The refractive index of a substance. The law of refraction of light. Absolute and relative refractive indices. total internal reflection. What does the refractive index of a substance depend on?

Refraction is called a certain abstract number that characterizes the refractive power of any transparent medium. It is customary to designate it n. There are absolute refractive index and relative coefficient.

The first is calculated using one of two formulas:

n = sin α / sin β = const (where sin α is the sine of the angle of incidence, and sin β is the sine of the light beam entering the medium under consideration from the void)

n = c / υ λ (where c is the speed of light in a vacuum, υ λ is the speed of light in the medium under study).

Here, the calculation shows how many times light changes its speed of propagation at the moment of transition from vacuum to a transparent medium. In this way, the refractive index (absolute) is determined. In order to find out the relative, use the formula:

That is, the absolute refractive indices of substances of different densities, such as air and glass, are considered.

Generally speaking, the absolute coefficients of any bodies, whether gaseous, liquid or solid, are always greater than 1. Basically, their values ​​range from 1 to 2. Above 2, this value can only be in exceptional cases. The value of this parameter for some environments:

This value, when applied to the hardest natural substance on the planet, diamond, is 2.42. Very often, when conducting scientific research, etc., it is required to know the refractive index of water. This parameter is 1.334.

Since the wavelength is an indicator, of course, not constant, an index is assigned to the letter n. Its value helps to understand which wave of the spectrum this coefficient refers to. When considering the same substance, but with increasing wavelength of light, the refractive index will decrease. This circumstance caused the decomposition of light into a spectrum when passing through a lens, prism, etc.

By the value of the refractive index, you can determine, for example, how much of one substance is dissolved in another. This is useful, for example, in brewing or when you need to know the concentration of sugar, fruit or berries in the juice. This indicator is also important in determining the quality of petroleum products, and in jewelry, when it is necessary to prove the authenticity of a stone, etc.

Without the use of any substance, the scale visible in the eyepiece of the instrument will be completely blue. If you drop ordinary distilled water on a prism, with the correct calibration of the instrument, the border of blue and white colors will pass strictly along the zero mark. When examining another substance, it will shift along the scale according to what refractive index it has.

If a light wave falls on a flat boundary separating two dielectrics having different relative permittivities, then this wave is reflected from the interface and refracted, passing from one dielectric to another. The refractive power of a transparent medium is characterized by the refractive index, which is more often called the refractive index.

Absolute refractive index

DEFINITION

Absolute refractive index call a physical quantity equal to the ratio of the speed of propagation of light in a vacuum () to the phase speed of light in a medium (). This refractive index is denoted by the letter . Mathematically, this definition of the refractive index can be written as:

For any substance (the exception is vacuum), the value of the refractive index depends on the frequency of light and the parameters of the substance (temperature, density, etc.). For rarefied gases, the refractive index is taken equal to.

If the substance is anisotropic, then n depends on the direction in which the light propagates and how the light wave is polarized.

Based on definition (1), the absolute refractive index can be found as:

where is the dielectric constant of the medium, is the magnetic permeability of the medium.

The refractive index can be a complex quantity in absorbing media. In the range of optical waves at =1, the permittivity is written as:

then the refractive index:

where is the real part of the refractive index, equal to:

reflects refraction, imaginary part:

responsible for absorption.

Relative refractive index

DEFINITION

Relative refractive index() of the second medium relative to the first is the ratio of the phase velocities of light in the first substance to the phase velocity in the second substance:

where is the absolute refractive index of the second medium, is the absolute refractive index of the first substance. If title="(!LANG:Rendered by QuickLaTeX.com" height="16" width="60" style="vertical-align: -4px;">, то вторая среда считается оптически более плотной, чем первая.!}

For monochromatic waves, the lengths of which are much longer than the distance between molecules in a substance, Snell's law is fulfilled:

where is the angle of incidence, is the angle of refraction, is the relative refractive index of the substance in which the refracted light propagates relative to the medium in which the incident light wave propagated.

Units

The refractive index is a dimensionless quantity.

Examples of problem solving

EXAMPLE 1

Exercise	What will be the limiting angle of total internal reflection () if a beam of light passes from glass into air. The refractive index of glass is considered equal to n=1.52.
Solution	With total internal reflection, the angle of refraction () is greater than or equal to ). For an angle, the law of refraction is transformed to the form: Since the angle of incidence of the beam is equal to the angle of reflection, we can write that: According to the conditions of the problem, the beam passes from the glass into the air, which means that Let's do the calculations:
Answer

EXAMPLE 2

Exercise	What is the relationship between the angle of incidence of a ray of light () and the refractive index of a substance (n)? If the angle between the reflected and refracted rays is ? A beam falls from air into matter.
Solution	Let's make a drawing.

TO LECTURE №24

"INSTRUMENTAL METHODS OF ANALYSIS"

REFRACTOMETRY.

Literature:

1. V.D. Ponomarev "Analytical Chemistry" 1983 246-251

2. A.A. Ishchenko "Analytical Chemistry" 2004 pp 181-184

REFRACTOMETRY.

Refractometry is one of the simplest physical methods of analysis, requiring a minimum amount of analyte and is carried out in a very short time.

Refractometry- a method based on the phenomenon of refraction or refraction i.e. change in the direction of light propagation when passing from one medium to another.

Refraction, as well as the absorption of light, is a consequence of its interaction with the medium. The word refractometry means dimension refraction of light, which is estimated by the value of the refractive index.

Refractive index value n depends

1) on the composition of substances and systems,

2) from at what concentration and what molecules the light beam meets on its way, because Under the action of light, the molecules of different substances are polarized in different ways. It is on this dependence that the refractometric method is based.

This method has a number of advantages, as a result of which it has found wide application both in chemical research and in the control of technological processes.

1) The measurement of refractive indices is a very simple process that is carried out accurately and with a minimum investment of time and amount of substance.

2) Typically, refractometers provide up to 10% accuracy in determining the refractive index of light and the content of the analyte

The refractometry method is used to control authenticity and purity, to identify individual substances, to determine the structure of organic and inorganic compounds in the study of solutions. Refractometry is used to determine the composition of two-component solutions and for ternary systems.

Physical basis of the method

REFRACTIVE INDICATOR.

The deviation of a light beam from its original direction when it passes from one medium to another is the greater, the greater the difference in the speeds of light propagation in two

these environments.

Consider the refraction of a light beam at the boundary of any two transparent media I and II (See Fig.). Let us agree that medium II has a greater refractive power and, therefore, n 1 and n 2- shows the refraction of the corresponding media. If medium I is neither vacuum nor air, then the ratio sin of the angle of incidence of the light beam to sin of the angle of refraction will give the value of the relative refractive index n rel. The value of n rel. can also be defined as the ratio of the refractive indices of the media under consideration.

n rel. = ----- = ---

The value of the refractive index depends on

1) the nature of substances

The nature of a substance in this case is determined by the degree of deformability of its molecules under the action of light - the degree of polarizability. The more intense the polarizability, the stronger the refraction of light.

2)incident light wavelength

The measurement of the refractive index is carried out at a light wavelength of 589.3 nm (line D of the sodium spectrum).

The dependence of the refractive index on the wavelength of light is called dispersion. The shorter the wavelength, the greater the refraction. Therefore, rays of different wavelengths are refracted differently.

3)temperature at which the measurement is taken. A prerequisite for determining the refractive index is compliance with the temperature regime. Usually the determination is performed at 20±0.3 0 С.

As the temperature rises, the refractive index decreases, and as the temperature decreases, it increases..

The temperature correction is calculated using the following formula:

n t \u003d n 20 + (20-t) 0.0002, where

n t - bye refractive index at a given temperature,

n 20 - refractive index at 20 0 С

The influence of temperature on the values ​​of the refractive indices of gases and liquids is related to the values ​​of their coefficients of volumetric expansion. The volume of all gases and liquids increases when heated, the density decreases and, consequently, the indicator decreases

The refractive index, measured at 20 0 C and a light wavelength of 589.3 nm, is indicated by the index n D 20

The dependence of the refractive index of a homogeneous two-component system on its state is established experimentally by determining the refractive index for a number of standard systems (for example, solutions), the content of components in which is known.

4) the concentration of a substance in a solution.

For many aqueous solutions of substances, the refractive indices at various concentrations and temperatures have been reliably measured, and in these cases reference data can be used. refractometric tables. Practice shows that when the content of the dissolved substance does not exceed 10-20%, along with the graphical method, in very many cases it is possible to use linear equation like:

n=n o +FC,

n- refractive index of the solution,

no is the refractive index of the pure solvent,

C- concentration of the dissolved substance,%

F-empirical coefficient, the value of which is found

by determining the refractive indices of solutions of known concentration.

REFRACTOMETERS.

Refractometers are devices used to measure the refractive index. There are 2 types of these instruments: Abbe type refractometer and Pulfrich type. Both in those and in others, the measurements are based on determining the magnitude of the limiting angle of refraction. In practice, refractometers of various systems are used: laboratory-RL, universal RLU, etc.

The refractive index of distilled water n 0 \u003d 1.33299, in practice, this indicator takes as reference as n 0 =1,333.

The principle of operation on refractometers is based on the determination of the refractive index by the limiting angle method (the angle of total reflection of light).

Hand refractometer

Refractometer Abbe

Angle of incidence - cornera between the direction of the incident beam and the perpendicular to the interface between two media, reconstructed at the point of incidence.

Reflection angle - corner β between this perpendicular and the direction of the reflected beam.

Laws of light reflection:

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

2. The angle of reflection is equal to the angle of incidence.

refraction of light called the change in the direction of light rays when light passes from one transparent medium to another.

Refraction angle - cornerb between the same perpendicular and the direction of the refracted beam.

The speed of light in a vacuum With \u003d 3 * 10 8 m / s

The speed of light in a medium V< c

Absolute refractive index of the medium shows how many times the speed of lightv in this medium is less than the speed of light With in a vacuum.

Absolute refractive index of the first medium

Absolute refractive index of the second medium

Absolute refractive index for vacuum equals 1

The speed of light in air differs very little from the value With, that's why

Absolute refractive index for air we will assume equal to 1

Relative refractive index shows how many times the speed of light changes when the beam passes from the first medium to the second.

where V 1 and V 2 are the speeds of light propagation in the first and second medium.

Taking into account the refractive index, the law of light refraction can be written as

where n 21 – relative refractive index the second environment relative to the first;

n 2 and n 1– absolute refractive indices second and first environment respectively

The refractive index of the medium relative to air (vacuum) can be found in Table 12 (Rymkevich's problem book). Values ​​are given for the case the incidence of light from the air into the medium.

For example, we find in the table the refractive index of diamond n = 2.42.

This is the index of refraction diamond against air(vacuum), that is, for absolute refractive indices:

The laws of reflection and refraction are valid for the reverse direction of light rays.

From two transparent media optically less dense called a medium with a higher speed of light, or with a lower refractive index.

When falling into an optically denser medium

angle of refraction less than the angle of incidence.

When falling into an optically less dense medium

angle of refraction more angle of incidence

Total internal reflection

If light rays from an optically denser medium 1 fall on the interface with an optically less dense medium 2 ( n 1 > n 2), then the angle of incidence is less than the angle of refractiona < b . With an increase in the angle of incidence, one can approach its valuea pr , when the refracted beam slides along the interface between two media and does not fall into the second medium,

Refraction angle b= 90°, while all light energy is reflected from the interface.

The limiting angle of total internal reflection a pr is the angle at which a refracted ray glides along the surface of two media,

When passing from an optically less dense medium to a denser medium, total internal reflection is impossible.

Topics of the USE codifier: the law of refraction of light, total internal reflection.

At the interface between two transparent media, along with the reflection of light, its reflection is observed. refraction- light, passing into another medium, changes the direction of its propagation.

Refraction of a light beam occurs when it oblique falling on the interface (although not always - read on about total internal reflection). If the beam falls perpendicular to the surface, then there will be no refraction - in the second medium, the beam will retain its direction and also go perpendicular to the surface.

Law of refraction (special case).

We will start with the particular case where one of the media is air. This situation is present in the vast majority of tasks. We will discuss the corresponding particular case of the law of refraction, and then we will give its most general formulation.

Suppose that a ray of light traveling through air falls obliquely on the surface of glass, water, or some other transparent medium. When passing into the medium, the beam is refracted, and its further course is shown in Fig. one .

A perpendicular is drawn at the point of incidence (or, as they say, normal) to the surface of the medium. The beam, as before, is called incident beam, and the angle between the incident ray and the normal is angle of incidence. The beam is refracted beam; the angle between the refracted ray and the normal to the surface is called angle of refraction.

Any transparent medium is characterized by a quantity called refractive index this environment. The refractive indices of various media can be found in the tables. For example, for glass, and for water. In general, for any environment; the refractive index is equal to unity only in vacuum. At air, therefore, for air with sufficient accuracy can be assumed in problems (in optics, air does not differ much from vacuum).

Law of refraction (transition "air-medium") .

1) The incident ray, the refracted ray and the normal to the surface drawn at the point of incidence lie in the same plane.
2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the refractive index of the medium:

. (1)

Since from relation (1) it follows that , that is - the angle of refraction is less than the angle of incidence. Remember: passing from air to the medium, the beam after refraction goes closer to the normal.

The refractive index is directly related to the speed of light in a given medium. This speed is always less than the speed of light in vacuum: . And it turns out that

. (2)

Why this happens, we will understand when studying wave optics. In the meantime, let's combine the formulas. (1) and (2) :

. (3)

Since the refractive index of air is very close to unity, we can assume that the speed of light in air is approximately equal to the speed of light in vacuum. Taking this into account and looking at the formula . (3) , we conclude: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in air to the speed of light in a medium.

Reversibility of light rays.

Now consider the reverse course of the beam: its refraction during the transition from the medium to the air. The following useful principle will help us here.

The principle of reversibility of light rays. The trajectory of the beam does not depend on whether the beam propagates in the forward or backward direction. Moving in the opposite direction, the beam will follow exactly the same path as in the forward direction.

According to the principle of reversibility, when passing from the medium to the air, the beam will follow the same trajectory as during the corresponding transition from air to the medium (Fig. 2) The only difference in Fig. 2 from fig. 1 is that the direction of the beam has changed to the opposite.

Since the geometric picture has not changed, formula (1) will remain the same: the ratio of the sine of the angle to the sine of the angle is still equal to the refractive index of the medium. True, now the angles have changed roles: the angle has become the angle of incidence, and the angle has become the angle of refraction.

In any case, no matter how the beam goes - from the air to the environment or from the environment to the air - the following simple rule works. We take two angles - the angle of incidence and the angle of refraction; the ratio of the sine of the larger angle to the sine of the smaller angle is equal to the refractive index of the medium.

Now we are fully prepared to discuss the law of refraction in the most general case.

Law of refraction (general case).

Let light pass from medium 1 with refractive index to medium 2 with refractive index . A medium with a high refractive index is called optically denser; accordingly, a medium with a lower refractive index is called optically less dense.

Passing from an optically less dense medium to an optically denser one, the light beam after refraction goes closer to the normal (Fig. 3). In this case, the angle of incidence is greater than the angle of refraction: .

Rice. 3.

On the contrary, when passing from an optically denser medium to an optically less dense one, the beam deviates further from the normal (Fig. 4). Here the angle of incidence is less than the angle of refraction:

Rice. four.

It turns out that both of these cases are covered by one formula - the general law of refraction, valid for any two transparent media.

The law of refraction.
1) The incident beam, the refracted beam and the normal to the interface between the media, drawn at the point of incidence, lie in the same plane.
2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive index of the second medium to the refractive index of the first medium:

. (4)

It is easy to see that the previously formulated law of refraction for the "air-medium" transition is a special case of this law. Indeed, assuming in the formula (4) , we will come to the formula (1) .

Recall now that the refractive index is the ratio of the speed of light in vacuum to the speed of light in a given medium: . Substituting this into (4) , we get:

. (5)

Formula (5) generalizes formula (3) in a natural way. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium.

total internal reflection.

When light rays pass from an optically denser medium to an optically less dense one, an interesting phenomenon is observed - complete internal reflection. Let's see what it is.

Let us assume for definiteness that light goes from water to air. Let us assume that there is a point source of light in the depths of the reservoir, emitting rays in all directions. We will consider some of these rays (Fig. 5).

The beam falls on the surface of the water at the smallest angle. This beam is partly refracted (beam ) and partly reflected back into the water (beam ). Thus, part of the energy of the incident beam is transferred to the refracted beam, and the rest of the energy is transferred to the reflected beam.

The angle of incidence of the beam is greater. This beam is also divided into two beams - refracted and reflected. But the energy of the original beam is distributed between them in a different way: the refracted beam will be dimmer than the beam (that is, it will receive a smaller share of energy), and the reflected beam will be correspondingly brighter than the beam (it will receive a larger share of energy).

As the angle of incidence increases, the same regularity can be traced: an increasing share of the energy of the incident beam goes to the reflected beam, and an ever smaller share to the refracted beam. The refracted beam becomes dimmer and dimmer, and at some point it disappears completely!

This disappearance occurs when the angle of incidence is reached, which corresponds to the angle of refraction. In this situation, the refracted beam would have to go parallel to the water surface, but there is nothing to go - all the energy of the incident beam went entirely to the reflected beam.

With a further increase in the angle of incidence, the refracted beam will even be absent.

The described phenomenon is the total internal reflection. Water does not emit outward rays with angles of incidence equal to or greater than a certain value - all such rays are entirely reflected back into the water. Angle is called limiting angle of total reflection.

The value is easy to find from the law of refraction. We have:

But, therefore

So, for water, the limiting angle of total reflection is equal to:

You can easily observe the phenomenon of total internal reflection at home. Pour water into a glass, raise it and look at the surface of the water slightly from below through the wall of the glass. You will see a silvery sheen on the surface - due to total internal reflection, it behaves like a mirror.

The most important technical application of total internal reflection is fiber optics. Light beams launched into the fiber optic cable ( light guide) almost parallel to its axis, fall on the surface at large angles and completely, without loss of energy, are reflected back into the cable. Repeatedly reflected, the rays go farther and farther, transferring energy over a considerable distance. Fiber-optic communication is used, for example, in cable television networks and high-speed Internet access.