What does the refractive index of a substance depend on? The law of refraction of light. Absolute and relative refractive indices. Total internal reflection How to find the refractive index of a liquid formula

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 ratio of the refractive index of one medium to the refractive index of the second is called relative refractive index the first environment in relation to the second. For running:

where and are the phase velocities of light in the first and second media, respectively. Obviously, the relative refractive index of the second medium with respect to the first is a value equal to .

This value, 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 the environment optically more or less dense than the other (not to be confused with optical density as a measure of the opacity of a medium).

A beam falling from airless space onto the surface of some medium is refracted more strongly than when falling on it from another medium; the refractive index of a ray incident on a medium from airless space is called its absolute refractive index or simply the refractive index of a given medium, this is the refractive index, the definition of which is given at the beginning of the article. The refractive index of any gas, including air, under normal conditions is much less than the refractive indices of liquids or solids, therefore, approximately (and with relatively good accuracy) the absolute refractive index can be judged from the refractive index relative to air.

Examples

The refractive indices of some media are given in the table.

Materials with a negative refractive index

• the phase and group velocities of the waves have different directions;
• it is possible to overcome the diffraction limit when creating optical systems (“superlenses”), increasing the resolution of microscopes with their help, creating nanoscale microcircuits, increasing the recording density on optical information carriers).

see also

• Immersion method for measuring the refractive index.

Notes

Links

• RefractiveIndex.INFO refractive index database

Wikimedia Foundation. 2010 .

• Belfort
• Saxony-Anhalt

See what the "Refractive index" is in other dictionaries:

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

REFRACTIVE INDEX Modern Encyclopedia

Refractive index- REFRACTIVE INDEX, a value that characterizes the medium and is equal to the ratio of the speed of light in vacuum to the speed of light in the medium (absolute refractive index). The refractive index n depends on the dielectric e and magnetic permeability m ... ... Illustrated Encyclopedic Dictionary

REFRACTIVE INDEX- (see REFRACTIVE INDICATOR). Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1983... Physical Encyclopedia

refractive index- 1. The ratio of the speed of the incident wave to the speed of the refracted wave. 2. The ratio of the speeds of sound in two media. [Non-destructive testing system.… … Technical Translator's Handbook

refractive index- the ratio of the speed of light in vacuum to the speed of light in a medium (absolute refractive index). The relative refractive index of two media is the ratio of the speed of light in the medium from which light falls to the interface to the speed of light in ... ... encyclopedic Dictionary

refractive index- lūžio rodiklis statusas T sritis automatika atitikmenys: engl. index of refraction; refraction index; refractive index vok. Brechungsindex, m; Brechungsverhältnis, n; Brechungszahl, f; Brechzahl, f; Refraktionsindex, m rus. refractive index, m; … Automatikos terminų žodynas

refractive index- lūžio rodiklis statusas T sritis chemija apibrėžtis Medžiagos konstanta, apibūdinanti jos savybę laužti šviesos bangas. atitikmenys: engl. index of refraction; refraction index; Refractive index eng. refractive index; refractive index; ... ... Chemijos terminų aiskinamasis žodynas

refractive index- lūžio rodiklis statusas T sritis Standartizacija ir metrologija apibrėžtis Esant nesugeriančiai terpei, tai elektromagnetinės spinduliuotės sklidimo greičio vakuume ir tam tikro dažnio elektromagnetinės spinduliuotėės fazin…

refractive index- lūžio rodiklis statusas T sritis Standartizacija ir metrologija apibrėžtis Medžiagos parametras, apibūdinantis jos savybę laužti šviesos bangas. atitikmenys: engl. refraction index; refractive index vok. Brechungsindex, m rus. index… … Penkiakalbis aiskinamasis metrologijos terminų žodynas

Books

• Quantum. Popular science physics and mathematics journal. No. 07/2017 , Not available. If you are interested in mathematics and physics and like to solve problems, then the popular scientific physics and mathematics journal KVANT will become your friend and assistant. It has been published since 1970 and ... Buy for 50 rubles electronic book

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 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 at the entrance to the cuvette (a), near the input end (), in the middle (), near the output end of the cuvette ()

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

Two kinds of refractive index

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

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

In any case, it is denoted by the Latin letter "en" - n. This value is obtained by dividing the values ​​of the same name by each other, therefore it is simply a coefficient that does not have a name.

What is the formula for calculating the refractive index?

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

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

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

What does the index of refraction depend on?

It is determined by the speed with which light propagates in the medium under consideration. Air in this respect is very close to a vacuum, so light waves propagate in it practically do not deviate from their original direction. Therefore, if the refractive index of glass-air or some other substance adjoining air is determined, then the latter is conditionally taken as vacuum.

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

Not the least role in changing the direction of wave propagation is played by the characteristics of light. White light is made up of many colors, from red to purple. Each part of the spectrum is refracted in its own way. Moreover, the value of the indicator for the wave of the red part of the spectrum will always be less than that of the rest. For example, the refractive index of TF-1 glass varies from 1.6421 to 1.67298, respectively, from the red to the violet part of the spectrum.

Example values ​​for different substances

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

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

What other quantities are used in solving problems?

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

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

Task #1

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

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

The solution in all three cases is reduced to calculations using the formula:

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

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

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

In the second case, when determining the arcsine, you need to substitute the value of the refractive index of water. The fraction 1 / n of water will take the value 1 / 1.33 \u003d 0. 7519. This is the arcsine of the angle 48.75º.

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

Answer: 41.14º, 48.75º, 61.05º.

Task #2

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

In order for the beam to leave the prism in the manner described, it must fall at a limiting angle on the inner face (the one that is the hypotenuse of the triangle in the section of the prism). By construction, this limiting angle turns out to be equal to the required angle of a right triangle. From the law of refraction of light, it turns out that the sine of the limiting angle, divided by the sine of 90 degrees, is equal to the ratio of two refractive indices: water to glass.

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

Table 1. Refractive indices of crystals.

refractive index some crystals at 18 ° C for the rays of the visible part of the spectrum, the wavelengths of which correspond to certain spectral lines. The elements to which these lines belong are indicated; the approximate values ​​of the wavelengths λ of these lines are also indicated in angstrom units

Table 2. Refractive indices of optical glasses.

Lines C, D and F, whose wavelengths are approximately equal: 0.6563 μ (μm), 0.5893 μ and 0.4861 μ.

Table 3. Refractive indices of quartz in the visible part of the spectrum

Reference table gives values refractive index ordinary rays ( n 0) and extraordinary ( ne) for the range of the spectrum approximately from 0.4 to 0.70 μ.

Table 4. Refractive indices of liquids.

The table gives the values ​​of the refractive indices n liquids for a beam with a wavelength approximately equal to 0.5893 μ (yellow sodium line); temperature of the liquid at which measurements were made n, is indicated.

Table 5. Refractive indices of aqueous solutions of sugar.

The table below gives the values refractive index n aqueous solutions of sugar (at 20 ° C) depending on the concentration With solution ( With shows the weight percentage of sugar in the solution).

Table 6. Refractive indices of water

The table gives the values ​​of the refractive indices n water at a temperature of 20 ° C in the range of wavelengths from approximately 0.3 to 1 μ.

Table 7. Refractive indices of gases table

The table gives the values ​​of the refractive indices n of gases under normal conditions for the line D, the wavelength of which is approximately equal to 0.5893 μ.

The source of information: BRIEF PHYSICAL AND TECHNICAL HANDBOOK / Volume 1, - M .: 1960.

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 the energy), and the reflected beam will be correspondingly brighter than the beam (it will receive a larger share of the 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.