The law of refraction of light. Absolute and relative indices (coefficients) of refraction. Total internal reflection

Law of refraction of light was established empirically in the 17th century. When light passes from one transparent medium to another, the direction of light can change. Changing the direction of light at the boundary of different media is called light refraction. The omniscience of refraction is an apparent change in the shape of an object. (example: a spoon in a glass of water). The law of refraction of light: At the boundary of two media, the refracted beam lies in the plane of incidence and forms, with the normal to the interface restored at the point of incidence, an angle of refraction such that: = n 1-fall, 2 reflections, n-refractive index (f. Snelius) - relative indicator The refractive index of a beam incident on a medium from airless space is called its absolute index of refraction. The angle of incidence at which the refracted beam begins to slide along the interface between two media without transition to an optically denser medium - limiting angle of total internal reflection. Total internal reflection- internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its highest values ​​for polished surfaces. The reflection coefficient for total internal reflection does not depend on the wavelength. In optics, this phenomenon is observed for a wide spectrum of electromagnetic radiation, including the X-ray range. In geometric optics, the phenomenon is explained in terms of Snell's law. Considering that the angle of refraction cannot exceed 90°, we obtain that at an angle of incidence whose sine is greater than the ratio of the smaller refractive index to the larger one, the electromagnetic wave should be completely reflected into the first medium. Example: The bright brilliance of many natural crystals, and especially faceted precious and semiprecious stones, is explained by total internal reflection, as a result of which each ray that enters the crystal forms a large number of sufficiently bright rays that come out, colored as a result of dispersion.

REFRACTIVE INDICATOR(refractive index) - optical. environmental characteristic associated with refraction of light at the interface between two transparent optically homogeneous and isotropic media during its transition from one medium to another and due to the difference in the phase velocities of light propagation in the media. The value of P. p., equal to the ratio of these speeds. relative

P. p. of these environments. If light falls on the second or first medium from (where the speed of light propagation with), then the quantities are absolute P. p. of these environments. In this case, the law of refraction can be written in the form where and are the angles of incidence and refraction.

The magnitude of the absolute P. p. depends on the nature and structure of the substance, its state of aggregation, temperature, pressure, etc. At high intensities, the p. p. depends on the intensity of light (see. non-linear optics). In a number of substances, P. p. changes under the influence of external. electric fields ( Kerr effect- in liquids and gases; electro-optical Pockels effect- in crystals).

For a given medium, the absorption band depends on the wavelength l of light, and in the region of absorption bands this dependence is anomalous (see Fig. Light dispersion). For almost all media, the absorption band is close to 1; in the visible region for liquids and solids, it is about 1.5; in the IR region for a number of transparent media 4.0 (for Ge).

They are characterized by two parametric phenomena: ordinary (similar to isotropic media) and extraordinary, the magnitude of which depends on the angle of incidence of the beam and, consequently, the direction of propagation of light in the medium (see Fig. Crystal optics). For media with absorption (in particular, for metals), the absorption coefficient is a complex quantity and can be represented as where n is the usual absorption coefficient, is the absorption index (see. Light absorption, metal optics).

P. p. is macroscopic. characteristic of the environment and is associated with its permittivity n magn. permeability Classic electronic theory (cf. Light dispersion) allows you to associate the value of P. p. with microscopic. characteristics of the environment - electronic polarizability atom (or molecule) depending on the nature of the atoms and the frequency of light, and the medium: where N is the number of atoms per unit volume. Acting on an atom (molecule) electric. field of the light wave causes a shift of the optical. an electron from an equilibrium position; the atom becomes induced. dipole moment changing in time with the frequency of the incident light, and is a source of secondary coherent waves, to-rye. interfering with the wave incident on the medium, they form the resulting light wave propagating in the medium with phase velocity, and therefore

The intensity of conventional (non-laser) light sources is relatively low; the field of a light wave acting on an atom is much smaller than intra-atomic electric. fields, and an electron in an atom can be considered as harmonic. oscillator. In this approximation, the value of and P. p.

They are constant values ​​(at a given frequency), independent of light intensity. In intense light fluxes created by powerful lasers, the magnitude of the electric. the field of a light wave can be commensurate with the intra-atomic electric-rich. fields and the harmony model, the oscillator turns out to be unacceptable. Accounting for the anharmonicity of forces in the electron-atom system leads to the dependence of the polarizability of the atom, and hence the polarization coefficient, on the light intensity. The connection between and turns out to be non-linear; P. p. can be represented in the form

Where - P. p. at low light intensities; (usually accepted designation) - a non-linear addition to the P. p., or coefficient. non-linearity. P. p. depends on the nature of the environment, for example. for silicate glass

P. p. is also affected by high intensity as a result of the effect electrostriction, changing the density of the medium, high-frequency for anisotropic molecules (in a liquid), as well as as a result of an increase in temperature caused by absorption

The laws of physics play a very important role in carrying out calculations for planning a specific strategy for the production of any product or in drawing up a project for the construction of structures for various purposes. Many values ​​are calculated, so measurements and calculations are made before starting the planning work. 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 a process of measuring angles, then their sine is calculated, and only then you can get the desired value. Despite the availability of tabular data, it is worthwhile to carry out additional calculations every time, since reference books often use ideal conditions that are almost impossible to achieve in real life. Therefore, in reality, the indicator will necessarily differ from the tabular one, 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 exact indicator is important, then additional measurements are indispensable. But even they do not give a 100% reliable result, since the position of the sun in the sky and cloudiness on the day of measurements will affect the final value. 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 play a role.

On forums that help solve problems in physics, the question often flashes, 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 delusion.

The maximum refraction for glass will be around 1.7, while for diamond this figure reaches 2.42. This gem is one of the few materials on Earth whose refractive index exceeds 2. This is due to its crystalline structure and the large spread of light rays. Faceting 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.

Measurement of the indicator and calculation 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 classes in physics.

Determination of the refractive index

It is quite difficult to determine the refractive index of glass in practice, 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. For the reference value, that is, for the unit, the refractive index of gases is taken. This was done in order to be able to start from some value in the calculations.

If a sunbeam falls on a glass surface 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, in which the 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 see the road more clearly. Also, the film will hold back and ultraviolet radiation.
• 2. Paint the glass with paint. This is what manufacturers of cheap sunglasses do, but be aware that it can be harmful to your eyesight. In good models, glasses are immediately produced colored using a special technology.
• 3. Immerse the glass in some liquid. This is only useful for experiments.

If the light beam passes from glass, then the refractive index on the next material is calculated using the relative coefficient, which can be obtained by comparing the tabular values ​​​​to each other. These calculations are very important in the design of optical systems that carry a practical or experimental load. Errors are not allowed here, because they will cause the entire device to malfunction, and then any data received with it 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 vacuum by the refractive index. Vacuum is used as a reference medium, because refraction does not act there due to the absence of any substances that could interfere with the unhindered movement of light rays along a given trajectory.

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

Light refraction- a phenomenon in which a beam of light, passing from one medium to another, changes direction at the boundary of these media.

The refraction of light occurs according to the following law:
The incident and refracted rays and the perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media:
,
where α - angle of incidence,
β - angle of refraction
n - a constant value independent of the angle of incidence.

When the angle of incidence changes, the angle of refraction also changes. The larger the angle of incidence, the larger the angle of refraction.
If light goes from an optically less dense medium to a denser medium, then the angle of refraction is always less than the angle of incidence: β < α.
A beam of light directed perpendicular to the interface between two media passes from one medium to another without breaking.

absolute refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and in a given medium n=c/v
The value n included in the law of refraction is called the relative refractive index for a pair of media.

The value n is the relative refractive index of medium B with respect to medium A, and n" = 1/n is the relative refractive index of medium A with respect to medium B.
This value, ceteris paribus, is greater than unity when the beam passes from a denser medium to a less dense medium, and less than unity when the beam passes from a less dense medium to a denser medium (for example, from a gas or from vacuum to a liquid or solid). There are exceptions to this rule, and therefore it is customary to call a medium optically more or less dense than another.
A beam falling from airless space onto the surface of some medium B is refracted more strongly than when falling on it from another medium A; The refractive index of a ray incident on a medium from airless space is called its absolute refractive index.

(Absolute - relative to vacuum.
Relative - relative to any other substance (the same air, for example).
The relative index of two substances is the ratio of their absolute indices.)

Total internal reflection- internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its highest values ​​for polished surfaces. The reflection coefficient for total internal reflection does not depend on the wavelength.

In optics, this phenomenon is observed for a wide spectrum of electromagnetic radiation, including the X-ray range.

In geometric optics, the phenomenon is explained in terms of Snell's law. Considering that the angle of refraction cannot exceed 90°, we obtain that at an angle of incidence whose sine is greater than the ratio of the lower refractive index to the larger index, the electromagnetic wave should be completely reflected into the first medium.

In accordance with the wave theory of the phenomenon, the electromagnetic wave nevertheless penetrates into the second medium - the so-called "non-uniform wave" propagates there, which decays exponentially and does not carry away energy with it. The characteristic depth of penetration of an inhomogeneous wave into the second medium is of the order of the wavelength.

Laws of refraction of light.

From all that has been said, we conclude:
1 . At the interface between two media of different optical density, a beam of light changes its direction when passing from one medium to another.
2. When a light beam passes into a medium with a higher optical density, the angle of refraction is less than the angle of incidence; when a light beam passes from an optically denser medium to a less dense medium, the angle of refraction is greater than the angle of incidence.
The refraction of light is accompanied by reflection, and with an increase in the angle of incidence, the brightness of the reflected beam increases, while the refracted one weakens. This can be seen by conducting the experiment shown in the figure. Consequently, the reflected beam carries away with it the more light energy, the greater the angle of incidence.

Let be MN- the interface between two transparent media, for example, air and water, JSC- falling beam OV- refracted beam, - angle of incidence, - angle of refraction, - speed of light propagation in the first medium, - speed of light propagation in the second medium.

Refraction or refraction is a phenomenon in which a change in the direction of a beam of light, or other waves, occurs when they cross the boundary separating two media, both transparent (transmitting these waves) and inside a medium in which properties are continuously changing.

We encounter the phenomenon of refraction quite often and perceive it as an ordinary phenomenon: we can see that a stick in a transparent glass with a colored liquid is “broken” at the point where air and water separate (Fig. 1). When light is refracted and reflected during rain, we rejoice when we see a rainbow (Fig. 2).

The refractive index is an important characteristic of a substance related to its physicochemical properties. It depends on the temperature values, as well as on the wavelength of the light waves at which the determination is carried out. According to quality control data in a solution, the refractive index is affected by the concentration of the substance dissolved in it, as well as the nature of the solvent. In particular, the refractive index of blood serum is affected by the amount of protein contained in it. This is due to the fact that at different speeds of propagation of light rays in media with different densities, their direction changes at the interface between two media. If we divide the speed of light in vacuum by the speed of light in the substance under study, we get the absolute refractive index (refraction index). In practice, the relative refractive index (n) is determined, which is the ratio of the light speed in air to the light speed in the substance under study.

The refractive index is quantified using a special device - a refractometer.

Refractometry is one of the easiest methods of physical analysis and can be used in quality control laboratories in the production of chemical, food, biologically active food supplements, cosmetics and other types of products with minimal time and the number of samples to be tested.

The design of the refractometer is based on the fact that light rays are completely reflected when they pass through the boundary of two media (one of them is a glass prism, the other is the test solution) (Fig. 3).

Rice. 3. Scheme of the refractometer

From the source (1), the light beam falls on the mirror surface (2), then, being reflected, it passes into the upper illuminating prism (3), then into the lower measuring prism (4), which is made of glass with a high refractive index. Between the prisms (3) and (4) 1–2 drops of the sample are applied using a capillary. In order not to cause mechanical damage to the prism, it is necessary not to touch its surface with a capillary.

The eyepiece (9) sees a field with crossed lines to set the interface. By moving the eyepiece, the point of intersection of the fields must be aligned with the interface (Fig. 4). The plane of the prism (4) plays the role of the interface, on the surface of which the light beam is refracted. Since the rays are scattered, the border of light and shadow turns out to be blurry, iridescent. This phenomenon is eliminated by the dispersion compensator (5). Then the beam is passed through the lens (6) and prism (7). On the plate (8) there are reticle strokes (two straight lines crossed crosswise), as well as a scale with refractive indices, which is observed in the eyepiece (9). It is used to calculate the refractive index.

The dividing line of the field boundaries will correspond to the angle of internal total reflection, which depends on the refractive index of the sample.

Refractometry is used to determine the purity and authenticity of a substance. This method is also used to determine the concentration of substances in solutions during quality control, which is calculated from a calibration graph (a graph showing the dependence of the refractive index of a sample on its concentration).

In KorolevPharm, the refractive index is determined in accordance with the approved regulatory documentation during the incoming control of raw materials, in extracts of our own production, as well as in the production of finished products. The determination is made by qualified employees of an accredited physical and chemical laboratory using an IRF-454 B2M refractometer.

If, based on the results of the input control of raw materials, the refractive index does not meet the necessary requirements, the quality control department draws up an Act of Non-Conformity, on the basis of which this batch of raw materials is returned to the supplier.

Method of determination

1. Before starting measurements, the cleanliness of the surfaces of the prisms in contact with each other is checked.

2. Zero point check. We apply 2÷3 drops of distilled water on the surface of the measuring prism, carefully close it with an illuminating prism. Open the lighting window and, using a mirror, set the light source in the most intense direction. By turning the screws of the eyepiece, we obtain a clear, sharp distinction between dark and light fields in its field of view. We rotate the screw and direct the line of shadow and light so that it coincides with the point at which the lines intersect in the upper window of the eyepiece. On the vertical line in the lower window of the eyepiece we see the desired result - the refractive index of water distilled at 20 ° C (1.333). If the readings are different, set the refractive index to 1.333 with a screw, and with the help of a key (remove the adjusting screw) we bring the border of the shadow and light to the point of intersection of the lines.

3. Determine the refractive index. Raise the chamber of the prism lighting and remove the water with filter paper or a gauze napkin. Next, apply 1-2 drops of the test solution to the surface of the measuring prism and close the chamber. We rotate the screws until the borders of the shadow and light coincide with the point of intersection of the lines. On the vertical line in the lower window of the eyepiece, we see the desired result - the refractive index of the test sample. We calculate the refractive index on the scale in the lower window of the eyepiece.

4. Using the calibration graph, we establish the relationship between the concentration of the solution and the refractive index. To build a graph, it is necessary to prepare standard solutions of several concentrations using preparations of chemically pure substances, measure their refractive indices and plot the obtained values ​​on the ordinate axis, and plot the corresponding concentrations of solutions on the abscissa axis. It is necessary to choose the concentration intervals at which a linear relationship is observed between the concentration and the refractive index. We measure the refractive index of the test sample and use the graph to determine its concentration.