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Let us turn to a more detailed consideration of the refractive index introduced by us in § 81 when formulating the law of refraction.

The refractive index depends on the optical properties and the medium from which the beam falls and the medium into which it penetrates. The refractive index obtained when light from a vacuum falls on a medium is called the absolute refractive index of this medium.

Rice. 184. Relative refractive index of two media:

Let the absolute refractive index of the first medium be and the second medium - . Considering the refraction at the boundary of the first and second media, we make sure that the refractive index during the transition from the first medium to the second, the so-called relative refractive index, is equal to the ratio of the absolute refractive indices of the second and first media:

(Fig. 184). On the contrary, when passing from the second medium to the first, we have a relative refractive index

The established connection between the relative refractive index of two media and their absolute refractive indices could also be derived theoretically, without new experiments, just as it can be done for the law of reversibility (§82),

A medium with a higher refractive index is said to be optically denser. The refractive index of various media relative to air is usually measured. The absolute refractive index of air is . Thus, the absolute refractive index of any medium is related to its refractive index relative to air by the formula

Table 6. Refractive index of various substances relative to air

The refractive index depends on the wavelength of light, that is, on its color. Different colors correspond to different refractive indices. This phenomenon, called dispersion, plays an important role in optics. We will deal with this phenomenon repeatedly in later chapters. The data given in table. 6, refer to yellow light.

It is interesting to note that the law of reflection can be formally written in the same form as the law of refraction. Recall that we agreed to always measure the angles from the perpendicular to the corresponding ray. Therefore, we must consider the angle of incidence and the angle of reflection to have opposite signs, i.e. the law of reflection can be written as

Comparing (83.4) with the law of refraction, we see that the law of reflection can be considered as a special case of the law of refraction at . This formal similarity between the laws of reflection and refraction is of great use in solving practical problems.

In the previous presentation, the refractive index had the meaning of a constant of the medium, independent of the intensity of the light passing through it. Such an interpretation of the refractive index is quite natural; however, in the case of high radiation intensities achievable using modern lasers, it is not justified. The properties of the medium through which strong light radiation passes, in this case, depend on its intensity. As they say, the medium becomes non-linear. The nonlinearity of the medium manifests itself, in particular, in the fact that a light wave of high intensity changes the refractive index. The dependence of the refractive index on the radiation intensity has the form

Here, is the usual refractive index, a is the non-linear refractive index, and is the proportionality factor. The additional term in this formula can be either positive or negative.

The relative changes in the refractive index are relatively small. At non-linear refractive index. However, even such small changes in the refractive index are noticeable: they manifest themselves in a peculiar phenomenon of self-focusing of light.

Consider a medium with a positive nonlinear refractive index. In this case, the areas of increased light intensity are simultaneous areas of increased refractive index. Usually, in real laser radiation, the intensity distribution over the cross section of the beam is nonuniform: the intensity is maximum along the axis and smoothly decreases towards the edges of the beam, as shown in Fig. 185 solid curves. A similar distribution also describes the change in the refractive index over the cross section of a cell with a nonlinear medium, along the axis of which the laser beam propagates. The refractive index, which is greatest along the cell axis, gradually decreases towards its walls (dashed curves in Fig. 185).

A beam of rays emerging from the laser parallel to the axis, falling into a medium with a variable refractive index, is deflected in the direction where it is greater. Therefore, an increased intensity in the vicinity of the OSP cell leads to a concentration of light rays in this region, which is shown schematically in cross sections and in Fig. 185, and this leads to a further increase in . Ultimately, the effective cross section of a light beam passing through a nonlinear medium decreases significantly. Light passes as if through a narrow channel with an increased refractive index. Thus, the laser beam narrows, and the nonlinear medium acts as a converging lens under the action of intense radiation. This phenomenon is called self-focusing. It can be observed, for example, in liquid nitrobenzene.

Rice. 185. Distribution of radiation intensity and refractive index over the cross section of the laser beam of rays at the entrance to the cuvette (a), near the input end (), in the middle (), near the output end of the cuvette ()

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 each 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.

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

The processes that are associated with light are an important component of physics and surround us everywhere in our everyday life. The most important in this situation are the laws of reflection and refraction of light, on which modern optics is based. The refraction of light is an important part of modern science.

Distortion effect

This article will tell you what the phenomenon of light refraction is, as well as what the law of refraction looks like and what follows from it.

Fundamentals of a physical phenomenon

When a beam falls on a surface that is separated by two transparent substances having different optical densities (for example, different glasses or in water), some of the rays will be reflected, and some will penetrate into the second structure (for example, it will propagate in water or glass). When passing from one medium to another, the beam is characterized by a change in its direction. This is the phenomenon of light refraction.
Reflection and refraction of light can be seen especially well in water.

water distortion effect

Looking at things in the water, they seem distorted. This is especially noticeable at the border between air and water. Visually it seems that underwater objects are slightly deflected. The described physical phenomenon is precisely the reason why all objects seem distorted in water. When the rays hit the glass, this effect is less noticeable.
The refraction of light is a physical phenomenon, which is characterized by a change in the direction of the solar beam at the moment of moving from one medium (structure) to another.
To improve the understanding of this process, consider the example of a beam falling from air into water (similarly for glass). By drawing a perpendicular along the interface, the angle of refraction and return of the light beam can be measured. This indicator (the angle of refraction) will change when the flow penetrates into the water (inside the glass).
Note! This parameter is understood as the angle that forms a perpendicular drawn to the separation of two substances when the beam penetrates from the first structure to the second.

Beam passage

The same indicator is typical for other environments. It is established that this indicator depends on the density of the substance. If the beam is incident from a less dense to a denser structure, then the angle of distortion created will be larger. And if vice versa, then less.
At the same time, a change in the slope of the fall will also affect this indicator. But the relationship between them does not remain constant. At the same time, the ratio of their sines will remain constant, which is displayed by the following formula: sinα / sinγ = n, where:

• n is a constant value that is described for each specific substance (air, glass, water, etc.). Therefore, what this value will be can be determined from special tables;
• α is the angle of incidence;
• γ is the angle of refraction.

To determine this physical phenomenon, the law of refraction was created.

physical law

The law of refraction of light fluxes allows you to determine the characteristics of transparent substances. The law itself consists of two provisions:

• First part. The beam (incident, changed) and the perpendicular, which was restored at the point of incidence at the boundary, for example, air and water (glass, etc.), will be located in the same plane;
• The second part. The indicator of the ratio of the sine of the angle of incidence to the sine of the same angle formed when crossing the boundary will be a constant value.

Description of the law

In this case, at the moment the beam exits the second structure into the first (for example, when the light flux passes from the air, through the glass and back into the air), a distortion effect will also occur.

An important parameter for different objects

The main indicator in this situation is the ratio of the sine of the angle of incidence to a similar parameter, but for distortion. As follows from the law described above, this indicator is a constant value.
At the same time, when the value of the slope of the fall changes, the same situation will be typical for a similar indicator. This parameter is of great importance, since it is an integral characteristic of transparent substances.

Indicators for different objects

Thanks to this parameter, you can quite effectively distinguish between types of glass, as well as a variety of precious stones. It is also important for determining the speed of light in various media.

Note! The highest speed of the light flux is in vacuum.

When moving from one substance to another, its speed will decrease. For example, diamond, which has the highest refractive index, will have a photon propagation speed 2.42 times faster than air. In water, they will spread 1.33 times slower. For different types of glass, this parameter ranges from 1.4 to 2.2.

Note! Some glasses have a refractive index of 2.2, which is very close to diamond (2.4). Therefore, it is not always possible to distinguish a piece of glass from a real diamond.

Optical density of substances

Light can penetrate through different substances, which are characterized by different optical density. As we said earlier, using this law, you can determine the characteristic of the density of the medium (structure). The denser it is, the slower the speed of light will propagate in it. For example, glass or water will be more optically dense than air.
In addition to the fact that this parameter is a constant value, it also reflects the ratio of the speed of light in two substances. The physical meaning can be displayed as the following formula:

This indicator tells how the speed of propagation of photons changes when passing from one substance to another.

Another important indicator

When moving the light flux through transparent objects, its polarization is possible. It is observed during the passage of a light flux from dielectric isotropic media. Polarization occurs when photons pass through glass.

polarization effect

Partial polarization is observed when the angle of incidence of the light flux at the boundary of two dielectrics differs from zero. The degree of polarization depends on what the angles of incidence were (Brewster's law).

Full internal reflection

Concluding our short digression, it is still necessary to consider such an effect as a full-fledged internal reflection.

Full Display Phenomenon

For this effect to appear, it is necessary to increase the angle of incidence of the light flux at the moment of its transition from a denser to a less dense medium at the interface between substances. In a situation where this parameter exceeds a certain limit value, then the photons incident on the boundary of this section will be completely reflected. Actually, this will be our desired phenomenon. Without it, it was impossible to make fiber optics.

Conclusion

The practical application of the features of the behavior of the light flux gave a lot, creating a variety of technical devices to improve our lives. At the same time, light has not opened all its possibilities to mankind, and its practical potential has not yet been fully realized.

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There is nothing else than the ratio of the sine of the angle of incidence to the sine of the angle of refraction

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 areas of the frequency scale. The default is usually the optical range, or the range determined by the context.

The value of n, ceteris paribus, is usually less than unity when the beam passes from a denser medium to a less dense medium, and more 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 (not to be confused with optical density as a measure of the opacity of a medium).

The table shows some refractive index values ​​for some media:

A medium with a higher refractive index is said to be optically denser. The refractive index of various media relative to air is usually measured. The absolute refractive index of air is . Thus, the absolute refractive index of any medium is related to its refractive index relative to air by the formula:

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