The absolute refractive index of the medium is length. Law of light refraction

Ticket 75.

Law of Light Reflection: the incident and reflected rays, as well as the perpendicular to the interface between the two media, reconstructed at the point of incidence of the ray, lie in the same plane (plane of incidence). The angle of reflection γ is equal to the angle of incidence α.

Law of light refraction: the incident and refracted rays, as well as the perpendicular to the interface between the two media, reconstructed at the point of incidence of the ray, lie in the same plane. The ratio of the sine of the angle of incidence α to the sine of the angle of refraction β is a constant value for two given media:

The laws of reflection and refraction are explained in wave physics. According to wave concepts, refraction is a consequence of changes in the speed of propagation of waves when passing from one medium to another. Physical meaning of the refractive index is the ratio of the speed of propagation of waves in the first medium υ 1 to the speed of their propagation in the second medium υ 2:

Figure 3.1.1 illustrates the laws of reflection and refraction of light.

A medium with a lower absolute refractive index is called optically less dense.

When light passes from an optically denser medium to an optically less dense medium n 2< n 1 (например, из стекла в воздух) можно наблюдать total reflection phenomenon, that is, the disappearance of the refracted ray. This phenomenon is observed at angles of incidence exceeding a certain critical angle α pr, which is called limiting angle of total internal reflection(see Fig. 3.1.2).

For the angle of incidence α = α pr sin β = 1; value sin α pr = n 2 / n 1< 1.

If the second medium is air (n 2 ≈ 1), then it is convenient to rewrite the formula in the form

The phenomenon of total internal reflection is used in many optical devices. The most interesting and practically important application is the creation of optical fibers, which are thin (from several micrometers to millimeters) arbitrarily curved threads made of optically transparent material (glass, quartz). Light incident on the end of the light guide can travel along it over long distances due to total internal reflection from the side surfaces (Figure 3.1.3). The scientific and technical direction involved in the development and application of optical light guides is called fiber optics.

Dispersion of light (decomposition of light)- this is a phenomenon caused by 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 speed of light in a substance on the wavelength (or frequency). It was discovered experimentally by Newton around 1672, although theoretically quite well explained much later.

Spatial dispersion is called the dependence of the dielectric constant tensor of the medium on the wave vector. This dependence causes a number of phenomena called spatial polarization effects.

One of the most illustrative examples variances - white light decomposition when passing through a prism (Newton's experiment). The essence of the dispersion phenomenon is the difference in the speed of propagation of light rays of different wavelengths in a transparent substance - an optical medium (while in a vacuum the speed of light is always the same, regardless of the wavelength and therefore color). Typically, the higher the frequency of a light wave, the higher the refractive index of the medium for it and the lower the speed of the wave in the medium:

Newton's experiments Experiment on the decomposition of white light into a spectrum: Newton directed the beam sunlight through a small hole onto a glass prism. When hitting the prism, the beam was refracted and on the opposite wall gave an elongated image with a rainbow alternation of colors - a spectrum. Experiment on the passage of monochromatic light through a prism: Newton placed red glass in the path of the sun's ray, behind which he received monochromatic light (red), then a prism and observed on the screen only the red spot from the light ray. Experience in the synthesis (production) of white light: First, Newton directed a ray of sunlight onto a prism. Then, having collected the colored rays emerging from the prism using a collecting lens, Newton received a white image of a hole on a white wall instead of a colored stripe. Newton's conclusions:- a prism does not change light, but only decomposes it into its components - light rays that differ in color differ in the degree of refraction; Violet rays refract most strongly, red ones less strongly - red light, which refracts less, has the highest speed, and violet has the least, which is why the prism decomposes the light. The dependence of the refractive index of light on its color is called dispersion.

Conclusions:- a prism decomposes light - white light is complex (composite) - violet rays are refracted more strongly than red ones. The color of a light beam is determined by its vibration frequency. When moving from one medium to another, the speed of light and wavelength change, but the frequency that determines the color remains constant. The boundaries of the ranges of white light and its components are usually characterized by their wavelengths in vacuum. White light is a collection of waves with lengths from 380 to 760 nm.

Ticket 77.

Absorption of light. Bouguer's law

The absorption of light in matter is associated with the conversion of the energy of the electromagnetic field of the wave into thermal energy substances (or into the energy of secondary photoluminescent radiation). The law of light absorption (Bouguer's law) has the form:

I=I 0 exp(- x),(1)

Where I 0 , I-light intensity at the input (x=0) and leaving the layer of medium thickness X, - absorption coefficient, it depends on .

For dielectrics  =10 -1  10 -5 m -1 , for metals =10 5  10 7 m -1 , Therefore, metals are opaque to light.

Dependency  ( ) explains the color of absorbing bodies. For example, glass that absorbs red light poorly will appear red when illuminated with white light.

Scattering of light. Rayleigh's law

Diffraction of light can occur in an optically inhomogeneous medium, for example in a turbid environment (smoke, fog, dusty air, etc.). By diffracting on inhomogeneities of the medium, light waves create a diffraction pattern characterized by a fairly uniform distribution of intensity in all directions.

This diffraction by small inhomogeneities is called scattering of light.

This phenomenon is observed if a narrow beam sun rays passes through dusty air, dissipates into dust particles and becomes visible.

If the sizes of inhomogeneities are small compared to the wavelength (no more than 0,1  ), then the intensity of the scattered light turns out to be inversely proportional to the fourth power of the wavelength, i.e.

I diss ~ 1/  4 , (2)

this dependence is called Rayleigh's law.

Light scattering is also observed in clean media that do not contain foreign particles. For example, it can occur on fluctuations (random deviations) of density, anisotropy or concentration. This type of scattering is called molecular scattering. It explains, for example, the blue color of the sky. Indeed, according to (2), blue and blue rays are scattered more strongly than red and yellow ones, because have a shorter wavelength, thereby causing the blue color of the sky.

Ticket 78.

Polarization of light- a set of wave optics phenomena in which the transverse nature of electromagnetic light waves is manifested. Transverse wave- particles of the medium oscillate in directions perpendicular to the direction of wave propagation ( Fig.1).

Fig.1 Transverse wave

Electromagnetic light wave plane polarized(linear polarization), if the directions of oscillation of vectors E and B are strictly fixed and lie in certain planes ( Fig.1). A plane polarized light wave is called plane polarized(linearly polarized) light. Unpolarized(natural) wave - an electromagnetic light wave in which the directions of oscillation of the vectors E and B in this wave can lie in any planes perpendicular to the velocity vector v. Unpolarized light- light waves in which the directions of oscillations of the vectors E and B change chaotically so that all directions of oscillations in planes perpendicular to the ray of wave propagation are equally probable ( Fig.2).

Fig.2 Unpolarized light

Polarized waves- in which the directions of the vectors E and B remain unchanged in space or change according to a certain law. Radiation in which the direction of vector E changes chaotically - unpolarized. An example of such radiation is thermal radiation (chaotically distributed atoms and electrons). Plane of polarization- this is a plane perpendicular to the direction of oscillations of the vector E. The main mechanism for the occurrence of polarized radiation is the scattering of radiation by electrons, atoms, molecules, and dust particles.

1.2. Types of polarization There are three types of polarization. Let's give them definitions. 1. Linear Occurs if the electric vector E maintains its position in space. It seems to highlight the plane in which vector E oscillates. 2. Circular This is polarization that occurs when the electric vector E rotates around the direction of propagation of the wave with an angular velocity equal to the angular frequency of the wave, while maintaining its absolute value. This polarization characterizes the direction of rotation of the vector E in a plane perpendicular to the line of sight. An example is cyclotron radiation (a system of electrons rotating in a magnetic field). 3. Elliptical It occurs when the magnitude of the electric vector E changes so that it describes an ellipse (rotation of the vector E). Elliptical and circular polarization can be right-handed (vector E rotates clockwise when looking towards the propagating wave) and left-handed (vector E rotates counter-clockwise when looking towards the propagating wave).

In reality, it occurs most often partial polarization (partially polarized electromagnetic waves). Quantitatively, it is characterized by a certain quantity called degree of polarization R, which is defined as: P = (Imax - Imin) / (Imax + Imin) Where Imax,Immin- the highest and lowest density of electromagnetic energy flux through the analyzer (Polaroid, Nicolas prism...). In practice, radiation polarization is often described by Stokes parameters (they determine radiation fluxes with a given polarization direction).

Ticket 79.

If natural light falls on the interface between two dielectrics (for example, air and glass), then part of it is reflected, and part of it is refracted and spreads in the second medium. By installing an analyzer (for example, tourmaline) in the path of the reflected and refracted rays, we make sure that the reflected and refracted rays are partially polarized: when the analyzer is rotated around the rays, the light intensity periodically increases and weakens (complete quenching is not observed!). Further studies showed that in the reflected beam, vibrations perpendicular to the plane of incidence predominate (they are indicated by dots in Fig. 275), while in the refracted beam, vibrations parallel to the plane of incidence (depicted by arrows) predominate.

The degree of polarization (the degree of separation of light waves with a certain orientation of the electric (and magnetic) vector) depends on the angle of incidence of the rays and the refractive index. Scottish physicist D. Brewster(1781-1868) installed law, according to which at the angle of incidence i B (Brewster angle), determined by the relation

(n 21 - refractive index of the second medium relative to the first), the reflected beam is plane polarized(contains only vibrations perpendicular to the plane of incidence) (Fig. 276). The refracted ray at the angle of incidencei B polarized to the maximum, but not completely.

If light strikes an interface at the Brewster angle, then the reflected and refracted rays mutually perpendicular(tg i B = sin i B/cos i B, n 21 = sin i B / sin i 2 (i 2 - angle of refraction), whence cos i B=sin i 2). Hence, i B + i 2 =  /2, but i’ B= i B (law of reflection), therefore i’ B+ i 2 =  /2.

The degree of polarization of reflected and refracted light at different angles drops can be calculated from Maxwell's equations, if we take into account the boundary conditions for the electromagnetic field at the interface between two isotropic dielectrics (the so-called Fresnel formulas).

The degree of polarization of refracted light can be significantly increased (by multiple refraction, provided that the light is incident each time on the interface at the Brewster angle). If, for example, for glass ( n= 1.53) the degree of polarization of the refracted beam is 15%, then after refraction into 8-10 glass plates superimposed on each other, the light emerging from such a system will be almost completely polarized. Such a collection of plates is called foot. The foot can be used to analyze polarized light both during its reflection and during its refraction.

Ticket 79 (for Spur)

As experience shows, during the refraction and reflection of light, the refracted and reflected light turns out to be polarized, and the reflection. light can be completely polarized at a certain angle of incidence, but incidentally. light is always partially polarized. Based on Frinell's formulas, it can be shown that reflection. Light is polarized in a plane perpendicular to the plane of incidence and refracted. the light is polarized in a plane parallel to the plane of incidence.

The angle of incidence at which the reflection the light is completely polarized is called the Brewster angle. The Brewster angle is determined from Brewster's law: - Brewster's law. In this case, the angle between the reflections. and refraction. rays will be equal. For an air-glass system, the Brewster angle is equal. To obtain good polarization, i.e. , when refracting light, many edible surfaces are used, which are called Stoletov’s Stop.

Ticket 80.

Experience shows that when light interacts with matter, the main effect (physiological, photochemical, photoelectric, etc.) is caused by oscillations of the vector, which in this regard is sometimes called the light vector. Therefore, to describe the patterns of light polarization, the behavior of the vector is monitored.

The plane formed by the vectors and is called the plane of polarization.

If vector oscillations occur in one fixed plane, then such light (ray) is called linearly polarized. It is conventionally designated as follows. If the beam is polarized in a perpendicular plane (in the plane xoz, see fig. 2 in the second lecture), then it is designated.

Natural light (from ordinary sources, the sun) consists of waves that have different, chaotically distributed planes of polarization (see Fig. 3).

Natural light is sometimes conventionally designated as such. It is also called non-polarized.

If, as the wave propagates, the vector rotates and the end of the vector describes a circle, then such light is called circularly polarized, and the polarization is called circular or circular (right or left). There is also elliptical polarization.

There are optical devices (films, plates, etc.) - polarizers, which extract linearly polarized light or partially polarized light from natural light.

Polarizers used to analyze the polarization of light are called analyzers.

The plane of the polarizer (or analyzer) is the plane of polarization of the light transmitted by the polarizer (or analyzer).

Let linearly polarized light with amplitude fall on a polarizer (or analyzer) E 0 . The amplitude of the transmitted light will be equal to E=E 0 cos j, and intensity I=I 0 cos 2 j.

This formula expresses Malus's law:

The intensity of linearly polarized light passing through the analyzer is proportional to the square of the cosine of the angle j between the plane of oscillation of the incident light and the plane of the analyzer.

Ticket 80 (for spur)

Polarizers are devices that make it possible to obtain polarized light. Analyzers are devices that can be used to analyze whether light is polarized or not. Structurally, a polarizer and an analyzer are one and the same. Zn Malus. Let intensity light fall on the polarizer, if the light is natural -th then all directions of the vector E are equally probable. Each vector can be decomposed into two mutually perpendicular components: one of which is parallel to the plane of polarization of the polarizer, and the other is perpendicular to it.

Obviously, the intensity of the light emerging from the polarizer will be equal. Let us denote the intensity of the light emerging from the polarizer by (). If an analyzer is placed on the path of the polarized light, the main plane of which makes an angle with the main plane of the polarizer, then the intensity of the light emerging from the analyzer is determined by the law.

Ticket 81.

While studying the glow of a solution of uranium salts under the influence of radium rays, the Soviet physicist P. A. Cherenkov drew attention to the fact that the water itself also glows, in which there are no uranium salts. It turned out that when rays (see Gamma radiation) are passed through pure liquids, they all begin to glow. S. I. Vavilov, under whose leadership P. A. Cherenkov worked, hypothesized that the glow was associated with the movement of electrons knocked out of atoms by radium quanta. Indeed, the glow strongly depended on the direction of the magnetic field in the liquid (this suggested that it was caused by the movement of electrons).

But why do electrons moving in a liquid emit light? The correct answer to this question was given in 1937 by Soviet physicists I. E. Tamm and I. M. Frank.

An electron, moving in a substance, interacts with the atoms surrounding it. Under the influence of its electric field, atomic electrons and nuclei are shifted in opposite directions - the medium is polarized. Polarized and then returning to their original state, the atoms of the medium located along the electron trajectory emit electromagnetic light waves. If the speed of the electron v is less than the speed of light in the medium (the refractive index), then the electromagnetic field will overtake the electron, and the substance will have time to polarize in space ahead of the electron. The polarization of the medium in front of the electron and behind it is opposite in direction, and the radiation of oppositely polarized atoms, “added”, “quenches” each other. When atoms that have not yet been reached by an electron do not have time to polarize, and radiation appears directed along a narrow conical layer with an apex coinciding with the moving electron and an angle at the apex c. The appearance of the light "cone" and the radiation condition can be obtained from general principles wave propagation.

Rice. 1. Mechanism of wavefront formation

Let the electron move along the axis OE (see Fig. 1) of a very narrow empty channel in a homogeneous transparent substance with a refractive index (the empty channel is needed so that collisions of the electron with atoms are not taken into account in the theoretical consideration). Any point on the OE line successively occupied by an electron will be the center of light emission. Waves emanating from successive points O, D, E interfere with each other and are amplified if the phase difference between them is zero (see Interference). This condition is satisfied for a direction that makes an angle of 0 with the trajectory of the electron. Angle 0 is determined by the relation:.

Indeed, let us consider two waves emitted in a direction at an angle of 0 to the electron velocity from two points of the trajectory - point O and point D, separated by a distance . At point B, lying on line BE, perpendicular to OB, the first wave at - after time To point F, lying on line BE, a wave emitted from the point will arrive at the moment of time after the wave is emitted from point O. These two waves will be in phase, i.e. the straight line will be a wave front if these times are equal:. That gives the condition of equality of times. In all directions for which, the light will be extinguished due to the interference of waves emitted from sections of the trajectory separated by a distance D. The value of D is determined by the obvious equation, where T is the period of light oscillations. This equation always has a solution if.

If , then the direction in which the emitted waves, when interfering, are amplified, does not exist and cannot be greater than 1.

Rice. 2. Distribution of sound waves and the formation of a shock wave during body movement

Radiation is observed only if .

Experimentally, electrons fly in a finite solid angle, with some spread in speed, and as a result, radiation propagates in a conical layer near the main direction determined by the angle.

In our consideration, we neglected the electron slowdown. This is quite acceptable, since the losses due to Vavilov-Cerenkov radiation are small and, to a first approximation, we can assume that the energy lost by the electron does not affect its speed and it moves uniformly. In this fundamental difference and the unusualness of the Vavilov-Cherenkov radiation. Typically, charges emit while experiencing significant acceleration.

An electron outpacing its light is similar to an airplane flying at a speed greater than the speed of sound. In this case, a conical shock sound wave also propagates in front of the aircraft (see Fig. 2).

When solving problems in optics, you often need to know the refractive index of glass, water, or another substance. Moreover, in different situations, both absolute and relative values ​​of this quantity can be used.

Two types of refractive index

First, let’s talk about what this number shows: how the direction of light propagation changes in one or another transparent medium. Moreover, an electromagnetic wave can come from a vacuum, and then the refractive index of glass or other substance will be called absolute. In most cases, its value lies in the range from 1 to 2. Only in very rare cases the refractive index is greater than two.

If in front of the object there is a medium denser than vacuum, then they speak of a relative value. And it is calculated as the ratio of two absolute values. For example, the relative refractive index of water-glass will be equal to the quotient of the absolute values ​​for glass and water.

In any case, it is denoted by the Latin letter “en” - n. This value is obtained by dividing the same values ​​by each other, therefore it is simply a coefficient that has no name.

What formula can you use to calculate the refractive index?

If we take the angle of incidence as “alpha” and the angle of refraction as “beta”, then the formula for the absolute value of the refractive index looks like this: n = sin α/sin β. In English-language literature you can often find a different designation. When the angle of incidence is i, and the angle of refraction is r.

There is another formula for how to calculate the refractive index of light in glass and other transparent media. It is related to the speed of light in a vacuum and the same, but in the substance under consideration.

Then it looks like this: n = c/νλ. Here c is the speed of light in a vacuum, ν is its speed in a transparent medium, and λ is the wavelength.

What does the refractive index depend on?

It is determined by the speed at which light propagates in the medium under consideration. Air in this respect is very close to a vacuum, so light waves propagate in it practically without deviating from their original direction. Therefore, if the refractive index of glass-air or any other substance bordering air is determined, then the latter is conventionally taken as a vacuum.

Every other environment has its own characteristics. They have different densities, they have their own temperature, as well as elastic stresses. All this affects the result of light refraction by the substance.

The characteristics of light play an important role in changing the direction of wave propagation. White light is made up of many colors, from red to violet. Each part of the spectrum is refracted in its own way. Moreover, the value of the indicator for the wave of the red part of the spectrum will always be less than that of the others. For example, the refractive index of TF-1 glass varies from 1.6421 to 1.67298, respectively, from the red to violet part of the spectrum.

Examples of values ​​for different substances

Here are the values ​​of absolute values, that is, the refractive index when a beam passes from a vacuum (which is equivalent to air) through another substance.

These figures will be needed if it is necessary to determine the refractive index of glass relative to other media.

What other quantities are used when solving problems?

Total reflection. It is observed when light passes from a denser medium to a less dense one. Here, at a certain angle of incidence, refraction occurs at a right angle. That is, the beam slides along the boundary of two media.

The limiting angle of total reflection is its minimum value at which light does not escape into a less dense medium. Less of it means refraction, and more means reflection into the same medium from which the light moved.

Task No. 1

Condition. The refractive index of glass has a value of 1.52. It is necessary to determine the limiting angle at which light is completely reflected from the interface of surfaces: glass with air, water with air, glass with water.

You will need to use the refractive index data for water given in the table. It is taken equal to unity for air.

The solution in all three cases comes down to calculations using the formula:

sin α 0 /sin β = n 1 /n 2, where n 2 refers to the medium from which the light propagates, and n 1 where it penetrates.

The letter α 0 denotes the limit angle. The value of angle β is 90 degrees. That is, its sine will be one.

For the first case: sin α 0 = 1 /n glass, then the limiting angle turns out to be equal to the arcsine of 1 /n glass. 1/1.52 = 0.6579. The angle is 41.14º.

In the second case, when determining the arcsine, you need to substitute the value of the refractive index of water. The fraction 1 /n of water will take the value 1/1.33 = 0.7519. This is the arcsine of the angle 48.75º.

The third case is described by the ratio of n water and n glass. The arcsine will need to be calculated for the fraction: 1.33/1.52, that is, the number 0.875. We find the value of the limiting angle by its arcsine: 61.05º.

Answer: 41.14º, 48.75º, 61.05º.

Problem No. 2

Condition. A glass prism is immersed in a vessel with water. Its refractive index is 1.5. A prism is based on a right triangle. The larger leg is located perpendicular to the bottom, and the second is parallel to it. A ray of light falls normally on the upper face of the prism. What must be the smallest angle between a horizontal leg and the hypotenuse for light to reach the leg located perpendicular to the bottom of the vessel and exit the prism?

In order for the ray to exit the prism in the manner described, it needs to fall at a maximum angle onto the inner face (the one that is the hypotenuse of the triangle in the cross section of the prism). This limiting angle turns out to be equal to the desired angle right triangle. From the law of light refraction, it turns out that the sine of the limiting angle divided by the sine of 90 degrees is equal to the ratio of two refractive indices: water to glass.

Calculations lead to the following value for the limiting angle: 62º30´.

Refractive index

Refractive index substances - a quantity equal to the ratio of the phase speeds of light (electromagnetic waves) in a vacuum and in a given medium. Also, the refractive index is sometimes spoken of for any other waves, for example, sound, although in cases such as the latter, the definition, of course, has to be modified somehow.

The refractive index depends on the properties of the substance and the wavelength of the radiation; for some substances, the refractive index changes quite strongly when the frequency of electromagnetic waves changes from low frequencies to optical and beyond, and can also change even more sharply in certain regions of the frequency scale. The default usually refers to the optical range or the range determined by the context.

Links

• RefractiveIndex.INFO refractive index database

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See what “Refractive Index” is in other dictionaries:

Relative of two media n21, dimensionless ratio of the propagation speeds of optical radiation (c veta) in the first (c1) and second (c2) media: n21 = c1/c2. At the same time it relates. P. p. is the ratio of the sines of the g l a p a d e n i j and y g l ... ... Physical encyclopedia

See Refractive Index...

See refractive index. * * * REFRACTION INDEX REFRACTIVE INDEX, see Refractive Index (see REFRACTIVE INDEX) ... Encyclopedic Dictionary- REFRACTIVE INDEX, a quantity characterizing the medium and equal to the ratio of the speed of light in a vacuum to the speed of light in the medium (absolute refractive index). The refractive index n depends on the dielectric e and magnetic permeability m... ... Illustrated Encyclopedic Dictionary

- (see REFRACTION INDEX). Physical encyclopedic dictionary. M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1983 ... Physical encyclopedia

See Refractive index... Great Soviet Encyclopedia

The ratio of the speed of light in a vacuum to the speed of light in a medium (absolute refractive index). The relative refractive index of 2 media is the ratio of the speed of light in the medium from which light falls on the interface to the speed of light in the second... ... Big Encyclopedic Dictionary

The laws of physics play a very important role when carrying out calculations to plan a specific strategy for the production of any product or when drawing up a project for the construction of structures for various purposes. Many quantities are calculated, so measurements and calculations are made before planning work begins. For example, the refractive index of glass is equal to the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

So first there is the process of measuring the angles, then their sine is calculated, and only then can the desired value be obtained. Despite the presence of tabular data, it is worth carrying out each time additional calculations, since reference books often use ideal conditions that can be achieved in real life almost impossible. Therefore, in reality, the indicator will necessarily differ from the table, and in some situations this is of fundamental importance.

Absolute indicator

The absolute refractive index depends on the brand of glass, since in practice there are a huge number of options that differ in composition and degree of transparency. On average it is 1.5 and fluctuates around this value by 0.2 in one direction or another. In rare cases, there may be deviations from this figure.

Again, if an accurate indicator is important, then additional measurements cannot be avoided. But they also do not give a 100% reliable result, since the final value will be influenced by the position of the sun in the sky and cloudiness on the day of measurement. Fortunately, in 99.99% of cases it is enough to simply know that the refractive index of a material such as glass is greater than one and less than two, and all other tenths and hundredths do not matter.

On forums that help solve physics problems, the question often comes up: what is the refractive index of glass and diamond? Many people think that since these two substances are similar in appearance, then their properties should be approximately the same. But this is a misconception.

The maximum refraction of glass will be around 1.7, while for diamond this indicator reaches 2.42. Given gem is one of the few materials on Earth whose refractive index exceeds 2. This is due to its crystalline structure and the high level of scatter of light rays. The cut plays a minimal role in changes in the table value.

Relative indicator

The relative indicator for some environments can be characterized as follows:

• - the refractive index of glass relative to water is approximately 1.18;
• - the refractive index of the same material relative to air is equal to 1.5;
• - refractive index relative to alcohol - 1.1.

Measurements of the indicator and calculations of the relative value are carried out according to a well-known algorithm. To find a relative parameter, you need to divide one table value by another. Or make experimental calculations for two environments, and then divide the data obtained. Such operations are often carried out in laboratory physics classes.

Determination of refractive index

Determining the refractive index of glass in practice is quite difficult, because high-precision instruments are required to measure the initial data. Any error will increase, since the calculation uses complex formulas that require the absence of errors.

In general, this coefficient shows how many times the speed of propagation of light rays slows down when passing through a certain obstacle. Therefore, it is typical only for transparent materials. The refractive index of gases is taken as the reference value, that is, as a unit. This was done so that it was possible to start from some value when making calculations.

If a sunbeam falls on the surface of glass with a refractive index that is equal to the table value, then it can be changed in several ways:

• 1. Glue a film on top, whose refractive index will be higher than that of glass. This principle is used in car window tinting to improve passenger comfort and allow the driver to have a clearer view of traffic conditions. The film will also inhibit ultraviolet radiation.
• 2. Paint the glass with paint. This is what manufacturers of cheap products do sunglasses, but it is worth considering that this may be harmful to vision. IN good models The glass is immediately produced colored using a special technology.
• 3. Immerse the glass in some liquid. This is only useful for experiments.

If a ray of light passes from glass, then the refractive index on the next material is calculated using a relative coefficient, which can be obtained by comparing table values. These calculations are very important when designing optical systems, which carry a practical or experimental load. Errors here are unacceptable, because they will lead to incorrect operation of the entire device, and then any data obtained with its help will be useless.

To determine the speed of light in glass with a refractive index, you need to divide the absolute value of the speed in a vacuum by the refractive index. Vacuum is used as a reference medium because there is no refraction due to the absence of any substances that could interfere with the smooth movement of light rays along a given path.

In any calculated indicators, the speed will be less than in the reference medium, since the refractive index is always greater than unity.

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

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

Longest length waves and the lowest refractive index has red light, so red rays are deflected by the prism less than others. 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 them 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. The dependence of the refractive index of a substance on the electromagnetic wavelength (frequency) is explained on the basis of the theory of forced oscillations. Strictly speaking, the movement of electrons in an atom (molecule) obeys the laws of quantum mechanics. However, for a qualitative understanding of 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 - amplitude of the electric field strength in a light wave, - 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 the effective contribution of each type of oscillation to 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. Dependence of the dielectric constant of the mediumon 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 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, 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 real electromagnetic pulses, for example, known to us wave trains emitted by individual atomic emitters, propagate in a medium with dispersion, 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.