The highest refractive index. Law of refraction of light

This article reveals the essence of such a concept of optics as the refractive index. Formulas for obtaining this value are given, a brief overview of the application of the phenomenon of refraction of an electromagnetic wave is given.

Ability to see and refractive index

At the dawn of civilization, people asked the question: how does the eye see? It has been suggested that a person emits rays that feel the surrounding objects, or, conversely, all things emit such rays. The answer to this question was given in the seventeenth century. It is contained in optics and is related to what the refractive index is. Reflecting from various opaque surfaces and refracting at the border with transparent ones, light gives a person the opportunity to see.

Light and refractive index

Our planet is shrouded in the light of the Sun. And it is precisely with the wave nature of photons that such a concept as the absolute refractive index is associated. When propagating in a vacuum, a photon encounters no obstacles. On the planet, light encounters many different denser media: the atmosphere (a mixture of gases), water, crystals. Being an electromagnetic wave, photons of light have one phase velocity in vacuum (denoted c), and in the environment - another (denoted v). The ratio of the first and second is what is called the absolute refractive index. The formula looks like this: n = c / v.

Phase speed

It is worth giving a definition of the phase velocity of the electromagnetic medium. Otherwise understand what is the refractive index n, it is forbidden. A photon of light is a wave. So, it can be represented as a packet of energy that oscillates (imagine a segment of a sinusoid). Phase - this is the segment of the sinusoid that the wave passes at a given time (recall that this is important for understanding such a quantity as the refractive index).

For example, a phase can be a maximum of a sinusoid or some segment of its slope. The phase velocity of a wave is the speed at which that particular phase moves. As the definition of the refractive index explains, for a vacuum and for a medium, these values ​​differ. Moreover, each environment has its own value of this quantity. Any transparent compound, whatever its composition, has a refractive index different from all other substances.

Absolute and relative refractive index

It has already been shown above that the absolute value is measured relative to vacuum. However, this is difficult on our planet: light more often hits the border of air and water or quartz and spinel. For each of these media, as mentioned above, the refractive index is different. In air, a photon of light travels along one direction and has one phase velocity (v 1), but when it enters water, it changes the direction of propagation and phase velocity (v 2). However, both of these directions lie in the same plane. This is very important for understanding how the image of the surrounding world is formed on the retina of the eye or on the matrix of the camera. The ratio of the two absolute values ​​gives the relative refractive index. The formula looks like this: n 12 \u003d v 1 / v 2.

But what if the light, on the contrary, comes out of the water and enters the air? Then this value will be determined by the formula n 21 = v 2 / v 1. When multiplying the relative refractive indices, we get n 21 * n 12 \u003d (v 2 * v 1) / (v 1 * v 2) \u003d 1. This ratio is true for any pair of media. The relative refractive index can be found from the sines of the angles of incidence and refraction n 12 = sin Ɵ 1 / sin Ɵ 2. Do not forget that the angles are counted from the normal to the surface. A normal is a line that is perpendicular to the surface. That is, if the problem is given an angle α falling relative to the surface itself, then the sine of (90 - α) must be considered.

The beauty of the refractive index and its applications

On a calm sunny day, glare plays at the bottom of the lake. Dark blue ice covers the rock. On a woman's hand, a diamond scatters thousands of sparks. These phenomena are a consequence of the fact that all boundaries of transparent media have a relative refractive index. In addition to aesthetic pleasure, this phenomenon can also be used for practical applications.

Here are some examples:

• A glass lens collects a beam of sunlight and sets fire to the grass.
• The laser beam focuses on the diseased organ and cuts off unnecessary tissue.
• Sunlight refracts on an ancient stained glass window, creating a special atmosphere.
• Microscope magnifies very small details
• Spectrophotometer lenses collect laser light reflected from the surface of the substance under study. Thus, it is possible to understand the structure, and then the properties of new materials.
• There is even a project for a photonic computer, where information will be transmitted not by electrons, as it is now, but by photons. For such a device, refractive elements will definitely be required.

Wavelength

However, the Sun supplies us with photons not only in the visible spectrum. Infrared, ultraviolet, X-ray ranges are not perceived by human vision, but they affect our lives. IR rays keep us warm, UV photons ionize the upper atmosphere and enable plants to produce oxygen through photosynthesis.

And what the refractive index is equal to depends not only on the substances between which the boundary lies, but also on the wavelength of the incident radiation. It is usually clear from the context which value is being referred to. That is, if the book considers X-rays and its effect on a person, then n there it is defined for this range. But usually the visible spectrum of electromagnetic waves is meant, unless otherwise specified.

Refractive index and reflection

As it became clear from the above, we are talking about transparent environments. As examples, we cited air, water, diamond. But what about wood, granite, plastic? Is there such a thing as a refractive index for them? The answer is complex, but in general yes.

First of all, we should consider what kind of light we are dealing with. Those media that are opaque to visible photons are cut through by X-ray or gamma radiation. That is, if we were all supermen, then the whole world around us would be transparent to us, but to varying degrees. For example, walls made of concrete would be no denser than jelly, and metal fittings would look like pieces of denser fruit.

For other elementary particles, muons, our planet is generally transparent through and through. At one time, scientists brought a lot of trouble to prove the very fact of their existence. Muons pierce us in millions every second, but the probability of a collision of at least one particle with matter is very small, and it is very difficult to fix this. By the way, Baikal will soon become a place for "catching" muons. Its deep and clear water is ideal for this - especially in winter. The main thing is that the sensors do not freeze. Thus, the refractive index of concrete, for example, for x-ray photons makes sense. Moreover, X-ray irradiation of a substance is one of the most accurate and important methods for studying the structure of crystals.

It is also worth remembering that, in a mathematical sense, substances that are opaque for a given range have an imaginary refractive index. Finally, one must understand that the temperature of a substance can also affect its transparency.

Light refraction- a phenomenon in which a beam of light, passing from one medium to another, changes direction at the boundary of these media.

The refraction of light occurs according to the following law:
The incident and refracted rays and the perpendicular drawn to the interface between two media at the point of incidence of the beam lie in the same plane. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media:
,
where α - angle of incidence,
β - angle of refraction
n - a constant value independent of the angle of incidence.

When the angle of incidence changes, the angle of refraction also changes. The larger the angle of incidence, the larger the angle of refraction.
If light goes from an optically less dense medium to a denser medium, then the angle of refraction is always less than the angle of incidence: β < α.
A beam of light directed perpendicular to the interface between two media passes from one medium to another without breaking.

absolute refractive index of a substance- a value equal to the ratio of the phase velocities of light (electromagnetic waves) in vacuum and in a given medium n=c/v
The value n included in the law of refraction is called the relative refractive index for a pair of media.

The value n is the relative refractive index of medium B with respect to medium A, and n" = 1/n is the relative refractive index of medium A with respect to medium B.
This value, ceteris paribus, is greater than unity when the beam passes from a denser medium to a less dense medium, and less 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.
A beam falling from airless space onto the surface of some medium B is refracted more strongly than when falling on it from another medium A; The refractive index of a ray incident on a medium from airless space is called its absolute refractive index.

(Absolute - relative to vacuum.
Relative - relative to any other substance (the same air, for example).
The relative index of two substances is the ratio of their absolute indices.)

Total internal reflection- internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its highest values ​​for polished surfaces. The reflection coefficient for total internal reflection does not depend on the wavelength.

In optics, this phenomenon is observed for a wide spectrum of electromagnetic radiation, including the X-ray range.

In geometric optics, the phenomenon is explained in terms of Snell's law. Considering that the angle of refraction cannot exceed 90°, we obtain that at an angle of incidence whose sine is greater than the ratio of the lower refractive index to the larger index, the electromagnetic wave should be completely reflected into the first medium.

In accordance with the wave theory of the phenomenon, the electromagnetic wave nevertheless penetrates into the second medium - the so-called "non-uniform wave" propagates there, which decays exponentially and does not carry away energy with it. The characteristic depth of penetration of an inhomogeneous wave into the second medium is of the order of the wavelength.

Laws of refraction of light.

From all that has been said, we conclude:
1 . At the interface between two media of different optical density, a beam of light changes its direction when passing from one medium to another.
2. When a light beam passes into a medium with a higher optical density, the angle of refraction is less than the angle of incidence; when a light beam passes from an optically denser medium to a less dense medium, the angle of refraction is greater than the angle of incidence.
The refraction of light is accompanied by reflection, and with an increase in the angle of incidence, the brightness of the reflected beam increases, and the refracted one weakens. This can be seen by conducting the experiment shown in the figure. Consequently, the reflected beam carries away with it the more light energy, the greater the angle of incidence.

Let be MN- the interface between two transparent media, for example, air and water, JSC- falling beam OV- refracted beam, - angle of incidence, - angle of refraction, - speed of light propagation in the first medium, - speed of light propagation in the second medium.

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 further, 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:

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.

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 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, 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, modified) 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;
• 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 the appearance of this effect, 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 will exceed 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.

How to make a paper lamp with your own hands
How to check the performance of the LED strip

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

Light beam refraction effect

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

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

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

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

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

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

Absolute refractive index

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

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

Two important conclusions follow from the formula above:

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

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

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

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

Refractive index of light in air

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

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

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

glass-air interface

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

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

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

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

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

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

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

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