovery when he stated: “White is not a color, but it is capable of perceiving any color.” The great English physicist Isaac Newton experimentally managed to prove that white sunlight is a mixture of various colors. And today every schoolchild knows that if a narrow beam of sunlight is passed through a triangular prism, then an amazingly beautiful light effect appears on the screen located behind it - a successive series of bright colors, similar to the one that everyone has seen in the natural phenomenon of a rainbow.

Fascinated by the search for an analogy between color and sound, Newton divided the spectrum he obtained into seven parts corresponding to the seven tones of the musical diatonic scale and designated them with the words: red, orange, yellow, green, blue, indigo and violet. This division of the spectrum was largely conditional and random, since it is possible to distinguish both a larger and smaller number of its parts, since the colors of the spectrum do not have clear boundaries, but gradually transform into one another. So, for example, between red and orange one can distinguish red-orange, between yellow and green - yellow-green or light green and others. It would be more consistent with the actual composition of the spectrum if it were divided into 6 parts. As the seventh, Newton singled out indigo, which would more correctly be considered only a variety of blue. Newton simultaneously discovered that white light consists of light rays that are refracted differently when passing through the same medium, and that this physical heterogeneity of the rays corresponds to the difference in the sensations of color that they cause when entering the human eye. He also drew attention to the fact that each of these colors occupies a different width in the spectrum.

Newton's experiments were important for the development of scientific views on nature in general and the nature of color in particular. They provided an objective basis for solving some problems of color theory in painting - for example, the theory of complementary colors, the theory of optical mixing of paints. Thus, in an area that seemed subjective and not amenable to any ordering, the road opened for strict scientific analysis.

According to modern views, the spectrum is formed by a stream of light rays with different wavelengths. If the stream consists of rays having the same wavelength, it is called monochromatic. Theoretically, a luminous flux consisting of, say, rays having a wavelength of 637 nm, causes a different sensation of color than a flux of rays of 638 nm. However, the eye does not respond to such minor changes in the wave composition of radiation, and one that contains different waves within approximately ±10 nm can be considered practically monochromatic.

Radiation consisting of waves of only one length or of waves forming a very narrow part of the spectrum corresponds to a certain fully saturated spectral color. In everyday reality, however, we have almost nothing to do with such spectral color; Usually the eye receives streams of mixed composition, consisting of waves of different lengths.

Table 1.

a) Continuous spectrum;

b) Conventional division of the spectrum into seven colors (according to Newton)

Each color spot in a picture can have a different lightness, color, purity, defined in color science, as already noted, by the terms “lightness”, “color tone”, “saturation”. For color theory, both natural science and art, these concepts are extremely important, since they are the basis for systematizing the entire wealth of color phenomena in nature and in art. It is impossible to do without these characteristics when understanding such fundamental concepts of the theory of painting as “color harmony,” “color,” and “picturesqueness.”

Table 2.

a) Changes in color tone (and lightness);

b) changes in lightness (and saturation);

c) changes in saturation (and lightness)

The sensation of “red” or “blue” color in this case is determined only by the predominance of rays with the corresponding wavelength in the stream; In addition to them, the light flux will also contain rays of other wavelengths, of a different “color,” only in smaller quantities. The more the rays of any one particular wavelength predominate, the purer the color will be; and vice versa - the less this predominance is, the more dirty and dull it will be. With a certain mixture of rays from the entire spectrum, that is, all wavelengths, we get white or gray color. Observations show that currents of different wave composition can produce sensations of the same color, and surfaces that appear identical in color can reflect currents of unequal wave composition. This phenomenon can be explained by the laws of optical color mixing, which will be discussed below.

Alternative visualizations. Visualization of Inner Light Imagine that at the top of your head there is a sparkling star that emits a bright glow and powerful energy

Accounting for transactions in foreign currency. Reflection in accounting for exchange rate differences

Types of deductions from wages. The procedure for calculating the amount of deductions and their reflection in accounting. Analytical and synthetic accounting of wage calculations

Impact of infrared radiation on the human body. Features of the biological action of laser light

At the interface between two different media, if this interface significantly exceeds the wavelength, a change in the direction of light propagation occurs: part of the light energy returns to the first medium, that is reflected, and part penetrates into the second environment and at the same time refracted. The AO beam is called incident ray, and ray OD – reflected beam(see Fig. 1.3). The relative position of these rays is determined laws of reflection and refraction of light.

Rice. 1.3. Reflection and refraction of light.

The angle α between the incident ray and the perpendicular to the interface, restored to the surface at the point of incidence of the ray, is called angle of incidence.

The angle γ between the reflected ray and the same perpendicular is called reflection angle.

Each medium to a certain extent (that is, in its own way) reflects and absorbs light radiation. The quantity that characterizes the reflectivity of the surface of a substance is called reflection coefficient. The reflection coefficient shows what part of the energy brought by radiation to the surface of a body is the energy carried away from this surface by reflected radiation. This coefficient depends on many factors, for example, on the composition of the radiation and on the angle of incidence. The light is completely reflected from a thin film of silver or liquid mercury deposited on a sheet of glass.

Laws of light reflection

The laws of light reflection were discovered experimentally in the 3rd century BC by the ancient Greek scientist Euclid. Also, these laws can be obtained as a consequence of Huygens’ principle, according to which every point in the medium to which a disturbance has reached is a source of secondary waves. The wave surface (wave front) at the next moment is a tangent surface to all secondary waves. Huygens' principle is purely geometric.

A plane wave falls on the smooth reflective surface of a CM (Fig. 1.4), that is, a wave whose wave surfaces are stripes.

Rice. 1.4. Huygens' construction.

A 1 A and B 1 B are the rays of the incident wave, AC is the wave surface of this wave (or the wave front).

Bye wave front from point C will move in time t to point B, from point A a secondary wave will spread across the hemisphere to a distance AD = CB, since AD = vt and CB = vt, where v is the speed of wave propagation.

The wave surface of the reflected wave is a straight line BD, tangent to the hemispheres. Further, the wave surface will move parallel to itself in the direction of the reflected rays AA 2 and BB 2.

Right triangles ΔACB and ΔADB have a common hypotenuse AB and equal legs AD = CB. Therefore they are equal.

Angles CAB = = α and DBA = = γ are equal because these are angles with mutually perpendicular sides. And from the equality of triangles it follows that α = γ.

From Huygens' construction it also follows that the incident and reflected rays lie in the same plane with the perpendicular to the surface restored at the point of incidence of the ray.

The laws of reflection are valid when light rays travel in the opposite direction. As a consequence of the reversibility of the path of light rays, we have that a ray propagating along the path of the reflected one is reflected along the path of the incident one.

Most bodies only reflect the radiation incident on them, without being a source of light. Illuminated objects are visible from all sides, since light is reflected from their surface in different directions, scattering. This phenomenon is called diffuse reflection or diffuse reflection. Diffuse reflection of light (Fig. 1.5) occurs from all rough surfaces. To determine the path of the reflected ray of such a surface, a plane tangent to the surface is drawn at the point of incidence of the ray, and the angles of incidence and reflection are constructed in relation to this plane.

Rice. 1.5. Diffuse reflection of light.

For example, 85% of white light is reflected from the surface of snow, 75% from white paper, 0.5% from black velvet. Diffuse reflection of light does not cause unpleasant sensations in the human eye, unlike specular reflection.

- this is when light rays incident on a smooth surface at a certain angle are reflected predominantly in one direction (Fig. 1.6). The reflective surface in this case is called mirror(or mirror surface). Mirror surfaces can be considered optically smooth if the size of irregularities and inhomogeneities on them does not exceed the light wavelength (less than 1 micron). For such surfaces, the law of light reflection is satisfied.

Rice. 1.6. Specular reflection of light.

Flat mirror is a mirror whose reflecting surface is a plane. A flat mirror makes it possible to see objects in front of it, and these objects appear to be located behind the mirror plane. In geometric optics, each point of the light source S is considered the center of a diverging beam of rays (Fig. 1.7). Such a beam of rays is called homocentric. The image of point S in an optical device is the center S’ of a homocentric reflected and refracted beam of rays in various media. If light scattered by the surfaces of various bodies falls on a flat mirror, and then, reflected from it, falls into the eye of the observer, then images of these bodies are visible in the mirror.

Rice. 1.7. An image created by a plane mirror.

The image S’ is called real if the reflected (refracted) rays of the beam intersect at point S’. The image S’ is called imaginary if it is not the reflected (refracted) rays themselves that intersect, but their continuations. Light energy does not reach this point. In Fig. Figure 1.7 shows an image of a luminous point S, which appears using a flat mirror.

Beam SO falls on the CM mirror at an angle of 0°, therefore, the angle of reflection is 0°, and this ray, after reflection, follows the path OS. From the entire set of rays falling from point S onto a flat mirror, we select the ray SO 1.

The SO 1 beam falls on the mirror at an angle α and is reflected at an angle γ (α = γ). If we continue the reflected rays behind the mirror, they will converge at point S 1, which is a virtual image of point S in a plane mirror. Thus, it seems to a person that the rays are coming out of point S 1, although in fact there are no rays leaving this point and entering the eye. The image of point S 1 is located symmetrically to the most luminous point S relative to the CM mirror. Let's prove it.

Beam SB incident on the mirror at an angle of 2 (Fig. 1.8), according to the law of light reflection, is reflected at an angle of 1 = 2.

Rice. 1.8. Reflection from a flat mirror.

From Fig. 1.8 you can see that angles 1 and 5 are equal – like vertical ones. The sums of the angles are 2 + 3 = 5 + 4 = 90°. Therefore, angles 3 = 4 and 2 = 5.

Right triangles ΔSOB and ΔS 1 OB have a common leg OB and equal acute angles 3 and 4, therefore, these triangles are equal in side and two angles adjacent to the leg. This means that SO = OS 1, that is, point S 1 is located symmetrically to point S relative to the mirror.

In order to find the image of an object AB in a flat mirror, it is enough to lower perpendiculars from the extreme points of the object onto the mirror and, continuing them beyond the mirror, set aside a distance behind it equal to the distance from the mirror to the extreme point of the object (Fig. 1.9). This image will be virtual and life-size. The dimensions and relative position of the objects are preserved, but at the same time, in the mirror, the left and right sides of the image change places compared to the object itself. The parallelism of light rays incident on a flat mirror after reflection is also not violated.

Rice. 1.9. Image of an object in a plane mirror.

In technology, mirrors with a complex curved reflecting surface, for example, spherical mirrors, are often used. Spherical mirror- this is the surface of the body, having the shape of a spherical segment and specularly reflecting light. The parallelism of rays when reflected from such surfaces is violated. The mirror is called concave, if the rays are reflected from the inner surface of the spherical segment. Parallel light rays, after reflection from such a surface, are collected at one point, which is why a concave mirror is called collecting. If the rays are reflected from the outer surface of the mirror, then it will convex. Parallel light rays are scattered in different directions, so convex mirror called dispersive.

SHADOW OF FLAME

Light a burning candle with a powerful electric lamp. On a screen made from a white sheet of paper, not only the shadow of a candle will appear, but also the shadow of its flame.

At first glance, it seems strange that the light source itself can have its own shadow. This is explained by the fact that in the candle flame there are opaque hot particles and that the difference in the brightness of the candle flame and the powerful light source illuminating it is very large. This experience is very good to observe when the candle is illuminated by the bright rays of the Sun.

LAW OF LIGHT REFLECTION

For this experiment we will need: a small rectangular mirror and two long pencils.
Place a piece of paper on the table and draw a straight line on it. Place a mirror on the paper perpendicular to the drawn line. To prevent the mirror from falling, place books behind it.

To check that the line drawn on the paper is strictly perpendicular to the mirror, make sure that
and this line and its reflection in the mirror were straight, without a break at the surface of the mirror. It was you and I who created the perpendicular.

Pencils will act as light rays in our experiment. Place the pencils on a piece of paper on opposite sides of the drawn line with their ends facing each other and to the point where the line rests on the mirror.

Now make sure that the reflections of the pencils in the mirror and the pencils lying in front of the mirror form straight lines, without a break. One of the pencils will play the role of an incident ray, the other - a reflected ray. The angles between the pencils and the drawn perpendicular are equal to each other.

If you now rotate one of the pencils (for example, increasing the angle of incidence), then you must also rotate the second pencil so that there is no break between the first pencil and its continuation in the mirror.
Whenever you change the angle between one pencil and the perpendicular, you need to do the same with the other pencil so as not to disturb the straightness of the light beam that the pencil represents.

MIRROR REFLECTION

Paper comes in different grades and is distinguished by its smoothness. But even very smooth paper is not capable of reflecting like a mirror; it does not look like a mirror at all. If you examine such smooth paper through a magnifying glass, you can immediately see its fibrous structure and see the depressions and tubercles on its surface. The light falling on the paper is reflected by both tubercles and depressions. This randomness of reflections creates diffuse light.

However, paper can also be made to reflect light rays in a different way so that scattered light is not obtained. True, even very smooth paper is far from a real mirror, but still you can achieve some specularity from it.

Take a sheet of very smooth paper and, placing its edge against the bridge of your nose, turn towards the window (this experiment should be done on a bright, sunny day). Your gaze should glide over the paper. You will see on it a very pale reflection of the sky, vague silhouettes of trees and houses. And the smaller the angle between the direction of view and the sheet of paper, the clearer the reflection will be. In a similar way, you can get a mirror image of a candle or light bulb on paper.

How can we explain that on paper, although poorly, you can still see the reflection?
When you look along the sheet, all the tubercles of the paper surface block the depressions and turn into one continuous surface. We no longer see random rays from the depressions; they now do not interfere with us seeing what the tubercles reflect.

REFLECTION OF PARALLEL RAYS

Place a sheet of thick white paper at a distance of two meters from the table lamp (at the same level as it). Place a large-toothed comb on one edge of the paper. Make sure that the light from the lamp passes onto the paper through the teeth of the comb. Near the comb itself you will get a strip of shadow from its “back”. On the paper, from this shadow stripe there should be parallel stripes of light passing between the teeth of the comb

Take a small rectangular mirror and place it across the light stripes. Stripes of reflected rays will appear on the paper.

Rotate the mirror so that the rays fall on it at a certain angle. The reflected rays will also turn. If you mentally draw a perpendicular to the mirror at the point of incidence of a ray, then the angle between this perpendicular and the incident ray will be equal to the angle of the reflected ray. No matter how you change the angle of incidence of the rays on the reflecting surface, no matter how you turn the mirror, the reflected rays will always come out at the same angle.

If you don't have a small mirror, you can replace it with a shiny steel ruler or a safety razor blade. The result will be somewhat worse than with a mirror, but the experiment can still be carried out.

You can also do similar experiments with a razor or ruler. Bend a ruler or razor and place it in the path of parallel rays. If the rays hit a concave surface, they will be reflected and converge at one point.

Once on a convex surface, the rays will be reflected from it like a fan. To observe these phenomena, the shadow that comes from the “back” of the comb is very useful.

TOTAL INTERNAL REFLECTION

An interesting phenomenon occurs with a ray of light that goes from a denser medium to a less dense one, for example, from water to air. A ray of light does not always manage to do this. It all depends on the angle at which he is trying to exit the water. Here the angle is the angle the ray makes with the perpendicular to the surface it wants to pass through. If this angle is zero, then it freely goes out. So, if you put a button on the bottom of a cup and look at it directly from above, then the button is clearly visible.

If we increase the angle, then a moment may come when it seems to us that the object has disappeared. At this moment, the rays will be completely reflected from the surface, go deep and will not reach our eyes. This phenomenon is called total internal reflection or total reflection.

Experience 1

Make a ball of plasticine with a diameter of 10-12 mm and stick a match into it. Cut a circle with a diameter of 65 mm from thick paper or cardboard. Take a deep plate and stretch two threads parallel to the diameter on it at a distance of three centimeters from each other. Secure the ends of the threads to the edges of the plate with plasticine or adhesive tape.

Then, having pierced the circle in the very center with an awl, insert a match with a ball into the hole. Make the distance between the ball and the circle about two millimeters. Place the circle, ball side down, on the stretched strings in the center of the plate. If you look from the side, the ball should be visible. Now pour water into the plate up to the mug. The ball disappeared. The light rays with his image no longer reached our eyes. They, reflected from the inner surface of the water, went deep into the plate. There was a complete reflection.

Experience 2

You need to find a metal ball with an eye or hole, hang it on a piece of wire and cover it with soot (it is best to set fire to a piece of cotton wool moistened with turpentine, machine or vegetable oil). Next, pour water into a thin glass and, when the ball has cooled, lower it into the water. A shiny ball with a “black bone” will be visible. This happens because the soot particles trap air, which creates a gas shell around the ball.

Experience 3

Pour water into a glass and place a glass pipette in it. If you look at it from above, tilting it slightly in the water so that its glass part is clearly visible, it will reflect light rays so strongly that it will become mirror-like, as if made of silver. But as soon as we press the rubber band with our fingers and draw water into the pipette, the illusion will immediately disappear, and we will see only a glass pipette - without a mirror outfit. It was made mirror-like by the surface of the water in contact with the glass, behind which there was air. From this boundary between water and air (glass is not taken into account in this case), the light rays were completely reflected and created the impression of specularity. When the pipette was filled with water, the air in it disappeared, the complete internal reflection of the rays stopped, because they simply began to pass into the water that filled the pipette.

Pay attention to the air bubbles that sometimes exist in the water on the inside of the glass. The shine of these bubbles is also the result of total internal reflection of light from the boundary of water and air in the bubble.

TRAVEL OF LIGHT RAYS IN A FIGHT GUIDE

Although light rays travel in straight lines from a light source, they can also be made to follow a curved path. Nowadays, the thinnest glass light guides are made, through which light rays travel long distances with various turns.

The simplest light guide can be made quite simply. This will be a stream of water. Light traveling along such a light guide, encountering a turn, is reflected from the inner surface of the jet, cannot escape outside and travels further inside the jet until its very end. Water partially scatters a small fraction of the light, and therefore in the dark we will still see a faintly luminous stream. If the water is slightly whitened with paint, the stream will glow more strongly.
Take a table tennis ball and make three holes in it: for a tap, for a short rubber tube, and opposite this hole, a third hole for a flashlight bulb. Insert the light bulb inside the ball with the base facing outward and attach two wires to it, which then connect to the battery from the flashlight. Secure the ball to the tap using insulating tape. Coat all joints with plasticine. Then wrap the ball with dark matter.

Open the tap, but not too much. The stream of water flowing from the tube should bend and fall close to the tap. Turn off the light. Connect the wires to the battery. The rays of light from the light bulb will pass through the water into the hole from which the water flows. The light will flow along the stream. You will only see its faint glow. The main stream of light follows the stream and does not escape from it even where it bends.

EXPERIENCE WITH A SPOON

Take a shiny spoon. If it is well polished, it even seems a little mirror-like, reflecting something. Smoke it over a candle flame, and make it blacker. Now the spoon no longer reflects anything. Soot absorbs all rays.

Well, now put the smoked spoon into a glass of water. Look: it sparkled like silver! Where did the soot go? Did you wash yourself off, or what? You take out the spoon - it’s still black...

The point here is that soot particles are poorly wetted by water. Therefore, a kind of film, like a “water skin,” forms around the sooty spoon. Like a soap bubble stretched over a spoon like a glove! But a soap bubble shines, it reflects light. This bubble surrounding the spoon also reflects.
You can, for example, smoke an egg over a candle and immerse it in water. It will shine there like silver.

The blacker the lighter!

LIGHT REFRACTION

You know that the beam of light is straight. Just remember a ray breaking through a crack in a shutter or curtain. A golden beam full of swirling dust particles!

But... physicists are used to testing everything experimentally. The experience with shutters is, of course, very clear. What can you say about the experience with a dime in a cup? Don't know this experience? Now we will do it with you. Place the dime in an empty cup and sit down so that it is no longer visible. The rays from the ten-kopeck piece would have gone straight into the eye, but the edge of the cup blocked their path. But now I will arrange it so that you will see the ten-kopeck coin again.

So I pour water into the cup... Carefully, little by little, so that the ten-kopeck piece does not move... More, more...

Look, here it is, a ten-kopeck piece!
It appeared as if it had floated up. Or rather, it lies at the bottom of the cup. But the bottom seemed to rise, the cup “shallowed”. Direct rays from the ten-kopeck coin did not reach you. Now the rays are reaching. But how do they go around the edge of the cup? Do they really bend or break?

You can lower a teaspoon obliquely into the same cup or glass. Look, it's broken! The end immersed in water broke upward! We take out the spoon - it is both whole and straight. So the rays really break!

Sources: F. Rabiza "Experiments without instruments", "Hello physics" L. Galperstein