The essence of the phenomenon of light dispersion. Which scientist discovered the phenomenon of dispersion

One of the results of the interaction of light with matter is its dispersion.

Light dispersion called the refractive index dependencen substances from frequencyν (wavelengthsλ) light or the dependence of the phase speed of light waves on their frequency.

Light dispersion is represented as a dependence:

The consequence of dispersion is the decomposition into a spectrum of a beam of white light when passing through a prism (Fig. 10.1). The first experimental observations of light dispersion were carried out in 1672 by I. Newton. He explained this phenomenon by the difference in the masses of the corpuscles.

Let's consider the dispersion of light in a prism. Let a monochromatic beam of light fall on a prism with refractive angle A and refractive index n(Fig. 10.2) at an angle.

Rice. 10.1	Rice. 10.2

After double refraction (on the left and right sides of the prism), the beam is refracted from the original direction by an angle φ. From Fig. it follows that

Let's assume that the angles A and are small, then the angles , , will also be small and instead of the sines of these angles, you can use their values. Therefore, , and because , then or .

It follows that

,

(10.1.1)

those. The greater the refractive angle of the prism, the greater the angle of deflection of rays by a prism..

From expression (10.1.1) it follows that the angle of deflection of rays by a prism depends on the refractive index n, A n is a function of wavelength, therefore rays of different wavelengths are deflected at different angles after passing through the prism. A beam of white light behind a prism is decomposed into a spectrum called dispersive or prismatic , as Newton observed. Thus, using a prism, as well as using a diffraction grating, decomposing light into a spectrum, it is possible to determine its spectral composition.

Let's consider differences in diffraction and prismatic spectra.

· Diffraction grating decomposes light directly by wavelength, therefore, from the measured angles (in the directions of the corresponding maxima), the wavelength (frequency) can be calculated. The decomposition of light into a spectrum in a prism occurs according to the values ​​of the refractive index, therefore, to determine the frequency or wavelength of light, you need to know the dependence or.

· Composite colors in diffraction And prismatic spectra are located differently. We know that the sine of the angle in a diffraction grating is proportional to the wavelength . Therefore, red rays having longer length waves are deflected more strongly by the diffraction grating than violet waves. The prism decomposes the rays of light in the spectrum according to the values ​​of the refractive index, which for all transparent substances decreases with increasing wavelength (i.e. with decreasing frequency) (Fig. 10.3).

Therefore, red rays are deflected weaker by the prism, unlike a diffraction grating.

Magnitude(or ), called dispersion of matter, shows how quickly the refractive index changes with wavelength.

From Fig. 10.3 it follows that the refractive index for transparent substances increases with increasing wavelength, therefore the absolute value also increases with decreasing λ. This dispersion is called normal . Near absorption lines and bands, the course of the dispersion curve will be different, namely n decreases with decreasing λ. Such a course of dependence n from λ is called anomalous dispersion . Let's take a closer look at these types of dispersion.

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 this is the totality of all colors, what does a rainbow, beautiful sunsets and sunrises, shine have to do with this precious stones? All these questions are answered by our lesson, the topic of which is: “Dispersion of Light.”

Until the second half of the 17th century, it was not completely clear what color was. Some scientists said that this is a property of the body itself, some stated that these are different combinations of light and dark, thereby confusing the concepts of color and illumination. Such color chaos reigned until Isaac Newton conducted an experiment on transmitting light through a prism (Fig. 1).

Rice. 1. Path of rays in a prism ()

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

Rice. 2. Newton's experiment ()

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

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

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

3. The speed of light depends on the medium.

Newton outlined these conclusions in his famous treatise “Optics”. What is the reason for this decomposition of light into a spectrum?

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

Let's remember how the refractive index is related to the speed of light:

n ~ ν; V ~ => ν =

n - refractive index

C - speed of light in vacuum

V - speed of light in the medium

ν - frequency of light

This means that the higher the frequency of light, the lower the speed of light propagating in glass, thus highest speed inside the glass prism is red, and lowest speed- violet.

The difference in the speed 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 at 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 light propagation in a medium on its frequency.

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

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

The dispersion that we talked about is called normal, that is, the frequency indicator 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 as the frequency decreases.

We saw that each color corresponds to a specific wavelength and frequency. Wave corresponding to the same color in different environments has the same frequency, but different lengths waves Most often, when talking 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” means one, “chromos” means color.

Rice. 3. Arrangement of colors in the spectrum according to 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 sum 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 body’s ability to reflect, that is, scatter radiation incident on it. For example, a white color, which is the sum of all colors, falls on some body, but this body best reflects the red color, and absorbs other colors, then it will seem exactly red to us. The body that best reflects blue will appear blue and so on. If the body reflects all colors, it will end up appearing white.

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

Rice. 4. The phenomenon of the rainbow ()

Rainbows occur when sunlight is 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, white color is decomposed into a spectrum, that is, dispersion occurs; an observer who stands with his back to the light source sees a multi-colored glow that emanates from space along concentric arcs.

Dispersion also explains the remarkable 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 a particular frequency of electromagnetic radiation.

References

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

Homework

1. What conclusions did Newton draw after 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 ().

Light dispersion

Each of us has ever seen how rays shimmer on cut glass products or, for example, on diamonds. This can be observed due to a phenomenon called light dispersion. This is an effect that reflects the dependence of the refractive index of an object (substance, medium) on the length (frequency) of the light wave that passes through this object. The consequence of this dependence is the decomposition of the beam into a color spectrum, for example, when passing through a prism.

Light dispersion is expressed by the following equality:

where n is the refractive index, ƛ is the frequency, and ƒ is the wavelength. The refractive index increases with increasing frequency and decreasing wavelength. We often observe dispersion in nature.

Its most beautiful manifestation is the rainbow, which is formed due to dispersion sun rays when passing through numerous raindrops.

History of discovery and research.

In 1665-1667, a plague epidemic raged in England, and young Isaac Newton decided to take refuge from it in his native Woolsthorpe. Before leaving for the village, he purchased glass prisms in order to “perform experiments with the famous phenomena of flowers.”

Already in the 1st century new era It was known that when passing through a transparent single crystal with the shape of a hexagonal prism, sunlight is decomposed into a colored stripe - a spectrum. Even earlier, in the 4th century BC, the ancient Greek scientist Aristotle put forward his theory of colors. He believed that the main thing is sunlight (white) light, and all other colors are obtained from it by adding to it various quantities dark light. This idea of ​​light dominated science until the 17th century, despite the fact that numerous experiments were carried out on the decomposition of sunlight using glass prisms.

While exploring the nature of flowers, Newton came up with and performed a whole range of different optical experiments. Some of them, without significant changes in the methodology, are still used in physics laboratories.

The first experiment on dispersion was traditional. Having made a small hole in the shutter of the window of a darkened room, Newton placed a glass prism in the path of the beam of rays passing through this hole. On the opposite wall he received an image in the form of a strip of alternating colors. Newton divided the spectrum of sunlight obtained in this way into seven colors of the rainbow - red, orange, yellow, green, blue, indigo, violet.

The establishment of exactly seven primary colors of the spectrum is to a certain extent arbitrary: Newton sought to draw an analogy between the spectrum of sunlight and musical sound. If we consider the spectrum without such a prejudice, then the spectrum band arising due to dispersion breaks up into three main parts - red, yellow-green and blue-violet. The remaining colors occupy relatively narrow areas between these basic ones. In general, the human eye is capable of distinguishing up to 160 different color shades in the spectrum of sunlight.

In subsequent dispersion experiments, Newton succeeded in combining colored rays into white light.

As a result of his research, Newton, in contrast to Aristotle, came to the conclusion that when “white and black are mixed, no color arises...”. All the colors of the spectrum are contained in the sunlight, and a glass prism only separates them, since different colors are refracted differently by glass. Violet rays are refracted most strongly, red rays refract weakest.

Subsequently, scientists established the fact that, considering light as a wave, each color should be associated with its own wavelength. It is very important that these wavelengths change in a continuous manner, corresponding to the different shades of each color.

The change in the refractive index of a medium depending on the length of the wave propagating in it is called dispersion (from the Latin verb “to scatter”). The refractive index of ordinary glass is close to 1.5 for all wavelengths of visible light.

The experiments of Newton and other scientists showed that as the wavelength of light increases, the refractive index of the substances under study monotonically decreases. However, in 1860, while measuring the refractive index of iodine vapor, the French physicist Leroux discovered that red rays are refracted by this substance more strongly than blue ones. He called this phenomenon anomalous dispersion of light. Subsequently, anomalous dispersion was discovered in many other substances.

In modern physics, both normal and anomalous dispersion of light are explained in the same way. The difference between normal and anomalous dispersion is as follows. Normal dispersion occurs with light rays whose wavelength is far from the region where the waves are absorbed by the substance. Anomalous dispersion is observed only in the absorption region.

If you look closely at the dispersion of light, you can discover its connection with the penetrating ability of electromagnetic radiation. Indeed, the shorter the wavelength of electromagnetic radiation, the greater the chance of radiation penetrating through matter, in the space between atoms. That is why X-ray and gamma radiation have a very high penetrating power.

Dispersion of light in nature and art

Due to dispersion it can be observed different colors Sveta.

The rainbow, whose colors are due to dispersion, is one of the key images of culture and art.

Thanks to light dispersion, it is possible to observe the colored “play of light” on the facets of a diamond and other transparent faceted objects or materials.

To one degree or another, rainbow effects are found quite often when light passes through almost any transparent object. In art they can be specifically intensified and emphasized.

The decomposition of light into a spectrum (due to dispersion) when refracted in a prism is a fairly common topic in fine arts. For example, the cover of the album Dark Side Of The Moon by Pink Floyd depicts the refraction of light in a prism with decomposition into a spectrum.

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

He investigated the difference in light rays and the various properties of colors that manifest themselves, which no one had previously suspected. …Let mortals rejoice that such an adornment of the human race existed.”

Light dispersion- this is the dependence of the refractive index n substances depending on the wavelength of light (in vacuum)

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

Dispersion of a substance called the derivative of n By

Dispersion - the dependence of the refractive index of a substance on the wave frequency - manifests itself especially clearly 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 passing 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 planes of transmission of the polarizers.

For all transparent, colorless substances in the visible part of the spectrum, as the wavelength decreases, 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 abnormal (Fig. 6.7, area 2–3).

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

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

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

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

A striking example the dispersion is a 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 their inner surface. Red rays are refracted less and enter the observer's eye from droplets located at a higher altitude. Therefore, the top stripe of the rainbow always turns out to be red (Fig. 26.8).

Rice. 6.9. The emergence of a rainbow

Using the laws of reflection and refraction of light, it is possible to calculate the path of light rays with total reflection and dispersion in raindrops. It turns out that the rays are scattered with the greatest intensity in a direction forming an angle of about 42° with the direction of the sun's rays (Fig. 6.10).

Rice. 6.10. Rainbow location

The geometric locus of such points is a circle with center 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. Double reflection of rays in raindrops is also possible, leading to 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 painted in purple, and the bottom one - in 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(frequencies) explained based on theory forced oscillations. Strictly speaking, the movement of electrons in an atom (molecule) obeys the laws of quantum mechanics. However, for a qualitative understanding optical phenomena we can limit ourselves to the idea 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 emit electromagnetic waves or transferring their energy to lattice nodes and heating the substance. As a result, the oscillations will be damped.

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

Where v- speed of an oscillating electron. In an electromagnetic wave, the ratio of the magnetic and electric field strengths is equal to

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

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

Where - tension amplitude electric field in a light wave, is the phase of the wave determined by the position of the electron in question. To simplify calculations, we neglect damping and write the electron motion equation in the form

where, is the natural frequency of vibrations of an electron in an atom. We have already considered the solution of such a differential inhomogeneous equation earlier and obtained

Consequently, the displacement of the electron from the equilibrium position is proportional to the electric field strength. Displacements of 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 now 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 in the form

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

Dimensionless proportionality coefficient fk characterizes effective contribution each type of oscillation into the total polarization of the medium:

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 the 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. Taking into account attenuation saves us from infinities, and the function has the form shown in Fig. 6.11.

Rice. 6.11. Addiction dielectric constant environmenton the frequency of the electromagnetic wave

Considering the relationship between frequency and electromagnetic wavelength in vacuum

it is possible to obtain the dependence of the refractive index of a substance n on the wavelength in the region of normal dispersion (sections 1–2 And 3–4 in Fig. 6.7):

The wavelengths corresponding to the natural frequencies of oscillations are constant coefficients.

In the area anomalous dispersion() the frequency of the external electromagnetic field is close to one of the natural frequencies of oscillations of molecular dipoles, that is, resonance occurs. It is in these areas (for example, area 2–3 in Fig. 6.7) that significant absorption of electromagnetic waves is observed; the light absorption coefficient of 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 an environment with dispersion of real electromagnetic pulses, for example, the trains of waves known to us emitted by individual atomic emitters, they “spread out” - an expansion of extent in space and duration in time. This is due to the fact that such pulses are not a monochromatic sine 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 the medium with its own phase velocity (6.13).

If a wave packet were propagating in a vacuum, then its shape and spatio-temporal extent would remain unchanged, and the speed of propagation of such a wave train would be the phase speed 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 nonlinear, and the speed of propagation of the wave train in the medium, that is, the speed of energy transfer, is determined by the derivative

where is the wave number for the “central” wave in the train (having the greatest amplitude).

We will not derive this formula in general view, but let’s use a particular example to explain its 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 identical amplitudes and initial phases, but differing 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.

DEFINITION

Light dispersion call the dependence of the refractive index of a substance (n) on the frequency () or wavelength () of light in a vacuum (often the index 0 is omitted):

Sometimes dispersion is defined as the dependence of the phase velocity (v) of light waves on frequency.

The well-known consequence of dispersion is the decomposition of white light into a spectrum when passing through a prism. I. Newton was the first to record his observations of light dispersion. Dispersion is a consequence of the dependence of the polarization of atoms on frequency.

Graphic dependence of the refractive index on frequency (or wavelength) - dispersion curve.

Dispersion occurs as a result of vibrations of electrons and ions.

Dispersion of light in a prism

If a monochromatic beam of light hits a prism, the refractive index of which is equal to n, at an angle (Fig. 1), then after double refraction the beam deviates from the original direction by an angle:

If angles A, are small, therefore all other angles in formula (2) are small. In this case, the law of refraction can be written not through the sines of these angles, but directly through the values ​​of the angles themselves in radians:

Knowing that , we have:

Consequently, the angle of deflection of rays using a prism is directly proportional to the value of the refractive angle of the prism:

and depends on the size. And we know that the refractive index is a function of wavelength. It turns out that rays having different wavelengths, after passing through the prism, will be deflected at different angles. It becomes clear why a beam of white light will decompose into a spectrum.

Dispersion of a substance

Value (D) equal to:

called dispersion of matter. It shows the rate of change in the refractive index depending on the wavelength.

The refractive index for transparent substances increases monotonically with decreasing wavelength, which means that the magnitude of D increases with decreasing wavelength. This dispersion is called normal. The phenomenon of normal dispersion is the basis for the operation of prism spectrographs, which can be used to study spectral composition Sveta.

Examples of problem solving

EXAMPLE 1

Exercise

What are the main differences in the diffraction and prismatic spectra?

Solution

A diffraction grating sorts light into wavelengths. From the obtained and measured angles to the directions of the corresponding maxima, the wavelength can be calculated. Unlike a diffraction grating, a prism sorts light according to refractive index values, therefore, to find the wavelength of light it is necessary to have a dependence. In addition to the above, the colors in the spectrum obtained as a result of diffraction and the prismatic spectrum are located differently. For a diffraction grating, it was found that the sine of the deflection angle is proportional to the wavelength. This means that the diffraction grating rejects red rays more than violet rays. The prism separates the rays according to the refractive index, and for all transparent substances it monotonically decreases with increasing wavelength. It turns out that red rays, which have a lower refractive index, will be deflected by the prism less than violet rays (Fig. 2).

EXAMPLE 2

Exercise	What will be the angle of deflection () of the beam by a glass prism if it falls normally on its face? The refractive index of the prism substance is n=1.5. The refractive angle of the prism is thirty degrees ().
Solution	When solving the problem, you can use Fig. 1 in the theoretical part of the article. It should be noted that. From Fig. 1 it follows that According to the law of refraction we write: Since , we get that . From formula (2.1) we obtain that: