The propagation of electromagnetic waves in various media obeys the laws of reflection and refraction. From these laws, under certain conditions, one interesting effect follows, which in physics is called the total internal reflection of light. Let's take a closer look at what this effect is.

Reflection and refraction

Before proceeding directly to the consideration of the internal total reflection of light, it is necessary to give an explanation of the processes of reflection and refraction.

Reflection is understood as a change in the direction of movement of a light beam in the same medium when it encounters an interface. For example, if you direct from a laser pointer to a mirror, you can observe the described effect.

Refraction is, like reflection, a change in the direction of light movement, but not in the first, but in the second medium. The result of this phenomenon will be a distortion of the outlines of objects and their spatial arrangement. A common example of refraction is the breaking of a pencil or pen if he/she is placed in a glass of water.

Refraction and reflection are related to each other. They are almost always present together: part of the energy of the beam is reflected, and the other part is refracted.

Both phenomena are the result of the application of Fermat's principle. He claims that light travels along a trajectory between two points that will take him the least time.

Since reflection is an effect that occurs in one medium, and refraction occurs in two media, it is important for the latter that both media are transparent to electromagnetic waves.

The concept of refractive index

The refractive index is an important quantity for the mathematical description of the phenomena under consideration. The refractive index of a particular medium is determined as follows:

Where c and v are the speeds of light in vacuum and matter, respectively. The value of v is always less than c, so the exponent n will be greater than one. The dimensionless coefficient n shows how much light in a substance (medium) will lag behind light in a vacuum. The difference between these speeds leads to the appearance of the phenomenon of refraction.

The speed of light in matter correlates with the density of the latter. The denser the medium, the harder it is for light to move in it. For example, for air n = 1.00029, that is, almost like for vacuum, for water n = 1.333.

Reflections, refraction and their laws

A striking example of the result of total reflection are the shiny surfaces of a diamond. The refractive index for a diamond is 2.43, so many light rays hitting a gem experience multiple total reflections before leaving it.

The problem of determining the critical angle θc for diamond

Let's consider a simple problem, where we will show how to use the above formulas. It is necessary to calculate how much the critical angle of total reflection will change if a diamond is placed from air into water.

Having looked in the table for the values ​​for the refractive indices of the indicated media, we write them out:

• for air: n 1 = 1.00029;
• for water: n 2 = 1.333;
• for diamond: n 3 = 2.43.

The critical angle for a diamond-air pair is:

θ c1 \u003d arcsin (n 1 / n 3) \u003d arcsin (1.00029 / 2.43) ≈ 24.31 o.

As you can see, the critical angle for this pair of media is quite small, that is, only those rays can leave the diamond into the air that will be closer to the normal than 24.31 o .

For the case of a diamond in water, we get:

θ c2 \u003d arcsin (n 2 / n 3) \u003d arcsin (1.333 / 2.43) ≈ 33.27 o.

The increase in the critical angle was:

Δθ c \u003d θ c2 - θ c1 ≈ 33.27 o - 24.31 o \u003d 8.96 o.

This slight increase in the critical angle for the total reflection of light in diamond leads to the fact that it glistens in water almost the same as in air.

If n 1 >n 2, then >α, i.e. if light passes from an optically denser medium to an optically less dense medium, then the angle of refraction is greater than the angle of incidence (Fig. 3)

Limit angle of incidence. If α=α p,=90˚ and the beam will slide along the air-water interface.

If α'>α p, then the light will not pass into the second transparent medium, because will be fully reflected. This phenomenon is called full reflection of light. The angle of incidence α p, at which the refracted beam slides along the interface between the media, is called the limiting angle of total reflection.

Total reflection can be observed in an isosceles rectangular glass prism (Fig. 4), which is widely used in periscopes, binoculars, refractometers, etc.

a) Light falls perpendicular to the first face and therefore does not undergo refraction here (α=0 and =0). The angle of incidence on the second face α=45˚, i.e.>α p, (for glass α p =42˚). Therefore, on this face, the light is completely reflected. This is a rotary prism that rotates the beam 90˚.

b) In this case, the light inside the prism experiences already twofold total reflection. This is also a rotary prism that rotates the beam by 180˚.

c) In this case, the prism is already inverted. When the rays leave the prism, they are parallel to the incident ones, but in this case the upper incident beam becomes lower, and the lower one becomes upper.

The phenomenon of total reflection has found wide technical application in light guides.

The light guide is a large number of thin glass filaments, the diameter of which is about 20 microns, and each is about 1 m long. These threads are parallel to each other and are located close (Fig. 5)

Each filament is surrounded by a thin shell of glass, the refractive index of which is less than that of the filament itself. The light guide has two ends, the mutual arrangement of the ends of the threads on both ends of the light guide is strictly the same.

If an object is placed at one end of the light guide and illuminated, then an image of this object will appear at the other end of the light guide.

The image is obtained due to the fact that light from some small area of ​​​​the object enters the end of each of the threads. Experiencing many total reflections, the light emerges from the opposite end of the filament, transmitting the reflection of a given small area of ​​the object.

Because the location of the threads relative to each other is strictly the same, then the corresponding image of the object appears at the other end. The clarity of the image depends on the diameter of the threads. The smaller the diameter of each thread, the clearer the image of the object will be. The loss of light energy along the path of the light beam is usually relatively small in bundles (light guides), since with total reflection the reflection coefficient is relatively high (~0.9999). Energy loss are mainly due to the absorption of light by the substance inside the fiber.

For example, in the visible part of the spectrum in a fiber 1 m long, 30-70% of the energy is lost (but in the bundle).

Therefore, in order to transmit large light fluxes and maintain the flexibility of the light-guiding system, individual fibers are assembled into bundles (bundles) - light guides.

Light guides are widely used in medicine for illuminating internal cavities with cold light and transmitting images. endoscope- a special device for examining internal cavities (stomach, rectum, etc.). With the help of light guides, laser radiation is transmitted for a therapeutic effect on tumors. Yes, and the human retina is a highly organized fiber-optic system consisting of ~ 130x10 8 fibers.

Geometric and wave optics. Conditions for applying these approaches (from the ratio of the wavelength and the size of the object). Wave coherence. The concept of spatial and temporal coherence. forced emission. Features of laser radiation. Structure and principle of operation of the laser.

Due to the fact that light is a wave phenomenon, interference occurs, as a result of which limited the beam of light does not propagate in any one direction, but has a finite angular distribution, i.e. diffraction takes place. However, in those cases where the characteristic transverse dimensions of light beams are sufficiently large compared to the wavelength, one can neglect the divergence of the light beam and assume that it propagates in one single direction: along the light beam.

Wave optics is a branch of optics that describes the propagation of light, taking into account its wave nature. Phenomena of wave optics - interference, diffraction, polarization, etc.

Wave interference - mutual amplification or attenuation of the amplitude of two or more coherent waves simultaneously propagating in space.

Diffraction of waves is a phenomenon that manifests itself as a deviation from the laws of geometric optics during the propagation of waves.

Polarization - processes and states associated with the separation of any objects, mainly in space.

In physics, coherence is the correlation (consistency) of several oscillatory or wave processes in time, which manifests itself when they are added. Oscillations are coherent if the difference between their phases is constant in time and when the oscillations are added, an oscillation of the same frequency is obtained.

If the phase difference of two oscillations changes very slowly, then the oscillations are said to remain coherent for some time. This time is called the coherence time.

Spatial coherence - the coherence of oscillations that occur at the same time at different points in a plane perpendicular to the direction of wave propagation.

Stimulated emission - the generation of a new photon during the transition of a quantum system (atom, molecule, nucleus, etc.) from an excited state to a stable state (lower energy level) under the influence of an inducing photon, the energy of which was equal to the difference in energy levels. The created photon has the same energy, momentum, phase and polarization as the inducing photon (which is not absorbed).

Laser radiation can be continuous, with a constant power, or pulsed, reaching extremely high peak powers. In some schemes, the working element of the laser is used as an optical amplifier for radiation from another source.

The physical basis for the operation of a laser is the phenomenon of stimulated (induced) radiation. The essence of the phenomenon is that an excited atom is able to emit a photon under the influence of another photon without its absorption, if the energy of the latter is equal to the difference in the energies of the levels of the atom before and after the radiation. In this case, the emitted photon is coherent to the photon that caused the radiation (it is its “exact copy”). This is how the light is amplified. This phenomenon differs from spontaneous emission, in which the emitted photons have random directions of propagation, polarization and phase.

All lasers consist of three main parts:

active (working) environment;

pumping systems (energy source);

optical resonator (may be absent if the laser operates in the amplifier mode).

Each of them provides for the operation of the laser to perform its specific functions.

Geometric optics. The phenomenon of total internal reflection. Limiting angle of total reflection. The course of the rays. fiber optics.

Geometric optics is a branch of optics that studies the laws of light propagation in transparent media and the principles of constructing images during the passage of light in optical systems without taking into account its wave properties.

Total internal reflection is internal reflection provided that the angle of incidence exceeds some 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.

Limiting angle of total internal reflection

The angle of incidence at which the refracted beam begins to slide along the interface between two media without transition to an optically denser medium

Ray path in mirrors, prisms and lenses

Light rays from a point source propagate in all directions. In optical systems, bending back and reflecting from the interface between the media, some of the rays can again intersect at some point. A point is called a point image. When a ray is bounced off mirrors, the law is fulfilled: "the reflected ray always lies in the same plane as the incident ray and the normal to the bouncing surface, which passes through the point of incidence, and the angle of incidence subtracted from this normal is equal to the bouncing angle."

Fiber optics - this term means

branch of optics that studies the physical phenomena that occur and occur in optical fibers, or

products of precision engineering industries, which include components based on optical fibers.

Fiber-optic devices include lasers, amplifiers, multiplexers, demultiplexers, and a number of others. Fiber optic components include insulators, mirrors, connectors, splitters, etc. The basis of a fiber optic device is its optical circuit - a set of fiber optic components connected in a certain sequence. Optical circuits can be closed or open, with or without feedback.

First, let's fantasize a little. Imagine a hot summer day BC, a primitive man hunts fish with a spear. He notices her position, aims and strikes for some reason not at all where the fish was visible. Missed? No, the fisherman has the prey in his hands! The thing is that our ancestor intuitively understood the topic that we will study now. In everyday life, we see that a spoon dipped into a glass of water appears crooked, when we look through a glass jar, objects appear crooked. We will consider all these questions in the lesson, the theme of which is: “Refraction of light. The law of refraction of light. Total internal reflection.

In previous lessons, we talked about the fate of a ray in two cases: what happens if a ray of light propagates in a transparently homogeneous medium? The correct answer is that it will spread in a straight line. And what will happen when a beam of light falls on the interface between two media? In the last lesson we talked about the reflected beam, today we will consider that part of the light beam that is absorbed by the medium.

What will be the fate of the beam that has penetrated from the first optically transparent medium into the second optically transparent medium?

Rice. 1. Refraction of light

If the beam falls on the interface between two transparent media, then part of the light energy returns to the first medium, creating a reflected beam, and the other part passes inward to the second medium and, as a rule, changes its direction.

The change in the direction of propagation of light in the case of its passage through the interface between two media is called refraction of light(Fig. 1).

Rice. 2. Angles of incidence, refraction and reflection

In Figure 2 we see an incident beam, the angle of incidence will be denoted by α. The beam that will set the direction of the refracted beam of light will be called the refracted beam. The angle between the perpendicular to the interface between the media, restored from the point of incidence, and the refracted beam is called the angle of refraction, in the figure this is the angle γ. To complete the picture, we also give an image of the reflected beam and, accordingly, the reflection angle β. What is the relationship between the angle of incidence and the angle of refraction, is it possible to predict, knowing the angle of incidence and from which medium the beam passed into which, what will be the angle of refraction? It turns out you can!

We obtain a law that quantitatively describes the relationship between the angle of incidence and the angle of refraction. Let us use the Huygens principle, which regulates the propagation of a wave in a medium. The law consists of two parts.

The incident ray, the refracted ray and the perpendicular restored to the point of incidence 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 given media and is equal to the ratio of the speeds of light in these media.

This law is called Snell's law, after the Dutch scientist who first formulated it. The reason for refraction is the difference in the speeds of light in different media. You can verify the validity of the law of refraction by experimentally directing a beam of light at different angles to the interface between two media and measuring the angles of incidence and refraction. If we change these angles, measure the sines and find the ratios of the sines of these angles, we will be convinced that the law of refraction is indeed valid.

Evidence of the law of refraction using the Huygens principle is another confirmation of the wave nature of light.

The relative refractive index n 21 shows how many times the speed of light V 1 in the first medium differs from the speed of light V 2 in the second medium.

The relative refractive index is a clear demonstration of the fact that the reason for the change in the direction of light when passing from one medium to another is the different speed of light in two media. The term "optical density of a medium" is often used to characterize the optical properties of a medium (Fig. 3).

Rice. 3. Optical density of the medium (α > γ)

If the beam passes from a medium with a higher speed of light to a medium with a lower speed of light, then, as can be seen from Figure 3 and the law of refraction of light, it will be pressed against the perpendicular, that is, the angle of refraction is less than the angle of incidence. In this case, the beam is said to have passed from a less dense optical medium to a more optically dense medium. Example: from air to water; from water to glass.

The reverse situation is also possible: the speed of light in the first medium is less than the speed of light in the second medium (Fig. 4).

Rice. 4. Optical density of the medium (α< γ)

Then the angle of refraction will be greater than the angle of incidence, and such a transition will be said to be made from an optically denser to a less optically dense medium (from glass to water).

The optical density of two media can differ quite significantly, so the situation shown in the photograph (Fig. 5) becomes possible:

Rice. 5. The difference between the optical density of media

Pay attention to how the head is displaced relative to the body, which is in the liquid, in a medium with a higher optical density.

However, the relative refractive index is not always a convenient characteristic for work, because it depends on the speeds of light in the first and second media, but there can be a lot of such combinations and combinations of two media (water - air, glass - diamond, glycerin - alcohol , glass - water and so on). The tables would be very cumbersome, it would be inconvenient to work, and then one absolute environment was introduced, in comparison with which the speed of light in other environments is compared. Vacuum was chosen as the absolute and the speeds of light are compared with the speed of light in vacuum.

Absolute refractive index of the medium n- this is a value that characterizes the optical density of the medium and is equal to the ratio of the speed of light With in vacuum to the speed of light in a given medium.

The absolute refractive index is more convenient for work, because we always know the speed of light in vacuum, it is equal to 3·10 8 m/s and is a universal physical constant.

The absolute refractive index depends on external parameters: temperature, density, and also on the wavelength of light, so tables usually indicate the average refractive index for a given wavelength range. If we compare the refractive indices of air, water and glass (Fig. 6), we see that the refractive index of air is close to unity, so we will take it as a unit when solving problems.

Rice. 6. Table of absolute refractive indices for different media

It is easy to get the relationship between the absolute and relative refractive index of media.

The relative refractive index, that is, for a beam passing from medium one to medium two, is equal to the ratio of the absolute refractive index in the second medium to the absolute refractive index in the first medium.

For example: = ≈ 1.16

If the absolute refractive indices of the two media are almost the same, this means that the relative refractive index during the transition from one medium to another will be equal to one, that is, the light beam will not actually be refracted. For example, when passing from anise oil to a gem, beryl will practically not deviate light, that is, it will behave as it does when passing through anise oil, since their refractive index is 1.56 and 1.57, respectively, so the gem can be how to hide in a liquid, it simply will not be visible.

If you pour water into a transparent glass and look through the wall of the glass into the light, then we will see a silvery sheen of the surface due to the phenomenon of total internal reflection, which will be discussed now. When a light beam passes from a denser optical medium to a less dense optical medium, an interesting effect can be observed. For definiteness, we will assume that light goes from water to air. Let us assume that there is a point source of light S in the depth of the reservoir, emitting rays in all directions. For example, a diver shines a flashlight.

Beam SO 1 falls on the surface of the water at the smallest angle, this beam is partially refracted - beam O 1 A 1 and partially reflected back into the water - beam O 1 B 1. Thus, part of the energy of the incident beam is transferred to the refracted beam, and the remaining part of the energy is transferred to the reflected beam.

Rice. 7. Total internal reflection

Beam SO 2, whose angle of incidence is larger, 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 O 2 A 2 will be dimmer than the beam O 1 A 1, that is, it will receive a smaller fraction of energy, and the reflected beam O 2 V 2, respectively, will be brighter than the beam O 1 V 1, that is, it will receive a larger share of energy. As the angle of incidence increases, the same regularity can be traced - an increasing share of the energy of the incident beam goes to the reflected beam and an ever smaller share to the refracted beam. The refracted beam becomes dimmer and at some point disappears completely, this disappearance occurs when the angle of incidence is reached, which corresponds to a refraction angle of 90 0 . In this situation, the refracted beam OA would have to go parallel to the water surface, but there is nothing to go - all the energy of the incident beam SO went entirely to the reflected beam OB. Naturally, with a further increase in the angle of incidence, the refracted beam will be absent. The described phenomenon is total internal reflection, that is, a denser optical medium at the considered angles does not emit rays from itself, they are all reflected inside it. The angle at which this phenomenon occurs is called limiting angle of total internal reflection.

The value of the limiting angle is easy to find from the law of refraction:

= => = arcsin, for water ≈ 49 0

The most interesting and popular application of the phenomenon of total internal reflection is the so-called waveguides, or fiber optics. This is exactly the way of signaling that is used by modern telecommunications companies on the Internet.

We got the law of refraction of light, introduced a new concept - relative and absolute refractive indices, and also figured out the phenomenon of total internal reflection and its applications, such as fiber optics. You can consolidate knowledge by examining the relevant tests and simulators in the lesson section.

Let's get the proof of the law of refraction of light using the Huygens principle. It is important to understand that the cause of refraction is the difference in the speeds of light in two different media. Let us denote the speed of light in the first medium V 1 , and in the second medium - V 2 (Fig. 8).

Rice. 8. Proof of the law of refraction of light

Let a plane light wave fall on a flat interface between two media, for example, from air into water. The wave surface AC is perpendicular to the rays and , the interface between the media MN first reaches the beam , and the beam reaches the same surface after a time interval ∆t, which will be equal to the path SW divided by the speed of light in the first medium .

Therefore, at the moment when the secondary wave at point B only begins to be excited, the wave from point A already has the form of a hemisphere with radius AD, which is equal to the speed of light in the second medium by ∆t: AD = ∆t, that is, the Huygens principle in visual action . The wave surface of a refracted wave can be obtained by drawing a surface tangent to all secondary waves in the second medium, the centers of which lie on the interface between the media, in this case it is the plane BD, it is the envelope of the secondary waves. The angle of incidence α of the beam is equal to the angle CAB in the triangle ABC, the sides of one of these angles are perpendicular to the sides of the other. Therefore, SW will be equal to the speed of light in the first medium by ∆t

CB = ∆t = AB sin α

In turn, the angle of refraction will be equal to the angle ABD in the triangle ABD, therefore:

AD = ∆t = AB sin γ

Dividing the expressions term by term, we get:

n is a constant value that does not depend on the angle of incidence.

We have obtained the law of refraction of light, the sine of the angle of incidence to the sine of the angle of refraction is a constant value for the given two media and equal to the ratio of the speeds of light in the two given media.

A cubic vessel with opaque walls is located in such a way that the observer's eye does not see its bottom, but completely sees the wall of the vessel CD. How much water must be poured into the vessel so that the observer can see the object F, located at a distance b = 10 cm from the corner D? Vessel edge α = 40 cm (Fig. 9).

What is very important in solving this problem? Guess that since the eye does not see the bottom of the vessel, but sees the extreme point of the side wall, and the vessel is a cube, then the angle of incidence of the beam on the surface of the water when we pour it will be equal to 45 0.

Rice. 9. The task of the exam

The beam falls to point F, which means that we clearly see the object, and the black dotted line shows the course of the beam if there were no water, that is, to point D. From the triangle NFC, the tangent of the angle β, the tangent of the angle of refraction, is the ratio of the opposite leg to the adjacent or, based on the figure, h minus b divided by h.

tg β = = , h is the height of the liquid that we poured;

The most intense phenomenon of total internal reflection is used in fiber optic systems.

Rice. 10. Fiber optics

If a beam of light is directed at the end of a solid glass tube, then after multiple total internal reflection the beam will emerge from the opposite side of the tube. It turns out that the glass tube is a conductor of a light wave or a waveguide. This will happen whether the tube is straight or curved (Figure 10). The first light guides, this is the second name of wave guides, were used to illuminate hard-to-reach places (during medical research, when light is supplied to one end of the light guide, and the other end illuminates the right place). The main application is medicine, defectoscopy of motors, however, such waveguides are most widely used in information transmission systems. The carrier frequency of a light wave is a million times the frequency of a radio signal, which means that the amount of information that we can transmit using a light wave is millions of times greater than the amount of information transmitted by radio waves. This is a great opportunity to convey a huge amount of information in a simple and inexpensive way. As a rule, information is transmitted over a fiber cable using laser radiation. Fiber optics is indispensable for fast and high-quality transmission of a computer signal containing a large amount of transmitted information. And at the heart of all this lies such a simple and common phenomenon as the refraction of light.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemozina, 2012.
2. Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

1. edu.glavsprav.ru ().
2. Nvtc.ee ().
3. Raal100.narod.ru ().
4. Optika.ucoz.ru ().

Homework

1. Define refraction of light.
2. Name the reason for the refraction of light.
3. Name the most popular applications of total internal reflection.

At a certain angle of incidence of light $(\alpha )_(pad)=(\alpha )_(pred)$, which is called limiting angle, the angle of refraction is equal to $\frac(\pi )(2),\ $in this case, the refracted beam slides along the interface between the media, therefore, there is no refracted beam. Then, from the law of refraction, we can write that:

Picture 1.

In the case of total reflection, the equation is:

has no solution in the region of real values ​​of the angle of refraction ($(\alpha )_(pr)$). In this case, $cos((\alpha )_(pr))$ is purely imaginary. If we turn to the Fresnel Formulas, then it is convenient to represent them in the form:

where the angle of incidence is denoted by $\alpha $ (for brevity), $n$ is the refractive index of the medium where the light propagates.

Fresnel formulas show that the modules $\left|E_(otr\bot )\right|=\left|E_(otr\bot )\right|$, $\left|E_(otr//)\right|=\ left|E_(otr//)\right|$ which means the reflection is "full".

Remark 1

It should be noted that the inhomogeneous wave does not disappear in the second medium. Thus, if $\alpha =(\alpha )_0=(arcsin \left(n\right),\ then\ )$ $E_(pr\bot )=2E_(pr\bot ).$ no case. Since the Fresnel formulas are valid for a monochromatic field, that is, for a steady process. In this case, the law of conservation of energy requires that the average change in energy over the period in the second medium be equal to zero. The wave and the corresponding fraction of energy penetrate through the interface into the second medium to a shallow depth of the order of the wavelength and move in it parallel to the interface with a phase velocity that is less than the phase velocity of the wave in the second medium. It returns to the first environment at a point that is offset from the entry point.

The penetration of the wave into the second medium can be observed in the experiment. The intensity of the light wave in the second medium is noticeable only at distances smaller than the wavelength. Near the interface on which the light wave falls, which experiences total reflection, on the side of the second medium, the glow of a thin layer can be seen if there is a fluorescent substance in the second medium.

Total reflection causes mirages to occur when the earth's surface is at a high temperature. So, the total reflection of light that comes from the clouds leads to the impression that there are puddles on the surface of the heated asphalt.

Under normal reflection, the relations $\frac(E_(otr\bot ))(E_(pad\bot ))$ and $\frac(E_(otr//))(E_(pad//))$ are always real. Under total reflection they are complex. This means that in this case the phase of the wave suffers a jump, while it is different from zero or $\pi $. If the wave is polarized perpendicular to the plane of incidence, then we can write:

where $(\delta )_(\bot )$ is the desired phase jump. Equating the real and imaginary parts, we have:

From expressions (5) we obtain:

Accordingly, for a wave that is polarized in the plane of incidence, one can obtain:

Phase jumps $(\delta )_(//)$ and $(\delta )_(\bot )$ are not the same. The reflected wave will be elliptically polarized.

Application of total reflection

Let us assume that two identical media are separated by a thin air gap. A light wave falls on it at an angle that is greater than the limit. It may happen that it will penetrate into the air gap as an inhomogeneous wave. If the gap thickness is small, then this wave will reach the second boundary of the substance and will not be very weakened. Having passed from the air gap into the substance, the wave will turn again into a homogeneous one. Such an experiment was carried out by Newton. The scientist pressed another prism, which was polished spherically, to the hypotenuse face of a rectangular prism. In this case, the light passed into the second prism not only where they touch, but also in a small ring around the contact, in the place where the gap thickness is comparable to the long wavelength. If the observations were made in white light, then the edge of the ring had a reddish color. This is as it should be, since the penetration depth is proportional to the wavelength (for red rays it is greater than for blue ones). By changing the thickness of the gap, it is possible to change the intensity of the transmitted light. This phenomenon formed the basis of the light telephone, which was patented by Zeiss. In this device, a transparent membrane acts as one of the media, which oscillates under the action of sound incident on it. Light that passes through the air gap changes intensity in time with changes in the strength of the sound. Getting on the photocell, it generates an alternating current, which changes in accordance with changes in the strength of the sound. The resulting current is amplified and used further.

The phenomena of wave penetration through thin gaps are not specific to optics. This is possible for a wave of any nature, if the phase velocity in the gap is higher than the phase velocity in the environment. This phenomenon is of great importance in nuclear and atomic physics.

The phenomenon of total internal reflection is used to change the direction of light propagation. For this purpose, prisms are used.

Example 1

Exercise: Give an example of the phenomenon of total reflection, which is often encountered.

Decision:

One can give such an example. If the highway is very hot, then the air temperature is maximum near the asphalt surface and decreases with increasing distance from the road. This means that the refractive index of air is minimal at the surface and increases with increasing distance. As a result of this, rays having a small angle with respect to the highway surface suffer total reflection. If you focus your attention, while driving in a car, on a suitable section of the surface of the highway, you can see a car going upside down quite far ahead.

Example 2

Exercise: What is the Brewster angle for a beam of light that falls on the surface of a crystal if the limiting angle of total reflection for this beam at the air-crystal interface is 400?

Decision:

\[(tg(\alpha )_b)=\frac(n)(n_v)=n\left(2.2\right).\]

From expression (2.1) we have:

We substitute the right side of expression (2.3) into formula (2.2), we express the desired angle:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left((\alpha )_(pred)\right)\ ))\right).\]

Let's do the calculations:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left(40()^\circ \right)\ ))\right)\approx 57()^\circ .\]

Answer:$(\alpha )_b=57()^\circ .$