Decomposition of white light into its component parts. School Encyclopedia

Lesson objectives:

• Educational:
  • introduce the concepts of spectrum, dispersion of light;
  • to acquaint students with the history of the discovery of this phenomenon.
  • visually demonstrate the process of decomposition of a narrow light beam into components of various color shades.
  • identify the differences between these elements of the beam of light.
  • continue the formation of the scientific worldview of students.
• Educational:
  • development of attention, figurative and logical thinking, memory in the study of this topic.
  • stimulation of cognitive motivation of students.
  • development of critical thinking.
• Educational:
  • fostering interest in the subject;
  • fostering a sense of beauty, the beauty of the world.

Lesson type: lesson of studying and primary consolidation of new knowledge.

Teaching methods: conversation, story, explanation, experiment. (Information-developing)

Requirements for the basic level of training: be able to describe and explain the phenomenon of dispersion.

Equipment and materials: computer, color cards, plane-parallel plates

Lesson plan:

Before the start of the lesson, at the break, conduct a diagnosis of “Class Coloring”. Each student, entering the class, chooses a card with a certain color that matches his mood, a “Class color scheme” diagram is drawn up at the beginning of the lesson.

• yellow is good
• Orange - very good
• Red - joyful
• Green - calm
• Blue - sad
• Brown - alarming
• Black is bad
• White - indifferent

Epigraph to the lesson:

Nature cannot be caught sloppy and half-dressed, she is always beautiful.

R. Emerson (American philosopher of the 19th century)

DURING THE CLASSES

1. Motivation

Sunlight has always been and remains for a person a symbol of joy, eternal youth, all the good, the best that can be in life:

“May there always be the Sun.
May there always be heaven...

Such words are in the famous song, the author of the words is Lev Oshanin.
Even a physicist. Accustomed to dealing with facts, with accurate registration of phenomena, sometimes feels embarrassed, saying that light is electromagnetic waves of a certain wavelength and nothing more.
The wavelength of light is very short. Imagine an average sea wave that would increase so much that it alone occupied the entire Atlantic Ocean - from America to Lisbon in Europe. The wavelength of light at the same magnification would only slightly exceed the width of a book page.
Question:
Where do these electromagnetic waves come from?
Answer:
- Their source is the Sun.
Together with visible radiation, the Sun sends us thermal radiation, infrared and ultraviolet. Heat the sun is the main cause of these electromagnetic waves.

2. Organizing moment

Formulation of the topic and objectives of the lesson.

The theme of our lesson is "Dispersion of Light". Today we need:

• Introduce the concept of "spectrum", "dispersion of light";
• To identify the features of this phenomenon - the dispersion of light;
• Get acquainted with the history of the discovery of this phenomenon.

Activation of mental activity:

student reads a poem

Flavor of the Sun

The scent of the sun? What nonsense!
No, not nonsense.
Sounds and dreams in the sun
Fragrances and flowers
All merged into a consonant choir,
All intertwined in one pattern.
The sun smells like herbs
fresh baths,
Awakened spring
And resinous pine
Gently light-colored
Drunk lilies of the valley
that blossomed victoriously
In the sharp smell of the earth.
The sun shines with bells
green leaves,
Breathes the external song of birds,
Breathes the laughter of young faces.
So say to all the blind:
Will you!
Do not see the gates of heaven,
The sun has a fragrance
Sweetly intelligible only to us,
Visible to birds and flowers!
A. Balmont

3. Learning new material

A bit of history

Speaking about these ideas, one should start with Aristotle's theory of colors (4th century BC). Aristotle argued that the difference in color is determined by the difference in the amount of darkness "mixed" into the sunlight (white) light. Violet color, according to Aristotle, occurs with the greatest addition of darkness to light, and red - with the least. Thus, the colors of the rainbow are complex colors, and the main one is white light. Interestingly, the appearance of glass prisms and the first experiments on observing the decomposition of light by prisms did not give rise to doubts about the correctness of Aristotle's theory of the origin of colors. Both Khariot and Martzi remained followers of this theory. This should not be surprising, since at first glance, the decomposition of light by a prism into different colors would seem to confirm the idea that color arises as a result of mixing light and darkness. The rainbow strip appears just at the transition from the shadow strip to the illuminated one, i.e., at the border of darkness and white light. From the fact that the violet ray travels the longest distance inside the prism compared to other colored rays, it is not surprising to conclude that the violet color occurs when white light loses its “whiteness” the most when passing through the prism. In other words, the greatest mixing of darkness into white light takes place on the longest path. It was not difficult to prove the falsity of such conclusions by setting up the corresponding experiments with the same prisms. However, no one had done this before Newton.

Sunlight has many secrets. One of them - dispersion phenomenon. It was first discovered by the great English physicist Isaac Newton in 1666 while improving the telescope.

Light dispersion(light decomposition) is a phenomenon due to the dependence of the absolute refractive index of a substance on the frequency (or wavelength) of light (frequency dispersion), or, the same thing, the dependence of the phase velocity of light in a substance on the wavelength (or frequency).

Experimentally, the dispersion of light was discovered by I. Newton around 1672, although it was theoretically well explained much later.
One of the most illustrative examples of dispersion is the decomposition of white light as it passes through a prism (Newton's experiment). The essence of the phenomenon of dispersion is the unequal speed of propagation of light rays with different wavelengths in a transparent substance - an optical medium (whereas in vacuum the speed of light is always the same, regardless of the wavelength and hence the color). Usually, the higher the frequency of the wave, the higher the refractive index of the medium and the lower its speed of light in it:

• at the red maximum speed in the medium and the minimum degree of refraction,
• violet has the minimum speed of light in the medium and the maximum degree of refraction.

The dispersion of light made it possible for the first time to quite convincingly show the composite nature of white light.

White light is also decomposed into a spectrum as a result of passing through a diffraction grating or reflecting from it (this is not related to the phenomenon of dispersion, but is explained by the nature of diffraction).

The diffraction and prismatic spectra are somewhat different: the prismatic spectrum is compressed in the red part and stretched in the violet, and is arranged in descending order of wavelength: from red to violet; the normal (diffraction) spectrum is uniform in all areas and is arranged in ascending order of wavelengths: from violet to red.

Knowing that white light has a complex structure, one can explain the amazing variety of colors in nature. If an object, such as a sheet of paper, reflects all the rays of various colors falling on it, then it will appear white. Covering the paper with a layer of red paint, we do not create light of a new color, but retain some of the existing one on the sheet. Only red rays will now be reflected, while the rest will be absorbed by a layer of paint. Grass and tree leaves appear green to us because of all the sun's rays falling on them, they reflect only green ones, absorbing the rest. If you look at the grass through red glass, which transmits only red rays, it will appear almost black.

The phenomenon of dispersion, discovered by Newton, is the first step towards understanding the nature of color. The depth of understanding of dispersion came after the dependence of color on the frequency (or length) of a light wave was clarified.

Thomas Young (1773-1829) was the first to measure the wavelengths of different colors in 1802.

After the discovery of the dispersion of light, the wavelength became the main quantity that determines the color of light. The main color receiver is the retina.

Color- there is a sensation that occurs in the retina of the eye when it is excited by a light wave of a certain length. Knowing the wavelength of the emitted light and the conditions for its propagation, it is possible to predict in advance with a high degree of accuracy what color the eye will see.

It may be that the retina of the eye does not perceive one of the primary colors well or does not react to it at all, then this person's color perception is disturbed. This lack of vision is called colorblind.

Good color perception is very important for a number of professions: sailors, pilots, railway workers, surgeons, artists. Special devices have been created anomaloscopes for the study of color vision disorders.

Dispersion explains the fact that the rainbow appears after the rain (more precisely, the fact that the rainbow is multi-colored, not white).
First attempt to explain rainbow as a natural phenomenon was made in 1611 by Archbishop Antonio Dominis.

1637 The scientific explanation of the rainbow was first given by Rene Descartes. He explained the rainbow in terms of the laws of refraction and reflection of sunlight in raindrops. The phenomenon of dispersion had not yet been discovered, so Descartes' rainbow turned out to be white.

After 30 years Isaac Newton supplemented the theory of Descartes, explained how colored rays are refracted in raindrops.

“Descartes hung the rainbow in the right place in the sky, and Newton colored it with all the colors of the spectrum”

American scientist A. Fraser

Rainbow- This is an optical phenomenon associated with the refraction of light rays on numerous raindrops. However, not everyone knows exactly how the refraction of light on raindrops leads to the appearance of a giant multi-colored arc in the sky. Therefore, it is useful to dwell in more detail on the physical explanation of this spectacular optical phenomenon.

Rainbow through the eyes of a careful observer. First of all, a rainbow can only be observed in the direction opposite to the Sun. If you stand facing the rainbow, then the Sun will be behind. A rainbow occurs when the Sun illuminates a curtain of rain. As the rain subsides and then stops, the rainbow fades and gradually disappears. The colors observed in the rainbow alternate in the same sequence as in the spectrum obtained by passing a beam of sunlight through a prism. In this case, the inner (facing the surface of the Earth) extreme region of the rainbow is colored in purple, and the outermost region is in red. Often, another (secondary) rainbow appears above the main rainbow - wider and blurry. The colors in the secondary rainbow alternate in reverse order, from red (the innermost region of the arc) to violet (the outermost region).

For an observer located on a relatively flat earth's surface, a rainbow appears provided that the angular height of the Sun above the horizon does not exceed about 42 °. The lower the Sun, the greater the angular height of the rainbow apex and, consequently, the larger the observed region of the rainbow. A secondary rainbow can be observed if the height of the Sun above the horizon does not exceed about 52.

The rainbow can be thought of as a gigantic wheel, which, like an axle, is put on an imaginary straight line passing through the Sun and the observer.

Dispersion is the cause of chromatic aberrations - one of the aberrations of optical systems, including photographic and video lenses.

Dispersion of light in nature and art

• Due to dispersion, different colors of light can be observed.
• The rainbow, whose colors are caused by dispersion, is one of key images culture and art.
• Due to the dispersion of light, one can observe the color "play of light" on the facets of a diamond and other transparent faceted objects or materials.
• To some extent, iridescent effects are found quite often when light passes through almost any transparent object. In art, they can be specially amplified, emphasized.
• The decomposition of light into a spectrum (due to dispersion) during refraction in a prism is a fairly common topic in fine arts. For example, the cover of Pink Floyd's album Dark Side Of The Moon depicts the refraction of light in a prism with decomposition into a spectrum.

The discovery of dispersion has become very significant in the history of science. On the tombstone of the scientist there is an inscription with the following words: “Here lies Sir Isaac Newton, a nobleman who ... was the first with a torch of mathematics to explain the movements of the planets, the paths of comets and the tides of the oceans.

He explored the difference in light rays and the different properties of colors manifested in this, which no one had previously suspected. ... Let mortals rejoice that such an adornment of the human race existed.

4. Fixing

• Answer questions about the topic.
• Heading "Think..."
• Q: Why is the rainbow round?
• Compilation of "Sinkwine" on the topic "Dispersion"

5. Summing up the lesson

At the end of the lesson, again carry out the diagnostics “Color painting class”. Find out what the mood was at the end of the lesson, on the basis of which the “Class Coloring” diagram is compiled and the result is compared, what mood the students had at the beginning of the lesson and at the end.

6. Homework:§66

Literature:

1. Myakishev G.Ya., Bukhovtsev B.B. Physics: Textbook for grade 11 high school. – M.: Enlightenment, 2006.
2. Rymkevich A.P. Collection of problems in physics for grades 9-11 of high school. – M.: Enlightenment, 2006.
3. Reader in physics: Tutorial for students in grades 8-10 of secondary school / Ed. B.I. Spassky. - M .: Education, 1987.
4. Journal "Physics at School" No. 1/1998

Sometimes, when the sun comes out again after a heavy downpour, you can see a rainbow. This is because the air is saturated with fine water dust. Each drop of water in the air plays the role of a tiny prism, crushing the light into different colors.

About 300 years ago, I. Newton passed the sun's rays through a prism. He discovered that white light is a "wonderful mixture of colors."

It is interesting… Why are there only 7 colors in the white light spectrum?

So, for example, Aristotle indicated only three colors of the rainbow: red, green, purple. Newton first identified five colors in the rainbow, and later ten. However, later, he settled on seven colors. The choice is explained, most likely, by the fact that the number seven was considered "magical" (seven wonders of the world, seven weeks, etc.).

The dispersion of light was first observed experimentally by Newton in 1666, when a narrow beam of sunlight was passed through a glass prism. In the spectrum of white light he obtained, he singled out seven colors: From this experience, Newton concluded that "light beams that differ in color differ in the degree of refraction." Violet rays are most strongly refracted, red ones are least refracted.

White light is a complex light consisting of waves of different wavelengths (frequency). Each color has its own wavelength and frequency: red, orange, green, blue, blue, violet - this decomposition of light is called the spectrum.

Waves of different colors are refracted differently in a prism: less red, more violet. A prism deflects waves of different colors to different angles.. Their behavior is explained by the fact that during the transition of light waves from air to a glass prism, the speed of the “red” waves changes less than that of the “violet”. Thus, the shorter the wavelength (the greater the frequency), the greater the refractive index of the medium for such waves.

Dispersion is the dependence of the refractive index of light on the oscillation frequency (or wavelength).

For waves of different chromaticity, the refractive indices given substance different; as a result, when deflected by a prism, white light decomposes into spectrum.

When a monochromatic light wave passes from air to matter, the wavelength of the light decreases, oscillation frequency remains unchanged. The color remains unchanged.

When all the colors of the spectrum are superimposed, white light is formed.

Why do we see objects colored? Paint doesn't create color, it selectively absorbs or reflects light.

Basic summary:

Questions for self-control on the topic "Dispersion of light"

1. What is the dispersion of light?
2. Draw diagrams for obtaining the spectrum of white light using a glass prism.
3. Why does white light pass through a prism giving off a spectrum?
4. Compare the refractive indices for red and violet light.
5. Which light travels faster in a prism, red or violet?
6. How to explain the diversity of colors in nature in terms of wave optics?
7. What color will be visible through the red light filter surrounding objects? Why?

17. 18. Interaction of light with matter. Dispersion and absorption of light. Normal and anomalous dispersion. Bouguer-Lambert law.

Dispersion of light call the phenomenon of the dependence of the absolute refractive index of a substance n on the frequency of light ω (or wavelength λ):

A consequence of the dispersion of light is the decomposition into a spectrum of a beam of white light when it passes through a prism. The first experimental study of the dispersion of light in a glass prism was carried out by I. Newton in 1672.

Light dispersion called normal if the refractive index increases monotonically with increasing frequency (decreases with increasing wavelength); otherwise, the variance is called anomalous, Fig.1.

Value

called substance dispersion and characterizes the rate of change in the refractive index with a change in wavelength.

Normal dispersion of light is observed far from the bands or lines of absorption of light by the substance, anomalous - within the bands or lines of absorption.

Consider the dispersion of light in a prism, Fig.2.

Let a monochromatic beam of light fall on a transparent prism with a refractive angle θ and a refractive index n at an angle α 1 . After a double deflection (on the left and right faces of the prism), the beam turns out to be deflected from the original direction by an angle φ. It follows from geometric transformations that

those. the angle of deflection of the rays by the prism is the greater, the greater the refractive angle and the refractive index of the substance of the prism. Since n = f(λ), then the rays of different wavelengths after passing through the prism will be deflected at different angles, i.e. a beam of white light incident on a prism decomposes into a spectrum behind the prism, which was observed for the first time by Newton. This means that with the help of a prism, as well as with the help of a diffraction grating, by decomposing light into a spectrum, it is possible to determine its spectral composition.

It should be remembered that the composite colors in the diffraction and prismatic spectra are located differently. In the diffraction spectrum, the sine of the deflection angle is proportional to the wavelength, therefore, red rays, which have a longer wavelength than violet ones, are deflected more by the diffraction grating. In a prism, for all transparent substances with normal dispersion, the refractive index n decreases with increasing wavelength, so red rays are deflected by the prism less than violet ones.

The action is based on the phenomenon of normal dispersion prism spectrometers widely used in spectral analysis. This is due to the fact that it is much easier to make a prism than grating. Prism spectrometers also have a large luminosity.

Electronic theory of light dispersion. It follows from Maxwell's macroscopic electromagnetic theory that

but in the optical region of the spectrum for all substances μ ≈ 1, therefore

n= ε. (one)

Formula (1) contradicts experience, because the quantity n, being a variable n = f(λ), is at the same time equal to a certain constant ε (a constant in Maxwell's theory). In addition, the values ​​of n obtained from this expression do not agree with the experimental data.

To explain the dispersion of light, it was proposed electron theory Lorentz, in which the dispersion of light is considered as a result of the interaction of electromagnetic waves with charged particles that are part of the substance and perform forced oscillations in the alternating electromagnetic field of the wave.

Let us get acquainted with this theory on the example of a homogeneous isotropic dielectric, assuming formally that the dispersion of light is a consequence of the dependence of ε on the frequency ω of light waves. The permittivity of a substance is

ε \u003d 1 + χ \u003d 1 + P / (ε 0 E),

where χ is the dielectric susceptibility of the medium, ε 0 is the electrical constant, P is the instantaneous value of the polarization (the induced dipole moment per unit volume of the dielectric in the wave field with strength E). Then

n 2 = 1 + Р/(ε 0 Е), (2)

those. depends on R. For visible light the frequency ω ~ 10 15 Hz is so high that only forced oscillations of the outer (most weakly bound) electrons of atoms, molecules or ions under the action of the electric component of the wave field are significant, and there will be no orientational polarization of molecules at such a frequency. These electrons are called optical electrons.

For simplicity, let us consider vibrations of one optical electron in a molecule. The induced dipole moment of an electron performing forced oscillations is p = ex, where e is the charge of the electron, x is the displacement of the electron from the equilibrium position under the action of the electric field of the light wave. Let n 0 be the concentration of atoms in the dielectric, then

P \u003d p n 0 \u003d n 0 e x. (3)

Substituting (3) into (2) we get

n 2 \u003d 1 + n 0 e x / (ε 0 E), (4)

those. the problem is reduced to determining the displacement x of an electron under the action of an external electric field E \u003d E 0 cos ωt.

The equation of forced vibrations of an electron for the simplest case

d 2 x/dt 2 +ω 0 2 x = (F 0 /m)cos ωt = (e/ m) E 0 cos ωt, (5)

where F 0 = eE 0 is the amplitude value of the force acting on the electron from the wave field, ω 0 = √k/m is the natural oscillation frequency of the electron, m is the mass of the electron. Solving equation (5), we find ε = n 2 depending on the constants of the atom (е, m, ω 0) and the frequency of the external field ω, i.e. solve the dispersion problem.

Solution (5) is

Х = А cos ωt, (6)

A \u003d eE 0 / m (ω 0 2 - ω 2). (7)

Substitute (6) and (7) into (4) and get

n 2 \u003d 1 + n 0 e 2 / ε 0 m (ω 0 2 - ω 2). (eight)

It can be seen from (8) that the refractive index of a substance depends on the frequency ω of the external field, and that in the frequency range from ω = 0 to ω = ω 0, the value of n 2 is greater than 1 and increases with increasing frequency ω ( normal dispersion). At ω = ω 0 the value n 2 = ± ∞; in the frequency range from ω = ω 0 to ω = ∞, the value of n 2 is less than 1 and increases from - ∞ to 1 (normal dispersion). Passing from n 2 to n, we get the dependence graph n = n(ω), Fig.1. Region AB - region anomalous dispersion. The study of anomalous dispersion - D.S. Christmas.

By absorbing light- is called the decrease in the energy of a light wave as it propagates in a substance due to the conversion of wave energy into other types of energy.

From the point of view of electronic theory, the interaction of light and matter is reduced to the interaction of the electromagnetic field of a light wave with atoms and molecules of matter. The electrons that make up atoms can oscillate under the action of an alternating electric field of a light wave. Part of the energy of the light wave is spent on the excitation of electron oscillations. Partially, the energy of electron oscillations again turns into the energy of light radiation, and also turns into other forms of energy, for example, into the energy of thermal radiation.

The absorption of light radiation can be described in general terms from the energy point of view, without entering into the details of the mechanism of interaction of light waves with atoms and molecules of the absorbing substance.

A formal description of the absorption of light by a substance was given Booger who established the relationship between the intensity of light passing through the final layer of an absorbing substance and the intensity of the light incident on it

I lλ = I 0λ e -K l (1)

where I 0 λ is the intensity of light radiation with a wavelength λ incident on the absorbing layer; I lλ- intensity of light radiation passing through an absorbing layer of a substance with a thickness l; K λ is the absorption coefficient depending on λ, i.e. Kλ = f(λ).

If the absorber is a substance in solution, then the absorption of light is the greater, the more molecules of the solute the light meets on its way. Therefore, the absorption coefficient depends on the concentration C. In the case of weak solutions, when the interaction of the solute molecules can be neglected, the absorption coefficient is proportional to C:

K λ = c λ С (2)

where c λ is the coefficient of proportionality, which also depends on λ. Taking into account (2), Bouguer's law (1) can be rewritten as:

I λ = I 0λ e - c C l (3)

c λ is the light absorption index per unit concentration of the substance. If the concentration of a solute is expressed in [mol / liter], then c λ is called molar absorption coefficient.

Relation (3) is called the Bouguer-Lambert-Beer law. The ratio of the magnitude of the light flux emerging from layer I lλ, to the incoming I 0λ is called coefficient of optical (or light) transmission of the layer T:

T = I lλ/I 0 λ = e - c C l (4)

or in percentage

T = I lλ/I 0λ 100%. (5)

The absorption of the layer is equal to the ratio

L
the logarithm of 1/T is called layer optical density D

D = log 1/T = log I 0 λ /I l λ \u003d 0.43c λ С l (6)

those. optical density characterizes the absorption of light by a medium. Relation (6) can be used both to determine the concentration of solutions and to characterize the absorption spectra of substances.

The dependence of the optical density on the wavelength D = f(λ) is the spectral absorption characteristic of a given substance, and the curve expressing this dependence is called absorption spectrum. Absorption spectra, like emission spectra, are line, striped and continuous, Fig. 3. According to Bohr's model of the atom, light quanta are emitted and absorbed during the transition of a system (atom) from one energy state to another. If in this case only the electronic energy of the system changes in optical transitions, as is the case in atoms, then the absorption line in the spectrum will be sharp.

Fig.3.a) line absorption spectrum, b) striped absorption spectrum, c) continuous absorption spectrum.

However, for complex molecules, the energy of which is composed of electronic E el, vibrational E col and rotational E r energy (E = E el + E col + E r), when light is absorbed, not only electronic energy changes, but necessarily vibrational and rotational. Moreover, since ∆E el >> ∆E kol >> ∆E vr, as a result of this, the set of lines corresponding to the electronic transition in the absorption spectrum of solutions looks like an absorption band.

The absorption coefficient for dielectrics is low (approximately 10 -3 - 10 -5 cm -1), for them broad absorption bands are observed, i.e. dielectrics have a continuous absorption spectrum. This is due to the fact that there are no free electrons in dielectrics and the absorption of light is due to the phenomenon of resonance of forced vibrations of electrons in atoms and atoms in dielectric molecules.

The absorption coefficient for metals is large (about 10 3 - 10 5 cm -1) and therefore the metals are opaque to light. In metals, due to the presence of free electrons moving under the action of the electric field of a light wave, rapidly alternating currents arise, accompanied by the release of Joule heat. Therefore, the energy of the light wave rapidly decreases, turning into the internal energy of the metal. The higher the conductivity of a metal, the more light is absorbed in it. On fig. 1 shows a typical dependence of the light absorption coefficient on frequency in the region of the absorption band. It can be seen that anomalous dispersion is observed inside the absorption band. However, the absorption of light by a substance must be significant in order to affect the behavior of the refractive index.

The dependence of the absorption coefficient on the wavelength (frequency) explains the coloration of absorbing bodies. For example, glass that weakly absorbs red and orange rays and strongly absorbs green and blue rays will appear red when illuminated with white light. If green and blue light is directed at such glass, then the glass will appear black due to the strong absorption of these wavelengths. This phenomenon is used in the manufacture filters, which, depending on the chem. The composition of glasses transmits light of only certain wavelengths, absorbing the rest.

Every hunter wants to know where the pheasant is sitting. As we remember, this phrase means the sequence of colors of the spectrum: red, orange, yellow, green, blue, indigo and violet. Who showed that White color it is the totality of all colors, what does the rainbow have to do with it, beautiful sunsets and sunrises, glitter precious stones? All these questions are answered by our lesson, the theme of which is: “Dispersion of light”.

Until the second half of the 17th century, there was no complete clarity about what color is. Some scientists said that this is a property of the body itself, some stated that these are various combinations of light and dark, thereby confusing the concepts of color and illumination. Such color chaos reigned until the time when Isaac Newton conducted an experiment on the transmission of light through a prism (Fig. 1).

Rice. 1. Ray path in a prism ()

Recall that a ray passing through a prism undergoes refraction when passing from air to glass and then another refraction - from glass to air. The ray trajectory is described by the law of refraction, and the degree of deflection is characterized by the refractive index. Formulas describing these phenomena:

Rice. 2. Newton's experience ()

In a dark room, a narrow beam of sunlight penetrates through the shutters; Newton placed a glass trihedral prism in its path. A beam of light, passing through a prism, was refracted in it, and a multi-colored band appeared on the screen behind the prism, which Newton called the spectrum (from the Latin "spectrum" - "vision"). The white color turned into all colors at once (Fig. 2). What conclusions did Newton draw?

1. Light has a complex structure (saying modern language- white light contains electromagnetic waves of different frequencies).

2. Light of different colors differs in the degree of refraction (characterized by different refractive indices in a given medium).

3. The speed of light depends on the medium.

These conclusions Newton outlined in his famous treatise "Optics". What is the reason for such a decomposition of light into a spectrum?

As Newton's experiment showed, the red color was refracted the weakest, and violet the strongest. Recall that the degree of refraction of light rays characterizes the refractive index n. Red differs from violet in frequency, red has a lower frequency than violet. Since the refractive index becomes larger from the red end of the spectrum to the violet, we can conclude that the refractive index of glass increases with increasing light frequency. This is the essence of the phenomenon of dispersion.

Recall how the index of refraction is related to the speed of light:

n~v; V ~ => ν =

n - refractive index

C is the speed of light in vacuum

V is the speed of light in the medium

ν - light frequency

This means that the higher the frequency of light, the slower the speed of light propagates in the glass, thus, top speed inside the glass prism is red, and the lowest speed is purple.

The difference in the speeds of light for different colors is carried out only in the presence of a medium, naturally, in a vacuum, any ray of light of any color propagates with the same speed m/s. Thus, we found out that the reason for the decomposition of white color into a spectrum is the phenomenon of dispersion.

Dispersion- dependence of the speed of propagation of light in the medium on its frequency.

The phenomenon of dispersion, discovered and studied by Newton, was waiting for its explanation for more than 200 years, only in the 19th century the Dutch scientist Lawrence proposed classical theory dispersion.

The reason for this phenomenon is in the interaction of external electromagnetic radiation, that is, light with the medium: the greater the frequency of this radiation, the stronger the interaction, which means that the more the beam will deviate.

The dispersion that we talked about is called normal, that is, the frequency index increases if the frequency of electromagnetic radiation increases.

In some rare media, anomalous dispersion is possible, that is, the refractive index of the medium increases if the frequency drops.

We have seen that each color has a specific wavelength and frequency. A wave corresponding to the same color, in different environments has the same frequency but different wavelengths. Most often, when speaking about the wavelength corresponding to a certain color, they mean the wavelength in vacuum or air. The light corresponding to each color is monochromatic. "Mono" - one, "chromos" - color.

Rice. 3. Arrangement of colors in the spectrum by wavelengths in the air ()

The longest wavelength is red (wavelength - from 620 to 760 nm), the shortest wavelength is violet (from 380 to 450 nm) and the corresponding frequencies (Fig. 3). As you can see, there is no white color in the table, white color is the totality of all colors, this color does not correspond to any strictly defined wavelength.

What explains the colors of the bodies that surround us? They are explained by the ability of the body to reflect, that is, to scatter the radiation incident on it. For example, a white color falls on some body, which is a combination of all colors, but this body reflects red best of all, and absorbs the rest of the colors, then it will appear to us as red. The body that best reflects blue will appear of blue color and so on. If the body reflects all colors, it will eventually appear white.

It is the dispersion of light, that is, the dependence of the refractive index on the frequency of the wave, that explains the beautiful phenomenon of nature - the rainbow (Fig. 4).

Rice. 4. The phenomenon of the rainbow ()

The rainbow is caused by sunlight refracted and reflected by droplets of water, rain or fog floating in the atmosphere. These droplets deflect light of different colors in different ways, as a result, the white color decomposes into a spectrum, that is, dispersion occurs, the observer, who stands with his back to the light source, sees a multi-colored glow that comes from space along concentric arcs.

Dispersion also explains the wonderful play of color on the facets of precious stones.

1. The phenomenon of dispersion is the decomposition of light into a spectrum, due to the dependence of the refractive index on the frequency of electromagnetic radiation, that is, the frequency of light. 2. Body color is determined by the body's ability to reflect or scatter one or another frequency of electromagnetic radiation.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - M.: Mnemozina, 2012.
2. Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

Homework

1. What conclusions did Newton draw from his experiment with a prism?
2. Define dispersion.
3. What determines body color?

1. Internet portal B-i-o-n.ru ().
2. Internet portal Sfiz.ru ().
3. Internet portal Femto.com.ua ().

or, which is the same, the dependence of the phase velocity of light waves on frequency:

Dispersion - the dependence of the refractive index of a substance on the frequency of the wave - manifests itself especially brightly and beautifully together with the effect of birefringence (see Video 6.6 in the previous paragraph), observed when light passes through anisotropic substances. The fact is that the refractive indices of ordinary and extraordinary waves depend differently on the frequency of the wave. As a result, the color (frequency) of light transmitted through an anisotropic substance placed between two polarizers depends both on the thickness of the layer of this substance and on the angle between the transmission planes of the polarizers.

For all transparent colorless substances in the visible part of the spectrum, with decreasing wavelength, the refractive index increases, that is, the dispersion of the substance is negative:. (fig. 6.7, areas 1-2, 3-4)

If a substance absorbs light in a certain range of wavelengths (frequencies), then in the absorption region the dispersion

turns out to be positive and is called anomalous (Figure 6.7, area 2–3).

Rice. 6.7. Dependence of the square of the refractive index (solid curve) and the coefficient of absorption of light by a substance
(dashed curve) on the wavelengthlnear one of the absorption bands()

Newton also studied normal dispersion. The decomposition of white light into a spectrum when passing through a prism is a consequence of the dispersion of light. When a beam of white light passes through a glass prism, a colorful spectrum (Fig. 6.8).

Rice. 6.8. The passage of white light through a prism: due to the difference in the refractive index of glass for different
wavelength, the beam is decomposed into monochromatic components - a spectrum appears on the screen

Red light has the longest wavelength and the lowest refractive index, so red rays are deflected by the prism less than others. Next to them will be rays of orange, then yellow, green, blue, blue, and finally purple light. The complex white light incident on the prism was decomposed into monochromatic components (spectrum).

A prime example dispersion is rainbow. A rainbow is observed if the sun is behind the observer. Red and violet rays are refracted by spherical water droplets and reflected from them. inner surface. Red rays are refracted less and fall into the observer's eye from droplets at a higher height. Therefore, the upper band of the rainbow always turns out to be red (Fig. 26.8).

Rice. 6.9. The appearance of the rainbow

Using the laws of reflection and refraction of light, it is possible to calculate the course of light rays at full reflection and dispersion in raindrops. It turns out that the rays scatter with the greatest intensity in the direction that forms an angle of about 42 ° with the direction of the sun's rays (Fig. 6.10).

Rice. 6.10. rainbow location

The locus of such points is a circle centered at the point 0. Part of it is hidden from the observer R below the horizon, the arc above the horizon is the visible rainbow. It is also possible double reflection of rays in raindrops, resulting in a second-order rainbow, the brightness of which, naturally, is less than the brightness of the main rainbow. For her, the theory gives an angle 51 °, that is, the second-order rainbow lies outside the main one. In it, the order of colors is reversed: the outer arc is colored purple, and the lower arc is red. Rainbows of the third and higher orders are rarely observed.

Elementary theory of dispersion. Dependence of the refractive index of a substance on length electromagnetic wave(frequency) is explained on the basis of the theory of forced oscillations. Strictly speaking, the motion of electrons in an atom (molecule) obeys the laws quantum mechanics. However, for a qualitative understanding optical phenomena one can confine oneself to the concept of electrons bound in an atom (molecule) by an elastic force. When deviating from the equilibrium position, such electrons begin to oscillate, gradually losing energy to the radiation of electromagnetic waves or transferring their energy to the lattice nodes and heating the substance. As a result of this, the oscillations will be damped.

When passing through matter, an electromagnetic wave acts on each electron with the Lorentz force:

where v- the speed of an oscillating electron. In an electromagnetic wave, the ratio of the strengths of the magnetic and electric fields is

Therefore, it is not difficult to estimate the ratio of the electric and magnetic forces acting on an electron:

Electrons in matter move at speeds much lower than the speed of light in vacuum:

where - the amplitude of the electric field strength in the light wave, - the phase of the wave, determined by the position of the considered electron. To simplify the calculations, we neglect damping and write the equation of electron motion in the form

where, is the natural frequency of oscillations of an electron in an atom. The solution of such a differential inhomogeneous equation we have already considered and obtained

Therefore, the displacement of the electron from the equilibrium position is proportional to the strength of the electric field. Displacements of the nuclei from the equilibrium position can be neglected, since the masses of the nuclei are very large compared to the mass of the electron.

An atom with a displaced electron acquires a dipole moment

(for simplicity, let us assume for the time being that there is only one "optical" electron in the atom, the displacement of which makes a decisive contribution to the polarization). If a unit volume contains N atoms, then the polarization of the medium (dipole moment per unit volume) can be written as

In real media, different types of charge oscillations (groups of electrons or ions) are possible, contributing to the polarization. These types of vibrations can have different amounts of charge e i and the masses t i , as well as various natural frequencies (we will denote them by the index k), the number of atoms per unit volume with a given type of vibration Nk proportional to the concentration of atoms N:

Dimensionless proportionality factor f k characterizes the effective contribution of each type of oscillations to the total value of the medium polarization:

On the other hand, as is known,

where is the dielectric susceptibility of the substance, which is related to the dielectric constant e ratio

As a result, we obtain an expression for the square of the refractive index of a substance:

Near each of the natural frequencies, the function defined by formula (6.24) suffers a discontinuity. This behavior of the refractive index is due to the fact that we neglected attenuation. Similarly, as we saw earlier, neglecting damping leads to an infinite increase in the amplitude of forced oscillations at resonance. Allowance for damping saves us from infinities, and the function has the form shown in Fig. 6.11.

Rice. 6.11. Addiction permittivity environmentson the frequency of the electromagnetic wave

Considering the relationship of frequency with the length of an electromagnetic wave in vacuum

you can get the dependence of the refractive index of the substance P on the wavelength in the region of normal dispersion (sections 1–2 and 3–4 in fig. 6.7):

The wavelengths corresponding to natural oscillation frequencies are constant coefficients.

In the region of anomalous dispersion (), the frequency of the external electromagnetic field is close to one of the natural frequencies of oscillations of molecular dipoles, that is, a resonance occurs. It is in these areas (for example, section 2–3 in Fig. 6.7) that significant absorption of electromagnetic waves is observed; the absorption coefficient of light by the substance is shown by the dashed line in Fig. 6.7.

The concept of group velocity. The concept of group velocity is closely related to the phenomenon of dispersion. When propagating in a medium with a dispersion of real electromagnetic impulses, for example, the trains of waves known to us emitted by individual atomic emitters, their “spreading” occurs - the extension of the extent in space and duration in time. This is due to the fact that such pulses are not a monochromatic sinusoidal wave, but a so-called wave packet, or a group of waves - a set of harmonic components with different frequencies and different amplitudes, each of which propagates in a medium with its own phase velocity (6.13).

If the wave packet propagated in vacuum, then its shape and space-time extension would remain unchanged, and the propagation velocity of such a train of waves would be the phase velocity of light in vacuum

Due to the presence of dispersion, the dependence of the frequency of an electromagnetic wave on the wave number k becomes non-linear, and the propagation velocity of the wave train in the medium, that is, the energy transfer rate, is determined by the derivative

where is the wave number for the "central" wave in the train (which has the highest amplitude).

We will not derive this formula in general view, but let's explain it with a particular example physical meaning. As a model of a wave packet, we will take a signal consisting of two plane waves propagating in the same direction with the same amplitudes and initial phases , but differing in frequencies shifted relative to the "central" frequency by a small amount . The corresponding wave numbers are shifted relative to the "central" wave number by a small amount . These waves are described by expressions.