Lesson 25/III-1 Propagation of light in various media. Refraction of light at the interface between two media.

Learning new material.

Until now, we have considered the propagation of light in one medium, as usual - in air. Light can propagate in various media: move from one medium to another; at the points of incidence, the rays are not only reflected from the surface, but also partially pass through it. Such transitions cause many beautiful and interesting phenomena.

The change in the direction of propagation of light passing through the boundary of two media is called the refraction of light.

Part of the light beam incident on the interface between two transparent media is reflected, and part goes into another medium. In this case, the direction of the light beam, which has passed into another medium, changes. Therefore, the phenomenon is called refraction, and the beam is called refracted.

1 - incident beam

2 - reflected beam

3 – refracted beam α β

OO 1 - the boundary between two media

MN - perpendicular O O 1

The angle formed by the beam and the perpendicular to the interface between two media, lowered to the point of incidence of the beam, is called the angle of refraction γ (gamma).

Light in a vacuum travels at a speed of 300,000 km/s. In any medium, the speed of light is always less than in vacuum. Therefore, when light passes from one medium to another, its speed decreases and this is the reason for the refraction of light. The lower the speed of light propagation in a given medium, the greater the optical density of this medium. For example, air has a higher optical density than vacuum, because the speed of light in air is somewhat less than in vacuum. The optical density of water is greater than the optical density of air, since the speed of light in air is greater than in water.

The more the optical densities of two media differ, the more light is refracted at their interface. The more the speed of light changes at the interface between two media, the more it is refracted.

For each transparent substance, there is such an important physical characteristic as the refractive index of light n. It shows how many times the speed of light in a given substance is less than in vacuum.

Refractive index

Substance		Substance		Substance
		rock salt		Turpentine
		Cedar oil		Ethanol
Glycerol		Plexiglass		Glass (light)
		carbon disulfide

The ratio between the angle of incidence and the angle of refraction depends on the optical density of each medium. If a beam of light passes from a medium with a lower optical density to a medium with a higher optical density, then the angle of refraction will be smaller than the angle of incidence. If a beam of light passes from a medium with a higher optical density, then the angle of refraction will be smaller than the angle of incidence. If a beam of light passes from a medium with a higher optical density to a medium with a lower optical density, then the angle of refraction is greater than the angle of incidence.

That is, if n 1 γ; if n 1 >n 2 , then α<γ.

Law of refraction of light :

The incident beam, the refracted beam and the perpendicular to the interface between two media at the point of incidence of the beam lie in the same plane.

The ratios of the angle of incidence and the angle of refraction are determined by the formula.

where is the sine of the angle of incidence, is the sine of the angle of refraction.

The value of sines and tangents for angles 0 - 900

degrees			degrees			degrees

The law of refraction of light was first formulated by the Dutch astronomer and mathematician W. Snelius around 1626, a professor at the University of Leiden (1613).

For the 16th century, optics was an ultra-modern science. From a glass ball filled with water, which was used as a lens, a magnifying glass arose. And from it they invented a spyglass and a microscope. At that time, the Netherlands needed telescopes to view the coast and escape from enemies in a timely manner. It was optics that ensured the success and reliability of navigation. Therefore, in the Netherlands, a lot of scientists were interested in optics. The Dutchman Skel Van Royen (Snelius) observed how a thin beam of light was reflected in a mirror. He measured the angle of incidence and the angle of reflection and found that the angle of reflection is equal to the angle of incidence. He also owns the laws of reflection of light. He deduced the law of refraction of light.

Consider the law of refraction of light.

In it - the relative refractive index of the second medium relative to the first, in the case when the second has a high optical density. If light is refracted and passes through a medium with a lower optical density, then α< γ, тогда

If the first medium is vacuum, then n 1 =1 then .

This index is called the absolute refractive index of the second medium:

where is the speed of light in vacuum, the speed of light in a given medium.

A consequence of the refraction of light in the Earth's atmosphere is the fact that we see the Sun and stars slightly above their actual position. The refraction of light can explain the occurrence of mirages, rainbows ... the phenomenon of refraction of light is the basis of the principle of operation of numerical optical devices: a microscope, a telescope, a camera.

In the 8th grade physics course, you got acquainted with the phenomenon of light refraction. Now you know that light is electromagnetic waves of a certain frequency range. Based on knowledge about the nature of light, you will be able to understand the physical cause of refraction and explain many other light phenomena associated with it.

Rice. 141. Passing from one medium to another, the beam is refracted, i.e., changes the direction of propagation

According to the law of light refraction (Fig. 141):

• rays incident, refracted and 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 these two media

where n 21 is the relative refractive index of the second medium relative to the first.

If the beam passes into any medium from a vacuum, then

where n is the absolute refractive index (or simply refractive index) of the second medium. In this case, the first "environment" is vacuum, the absolute index of which is taken as one.

The law of light refraction was discovered empirically by the Dutch scientist Willebord Snellius in 1621. The law was formulated in a treatise on optics, which was found in the scientist's papers after his death.

After the discovery of Snell, several scientists put forward a hypothesis that the refraction of light is due to a change in its speed when it passes through the boundary of two media. The validity of this hypothesis was confirmed by theoretical proofs carried out independently by the French mathematician Pierre Fermat (in 1662) and the Dutch physicist Christian Huygens (in 1690). By different paths they arrived at the same result, proving that

• the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media, equal to the ratio of the speeds of light in these media:

From equation (3) it follows that if the angle of refraction β is less than the angle of incidence a, then the light of a given frequency in the second medium propagates more slowly than in the first, i.e. V 2

The relationship of the quantities included in equation (3) served as a good reason for the appearance of another formulation of the definition of the relative refractive index:

• the relative refractive index of the second medium relative to the first is a physical quantity equal to the ratio of the speeds of light in these media:

n 21 \u003d v 1 / v 2 (4)

Let a beam of light pass from vacuum to some medium. Replacing v1 in equation (4) with the speed of light in vacuum c, and v 2 with the speed of light in a medium v, we obtain equation (5), which is the definition of the absolute refractive index:

• the absolute refractive index of a medium is a physical quantity equal to the ratio of the speed of light in vacuum to the speed of light in a given medium:

According to equations (4) and (5), n 21 shows how many times the speed of light changes when it passes from one medium to another, and n - when it passes from vacuum to a medium. This is the physical meaning of the refractive indices.

The value of the absolute refractive index n of any substance is greater than unity (this is confirmed by the data contained in the tables of physical reference books). Then, according to equation (5), c/v > 1 and c > v, i.e., the speed of light in any substance is less than the speed of light in vacuum.

Without giving rigorous justifications (they are complex and cumbersome), we note that the reason for the decrease in the speed of light during its transition from vacuum to matter is the interaction of a light wave with atoms and molecules of matter. The greater the optical density of the substance, the stronger this interaction, the lower the speed of light and the greater the refractive index. Thus, the speed of light in a medium and the absolute refractive index are determined by the properties of this medium.

According to the numerical values ​​of the refractive indices of substances, one can compare their optical densities. For example, the refractive indices of various types of glass range from 1.470 to 2.040, while the refractive index of water is 1.333. This means that glass is an optically denser medium than water.

Let us turn to Figure 142, with the help of which we can explain why, at the boundary of two media, with a change in speed, the direction of propagation of a light wave also changes.

Rice. 142. When light waves pass from air to water, the speed of light decreases, the front of the wave, and with it its speed, change direction

The figure shows a light wave passing from air into water and incident on the interface between these media at an angle a. In air, light propagates at a speed v 1 , and in water at a slower speed v 2 .

Point A of the wave reaches the boundary first. Over a period of time Δt, point B, moving in the air at the same speed v 1, will reach point B. "During the same time, point A, moving in water at a lower speed v 2, will cover a shorter distance, reaching only point A". In this case, the so-called wave front A "B" in the water will be rotated at a certain angle with respect to the front of the AB wave in the air. And the velocity vector (which is always perpendicular to the wave front and coincides with the direction of its propagation) rotates, approaching the straight line OO", perpendicular to the interface between the media. In this case, the angle of refraction β turns out to be less than the angle of incidence α. This is how the refraction of light occurs.

It can also be seen from the figure that when passing to another medium and turning the wave front, the wavelength also changes: when passing to an optically denser medium, the speed decreases, the wavelength also decreases (λ 2< λ 1). Это согласуется и с известной вам формулой λ = V/v, из которой следует, что при неизменной частоте v (которая не зависит от плотности среды и поэтому не меняется при переходе луча из одной среды в другую) уменьшение скорости распространения волны сопровождается пропорциональным уменьшением длины волны.

Questions

1. Which of the two substances is optically denser?
2. How are refractive indices determined in terms of the speed of light in media?
3. Where does light travel the fastest?
4. What is the physical reason for the decrease in the speed of light when it passes from vacuum to a medium or from a medium with a lower optical density to a medium with a higher one?
5. What determines (i.e., what do they depend on) the absolute refractive index of the medium and the speed of light in it?
6. Explain what Figure 142 illustrates.

An exercise

Optics is one of the oldest branches of physics. Since ancient Greece, many philosophers have been interested in the laws of motion and propagation of light in various transparent materials such as water, glass, diamond and air. In this article, the phenomenon of light refraction is considered, attention is focused on the refractive index of air.

Light beam refraction effect

Everyone in his life has encountered hundreds of times this effect when he looked at the bottom of a reservoir or at a glass of water with some object placed in it. At the same time, the reservoir did not seem as deep as it actually was, and objects in a glass of water looked deformed or broken.

The phenomenon of refraction consists in a break in its rectilinear trajectory when it crosses the interface between two transparent materials. Summarizing a large number of experimental data, at the beginning of the 17th century, the Dutchman Willebrord Snell obtained a mathematical expression that accurately described this phenomenon. This expression is written in the following form:

n 1 *sin(θ 1) = n 2 *sin(θ 2) = const.

Here n 1 , n 2 are the absolute refractive indices of light in the corresponding material, θ 1 and θ 2 are the angles between the incident and refracted beams and the perpendicular to the interface plane, which is drawn through the intersection point of the beam and this plane.

This formula is called the law of Snell or Snell-Descartes (it was the Frenchman who wrote it down in the form presented, the Dutchman used not sines, but units of length).

In addition to this formula, the phenomenon of refraction is described by another law, which is geometric in nature. It lies in the fact that the marked perpendicular to the plane and two rays (refracted and incident) lie in the same plane.

Absolute refractive index

This value is included in the Snell formula, and its value plays an important role. Mathematically, the refractive index n corresponds to the formula:

The symbol c is the speed of electromagnetic waves in vacuum. It is approximately 3*10 8 m/s. The value v is the speed of light in the medium. Thus, the refractive index reflects the amount of slowing down of light in a medium with respect to airless space.

Two important conclusions follow from the formula above:

• the value of n is always greater than 1 (for vacuum it is equal to one);
• it is a dimensionless quantity.

For example, the refractive index of air is 1.00029, while for water it is 1.33.

The refractive index is not a constant value for a particular medium. It depends on the temperature. Moreover, for each frequency of an electromagnetic wave, it has its own meaning. So, the above figures correspond to a temperature of 20 o C and the yellow part of the visible spectrum (wavelength - about 580-590 nm).

The dependence of the value of n on the frequency of light is manifested in the decomposition of white light by a prism into a number of colors, as well as in the formation of a rainbow in the sky during heavy rain.

Refractive index of light in air

Its value (1.00029) has already been given above. Since the refractive index of air differs only in the fourth decimal place from zero, then for solving practical problems it can be considered equal to one. A slight difference of n for air from unity indicates that light is practically not slowed down by air molecules, which is due to its relatively low density. Thus, the average density of air is 1.225 kg/m 3 , that is, it is more than 800 times lighter than fresh water.

Air is an optically thin medium. The very process of slowing down the speed of light in a material is of a quantum nature and is associated with the acts of absorption and emission of photons by the atoms of matter.

Changes in the composition of the air (for example, an increase in the content of water vapor in it) and changes in temperature lead to significant changes in the refractive index. A striking example is the mirage effect in the desert, which occurs due to the difference in the refractive indices of air layers with different temperatures.

glass-air interface

Glass is a much denser medium than air. Its absolute refractive index ranges from 1.5 to 1.66, depending on the type of glass. If we take the average value of 1.55, then the refraction of the beam at the air-glass interface can be calculated using the formula:

sin (θ 1) / sin (θ 2) \u003d n 2 / n 1 \u003d n 21 \u003d 1.55.

The value of n 21 is called the relative refractive index of air - glass. If the beam exits the glass into the air, then the following formula should be used:

sin (θ 1) / sin (θ 2) \u003d n 2 / n 1 \u003d n 21 \u003d 1 / 1.55 \u003d 0.645.

If the angle of the refracted beam in the latter case is equal to 90 o , then the corresponding one is called critical. For the glass-air boundary, it is equal to:

θ 1 \u003d arcsin (0.645) \u003d 40.17 o.

If the beam falls on the glass-air boundary with greater angles than 40.17 o , then it will be reflected completely back into the glass. This phenomenon is called "total internal reflection".

The critical angle exists only when the beam moves from a dense medium (from glass to air, but not vice versa).

Fields of application of refractometry.

The device and principle of operation of the IRF-22 refractometer.

The concept of the refractive index.

Plan

Refractometry. Characteristics and essence of the method.

To identify substances and check their purity, use

refractor.

Refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and the seen medium.

The refractive index depends on the properties of the substance and the wavelength

electromagnetic radiation. The ratio of the sine of the angle of incidence relative to

the normal drawn to the plane of refraction (α) of the beam to the sine of the angle of refraction

refraction (β) during the transition of the beam from medium A to medium B is called the relative refractive index for this pair of media.

The value n is the relative refractive index of the medium B according to

in relation to environment A, and

The relative refractive index of the medium A with respect to

The refractive index of a beam incident on a medium from an airless

th space is called its absolute refractive index or

simply the refractive index of a given medium (Table 1).

Table 1 - Refractive indices of various media

Liquids have a refractive index in the range of 1.2-1.9. Solid

substances 1.3-4.0. Some minerals do not have an exact value of the indicator

for refraction. Its value is in a certain "fork" and determines

due to the presence of impurities in the crystal structure, which determines the color

crystal.

Identification of the mineral by "color" is difficult. So, the mineral corundum exists in the form of ruby, sapphire, leucosapphire, differing in

refractive index and color. Red corundums are called rubies

(chromium admixture), colorless blue, light blue, pink, yellow, green,

violet - sapphires (impurities of cobalt, titanium, etc.). Light-colored

nye sapphires or colorless corundum is called leucosapphire (widely

used in optics as a light filter). The refractive index of these crystals

stall lies in the range of 1.757-1.778 and is the basis for identifying

Figure 3.1 - Ruby Figure 3.2 - Sapphire blue

Organic and inorganic liquids also have characteristic refractive index values ​​that characterize them as chemical

nye compounds and the quality of their synthesis (table 2):

Table 2 - Refractive indices of some liquids at 20 °C

4.2. Refractometry: concept, principle.

Method for the study of substances based on the determination of the indicator

(coefficient) of refraction (refraction) is called refractometry (from

lat. refractus - refracted and Greek. metreo - I measure). Refractometry

(refractometric method) is used to identify chemical

compounds, quantitative and structural analysis, determination of physico-

chemical parameters of substances. Refractometry principle implemented

in Abbe refractometers, illustrated by Figure 1.

Figure 1 - The principle of refractometry

The Abbe prism block consists of two rectangular prisms: illuminating

body and measuring, folded by hypotenuse faces. Illuminator-

prism has a rough (matte) hypotenuse face and is intended

chena for illuminating a liquid sample placed between the prisms.

Scattered light passes through a plane-parallel layer of the investigated liquid and, being refracted in the liquid, falls on the measuring prism. The measuring prism is made of optically dense glass (heavy flint) and has a refractive index greater than 1.7. For this reason, the Abbe refractometer measures n values ​​less than 1.7. An increase in the measuring range of the refractive index can only be achieved by changing the measuring prism.

The test sample is poured onto the hypotenuse face of the measuring prism and pressed against the illuminating prism. In this case, a gap of 0.1-0.2 mm remains between the prisms in which the sample is located, and through

which passes by refracting light. To measure the refractive index

use the phenomenon of total internal reflection. It consists in

next.

If rays 1, 2, 3 fall on the interface between two media, then depending on

the angle of incidence when observing them in a refractive medium will be

the presence of a transition of areas of different illumination is observed. It's connected

with the incidence of some part of the light on the boundary of refraction at an angle of approx.

kim to 90° with respect to the normal (beam 3). (Figure 2).

Figure 2 - Image of refracted rays

This part of the rays is not reflected and therefore forms a lighter object.

refraction. Rays with smaller angles experience and reflect

and refraction. Therefore, an area of ​​less illumination is formed. In volume

the boundary line of total internal reflection is visible on the lens, the position

which depends on the refractive properties of the sample.

The elimination of the phenomenon of dispersion (colouring the interface between two areas of illumination in the colors of the rainbow due to the use of complex white light in Abbe refractometers) is achieved by using two Amici prisms in the compensator, which are mounted in the telescope. At the same time, a scale is projected into the lens (Figure 3). 0.05 ml of liquid is sufficient for analysis.

Figure 3 - View through the eyepiece of the refractometer. (The right scale reflects

concentration of the measured component in ppm)

In addition to the analysis of single-component samples, there are widely analyzed

two-component systems (aqueous solutions, solutions of substances in which

or solvent). In ideal two-component systems (forming-

without changing the volume and polarizability of the components), the dependence is shown

refractive index on the composition is close to linear if the composition is expressed in terms of

volume fractions (percentage)

where: n, n1, n2 - refractive indices of the mixture and components,

V1 and V2 are the volume fractions of the components (V1 + V2 = 1).

The effect of temperature on the refractive index is determined by two

factors: a change in the number of liquid particles per unit volume and

dependence of the polarizability of molecules on temperature. The second factor became

becomes significant only at very large temperature changes.

The temperature coefficient of the refractive index is proportional to the temperature coefficient of the density. Since all liquids expand when heated, their refractive indices decrease as the temperature rises. The temperature coefficient depends on the temperature of the liquid, but in small temperature intervals it can be considered constant. For this reason, most refractometers do not have temperature control, however, some designs provide

water temperature control.

Linear extrapolation of the refractive index with temperature changes is acceptable for small temperature differences (10 - 20°C).

The exact determination of the refractive index in wide temperature ranges is carried out according to empirical formulas of the form:

nt=n0+at+bt2+…

For solution refractometry over wide concentration ranges

use tables or empirical formulas. Display dependency-

refractive index of aqueous solutions of certain substances on concentration

is close to linear and makes it possible to determine the concentrations of these substances in

water in a wide range of concentrations (Figure 4) using refraction

tometers.

Figure 4 - Refractive index of some aqueous solutions

Usually, n liquid and solid bodies are determined by refractometers with precision

up to 0.0001. The most common are Abbe refractometers (Figure 5) with prism blocks and dispersion compensators, which make it possible to determine nD in "white" light on a scale or digital indicator.

Figure 5 - Abbe refractometer (IRF-454; IRF-22)

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 length 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 additives, cosmetic 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 intersection point 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.