Refractive index less than 1. Absolute refractive index and its relationship with relative refractive index
The refractive index of the medium relative to vacuum, i.e. for the case of the transition of light rays from vacuum to medium, is called absolute and is determined by formula (27.10): n=c/v.
When calculating, absolute refractive indices are taken from tables, since their value is determined quite accurately through experiments. Since c is greater than v, then The absolute refractive index is always greater than unity.
If light radiation passes from a vacuum into a medium, then the formula of the second law of refraction is written as:
sin i/sin β = n. (29.6)
Formula (29.6) is often used in practice when rays pass from air to a medium, since the speed of light propagation in air differs very little from c. This can be seen from the fact that the absolute refractive index of air is 1.0029.
When a ray goes from a medium into a vacuum (into air), then the formula of the second law of refraction takes the form:
sin i/sin β = 1 /n. (29.7)
In this case, the rays, when leaving the medium, necessarily move away from the perpendicular to the interface between the medium and vacuum.
Let's find out how to find the relative refractive index n21 from the absolute refractive indices. Let light pass from a medium with absolute exponent n1 to a medium with absolute exponent n2. Then n1 = c/V1 andn2 = c/v2, from:
n2/n1=v1/v2=n21. (29.8)
The formula for the second law of refraction for such a case is often written as follows:
sin i/sin β = n2/n1. (29.9)
Let us remember that by Maxwell's theory absolute exponent refraction can be found from the relation: n = √(με). Since for substances that are transparent to light radiation, μ is practically equal to unity, we can assume that:
n = √ε. (29.10)
Since the frequency of oscillations in light radiation is of the order of 10 14 Hz, neither dipoles nor ions in a dielectric, which have a relatively large mass, have time to change their position with such a frequency, and the dielectric properties of a substance under these conditions are determined only by the electronic polarization of its atoms. This is precisely what explains the difference between the value ε=n 2 from (29.10) and ε st in electrostatics. So, for water ε = n 2 = 1.77, and ε st = 81; for the ionic solid dielectric NaCl ε = 2.25, and ε st = 5.6. When a substance consists of homogeneous atoms or non-polar molecules, that is, it contains neither ions nor natural dipoles, then its polarization can only be electronic. For similar substances, ε from (29.10) and ε st coincide. An example of such a substance is diamond, which consists only of carbon atoms.
Note that the value of the absolute refractive index, in addition to the type of substance, also depends on the oscillation frequency, or on the wavelength of the radiation . As the wavelength decreases, as a rule, the refractive index increases.
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.
Basics of a physical phenomenon
When a beam falls on a surface that is separated by two transparent substances that have 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, they will propagate in water or glass). When moving from one medium to another, a ray typically changes its direction. This is the phenomenon of light refraction.
The reflection and refraction of light is especially visible in water.
Distortion effect in water
Looking at things in water, they appear distorted. This is especially noticeable at the boundary between air and water. Visually, underwater objects appear to be slightly deflected. The described physical phenomenon is precisely the reason why all objects appear distorted in water. When the rays hit the glass, this effect is less noticeable.
Refraction of light is a physical phenomenon that is characterized by a change in the direction of movement of a solar ray at the moment it moves from one medium (structure) to another.
To improve our understanding of this process, consider an example of a beam hitting water from air (similarly for glass). By drawing a perpendicular line along the interface, the angle of refraction and return of the light beam can be measured. This index (angle of refraction) will change as the flow penetrates the water (inside the glass).
Note! This parameter is understood as the angle formed by a perpendicular drawn to the separation of two substances when a beam penetrates from the first structure to the second.
Beam Passage
The same indicator is typical for other environments. It has been established that this indicator depends on the density of the substance. If the beam falls from a less dense to a denser structure, then the angle of distortion created will be greater. And if it’s the other way around, then it’s less.
At the same time, a change in the slope of the decline 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 a constant value, which is reflected 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 using special tables;
- α – angle of incidence;
- γ – angle of refraction.
To determine this physical phenomenon, the law of refraction was created.
Physical law
The law of refraction of light fluxes allows us to determine the characteristics of transparent substances. The law itself consists of two provisions:
- First part. The beam (incident, modified) and the perpendicular, which was restored at the point of incidence on the boundary, for example, of air and water (glass, etc.), will be located in the same plane;
- The second part. 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.
Moreover, when the value of the decline slope changes, the same situation will be typical for a similar indicator. This parameter is of great importance because 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 various precious stones. It is also important for determining the speed of light in various environments.
Note! The highest speed of light flow is in a 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 higher 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 densities. As we said earlier, using this law you can determine the density characteristic of the medium (structure). The denser it is, the slower the speed at which light will propagate through 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 moving from one substance to another.
Another important indicator
When a light flux moves 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 excursion, it is still necessary to consider such an effect as full internal reflection.
The phenomenon of full display 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 more dense to a less dense medium at the interface between substances. In a situation where this parameter exceeds a certain limiting value, then 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.
The practical application of the behavior of light flux has given a lot, creating a variety of technical devices to improve our lives. At the same time, light has not yet revealed all its possibilities to humanity and its practical potential has not yet been fully realized.
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The laws of physics play a very important role when carrying out calculations to plan a specific strategy for the production of any product or when drawing up a project for the construction of structures for various purposes. Many quantities are calculated, so measurements and calculations are made before planning work begins. 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 the process of measuring the angles, then their sine is calculated, and only then can the desired value be obtained. Despite the availability of tabular data, it is worth carrying out additional calculations each time, since reference books often use ideal conditions, which are almost impossible to achieve in real life. Therefore, in reality, the indicator will necessarily differ from the table, 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 accurate indicator is important, then additional measurements cannot be avoided. But they also do not give a 100% reliable result, since the final value will be influenced by the position of the sun in the sky and cloudiness on the day of measurement. 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 matter.
On forums that help solve physics problems, the question often comes up: 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 misconception.
The maximum refraction of glass will be around 1.7, while for diamond this indicator reaches 2.42. This gemstone is one of the few materials on Earth whose refractive index exceeds 2. This is due to its crystalline structure and the high level of scattering of light rays. The cut 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.
Measurements of the indicator and calculations 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 physics classes.
Determination of refractive index
Determining the refractive index of glass in practice is quite difficult, 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. The refractive index of gases is taken as the reference value, that is, as a unit. This was done so that it was possible to start from some value when making calculations.
If a sunbeam falls on the surface of glass 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 whose 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 have a clearer view of traffic conditions. The film will also inhibit ultraviolet radiation.
- 2. Paint the glass with paint. Manufacturers of cheap sunglasses do this, but it is worth considering that this can be harmful to vision. In good models, the glass is immediately produced colored using a special technology.
- 3. Immerse the glass in some liquid. This is only useful for experiments.
If a ray of light passes from glass, then the refractive index on the next material is calculated using a relative coefficient, which can be obtained by comparing table values. These calculations are very important in the design of optical systems that carry practical or experimental loads. Errors here are unacceptable, because they will lead to incorrect operation of the entire device, and then any data obtained with its help 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 a vacuum by the refractive index. Vacuum is used as a reference medium because refraction does not operate there due to the absence of any substances that could interfere with the smooth movement of light rays along a given path.
In any calculated indicators, the speed will be less than in the reference medium, since the refractive index is always greater than unity.
Refractive index
Refractive index substances - a quantity equal to the ratio of the phase speeds of light (electromagnetic waves) in a vacuum and in a given medium. Also, the refractive index is sometimes spoken of for any other waves, for example, sound, although in cases such as the latter, the definition, of course, has to be modified somehow.
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 regions of the frequency scale. The default usually refers to the optical range or the range determined by the context.
Links
- RefractiveIndex.INFO refractive index database
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See what “Refractive index” is in other dictionaries: Relative of two media n21, dimensionless ratio of the propagation speeds of optical radiation (c light) in the first (c1) and second (c2) media: n21 = c1/c2. At the same time it relates. P. p. is the ratio of the sines of the g l a p a d e n i j and y g l ... ...
Physical encyclopedia
See Refractive Index... See refractive index. * * * REFRACTION INDEX REFRACTIVE INDEX, see Refractive Index (see REFRACTIVE INDEX) ...- REFRACTIVE INDEX, a quantity characterizing the medium and equal to the ratio of the speed of light in a 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
- (see REFRACTION INDEX). Physical encyclopedic dictionary. M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1983 ... Relative of two media n21, dimensionless ratio of the propagation speeds of optical radiation (c light) in the first (c1) and second (c2) media: n21 = c1/c2. At the same time it relates. P. p. is the ratio of the sines of the g l a p a d e n i j and y g l ... ...
See Refractive index... Great Soviet Encyclopedia
The ratio of the speed of light in a 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
In your 8th grade physics course, you learned about 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 can understand the physical cause of refraction and explain many other light phenomena associated with it.
Rice. 141. Passing from one medium to another, the ray is refracted, i.e. changes the direction of propagation
According to the law of light refraction (Fig. 141):
- the incident, refracted and perpendicular rays drawn to the interface between two media at the point of incidence of the ray 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 vacuum, then
where n is the absolute refractive index (or simply refractive index) of the second medium. In this case, the first “medium” is vacuum, the absolute value of which is taken as unity.
The law of light refraction was experimentally discovered 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 Snell's discovery, several scientists hypothesized that the refraction of light is due to a change in its speed when passing 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 Christiaan Huygens (in 1690). They came to the same result in different ways, 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 light of a given frequency in the second medium propagates more slowly than in the first, i.e. V 2 The relationship between the quantities included in equation (3) served as a compelling reason for the emergence of another formulation for the definition of the relative refractive index: n 21 = v 1 / v 2 (4) Let a beam of light pass from a vacuum into some medium. Replacing v1 in equation (4) with the speed of light in a 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: 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 passing from vacuum to medium. This is the physical meaning of refractive indices. The value of the absolute refractive index n of any substance is greater than one (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 strict 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 the light wave with atoms and molecules of matter. The greater the optical density of a substance, the stronger this interaction, the lower the speed of light and the higher the refractive index. Thus, the speed of light in a medium and the absolute refractive index are determined by the properties of this medium. Based on the numerical values of the refractive indices of substances, their optical densities can be compared. For example, the refractive index of different types of glass ranges from 1.470 to 2.040, and the refractive index of water is 1.333. This means that glass is a medium optically denser 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 the 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, changes 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 travels at a speed v 1, and in water at a lower speed v 2. Point A of the wave reaches the boundary first. Over a period of time Δt, point B, moving in the air with the same speed v 1, will reach point B." During the same time, point A, moving in water with a lower speed v 2, will travel a shorter distance, reaching only point A." In this case, the so-called front of the AB wave in the water will be rotated at a certain angle relative to the front of the AB wave in the air. And the velocity vector (which is always perpendicular to the front of the wave 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 is also clear from the figure that when moving to another medium and rotating the wave front, the wavelength also changes: when moving 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
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