Define the limiting angle of total internal reflection. Critical angle or limiting angle c and total internal reflection

On the image Ashows a normal ray that passes through the air-Plexiglas interface and exits the Plexiglas plate without undergoing any deflection as it passes through the two boundaries between the Plexiglas and the air. On the image b shows a ray of light entering a semicircular plate normally without deflection, but making an angle y with the normal at point O inside the plexiglass plate. When the beam leaves a denser medium (plexiglass), its speed of propagation in a less dense medium (air) increases. Therefore, it is refracted, making an angle x with respect to the normal in air, which is greater than y.



Based on the fact that n = sin (the angle that the beam makes with the normal in the air) / sin (the angle that the beam makes with the normal in the medium), plexiglass n n = sin x/sin y. If multiple measurements of x and y are made, the refractive index of the plexiglass can be calculated by averaging the results for each pair of values. Angle y can be increased by moving the light source in an arc of a circle centered at point O.

The effect of this is to increase the angle x until the position shown in the figure is reached V, i.e. until x becomes equal to 90 o. It is clear that the angle x cannot be greater. The angle that the ray now makes with the normal inside the plexiglass is called critical or limiting angle with(this is the angle of incidence on the boundary from a denser medium to a less dense one, when the angle of refraction in the less dense medium is 90°).

A weak reflected beam is usually observed, as is a bright beam that is refracted along the straight edge of the plate. This is a consequence of partial internal reflection. Note also that when white light is used, the light appearing along the straight edge is split into the colors of the spectrum. If the light source is moved further around the arc, as in the figure G, so that I inside the plexiglass becomes greater than the critical angle c and refraction does not occur at the boundary of the two media. Instead, the beam experiences total internal reflection at an angle r with respect to the normal, where r = i.

To make it happen total internal reflection, the angle of incidence i must be measured inside a denser medium (plexiglass) and it must be greater than the critical angle c. Note that the law of reflection is also valid for all angles of incidence greater than the critical angle.

Diamond critical angle is only 24°38". Its "flare" therefore depends on the ease with which multiple total internal reflection occurs when it is illuminated by light, which depends largely on the skillful cutting and polishing which enhances this effect. Previously it was it is determined that n = 1 /sin c, so an accurate measurement of the critical angle c will determine n.

Study 1. Determine n for plexiglass by finding the critical angle

Place a half-circle piece of plexiglass in the center of a large piece of white paper and carefully trace its outline. Find the midpoint O of the straight edge of the plate. Using a protractor, construct a normal NO perpendicular to this straight edge at point O. Place the plate again in its outline. Move the light source around the arc to the left of NO, all the time directing the incident ray to point O. When the refracted ray goes along the straight edge, as shown in the figure, mark the path of the incident ray with three points P 1, P 2, and P 3.



Temporarily remove the plate and connect these three points with a straight line that should pass through O. Using a protractor, measure the critical angle c between the drawn incident ray and the normal. Carefully place the plate again in its outline and repeat what was done before, but this time move the light source around the arc to the right of NO, continuously directing the beam to point O. Record the two measured values ​​of c in the results table and determine the average value of the critical angle c. Then determine the refractive index n n for plexiglass using the formula n n = 1 /sin s.


The apparatus for Study 1 can also be used to show that for light rays propagating in a denser medium (Plexiglas) and incident on the Plexiglas-air interface at angles greater than the critical angle c, the angle of incidence i is equal to the angle reflections r.

Study 2. Check the law of light reflection for angles of incidence greater than the critical angle

Place the semi-circular plexiglass plate on a large piece of white paper and carefully trace its outline. As in the first case, find the midpoint O and construct the normal NO. For plexiglass, the critical angle c = 42°, therefore, angles of incidence i > 42° are greater than the critical angle. Using a protractor, construct rays at angles of 45°, 50°, 60°, 70° and 80° to the normal NO.

Carefully place the plexiglass plate back into its outline and direct the light beam from the light source along the 45° line. The beam will go to point O, be reflected and appear on the arcuate side of the plate on the other side of the normal. Mark three points P 1, P 2 and P 3 on the reflected ray. Temporarily remove the plate and connect the three points with a straight line that should pass through point O.



Using a protractor, measure the angle of reflection r between and the reflected ray, recording the results in a table. Carefully place the plate into its outline and repeat for angles of 50°, 60°, 70° and 80° to the normal. Record the value of r in the appropriate space in the results table. Plot a graph of the angle of reflection r versus the angle of incidence i. A straight line graph drawn over the range of incidence angles from 45° to 80° will be sufficient to show that angle i is equal to angle r.

We pointed out in § 81 that when light falls on the interface between two media, the light energy is divided into two parts: one part is reflected, the other part penetrates through the interface into the second medium. Using the example of the transition of light from air to glass, i.e. from a medium that is optically less dense to a medium that is optically denser, we saw that the proportion of reflected energy depends on the angle of incidence. In this case, the fraction of reflected energy increases greatly as the angle of incidence increases; however, even at very large angles of incidence, close to , when the light beam almost slides along the interface, some of the light energy still passes into the second medium (see §81, tables 4 and 5).

A new interesting phenomenon arises if light propagating in any medium falls on the interface between this medium and a medium that is optically less dense, that is, having a lower absolute refractive index. Here, too, the fraction of reflected energy increases with increasing angle of incidence, but the increase follows a different law: starting from a certain angle of incidence, all light energy is reflected from the interface. This phenomenon is called total internal reflection.

Let us consider again, as in §81, the incidence of light at the interface between glass and air. Let a light beam fall from the glass onto the interface at different angles of incidence (Fig. 186). If we measure the fraction of reflected light energy and the fraction of light energy passing through the interface, we obtain the values ​​given in Table. 7 (glass, like in Table 4, had a refractive index ).

Rice. 186. Total internal reflection: the thickness of the rays corresponds to the fraction of light energy charged or passed through the interface

The angle of incidence from which all light energy is reflected from the interface is called the limiting angle of total internal reflection. For the glass for which the table was compiled. 7 (), the limiting angle is approximately .

Table 7. Fractions of reflected energy for various angles of incidence when light passes from glass to air

Let us note that when light is incident on the interface at a limiting angle, the angle of refraction is equal to , i.e., in the formula expressing the law of refraction for this case,

when we have to put or . From here we find

At angles of incidence greater than that, there is no refracted ray. Formally, this follows from the fact that at angles of incidence large from the law of refraction for, values ​​larger than unity are obtained, which is obviously impossible.

In table Table 8 shows the limiting angles of total internal reflection for some substances, the refractive indices of which are given in table. 6. It is easy to verify the validity of relation (84.1).

Table 8. Limiting angle of total internal reflection at the boundary with air

Total internal reflection can be observed at the boundary of air bubbles in water. They shine because the sunlight falling on them is completely reflected without passing into the bubbles. This is especially noticeable in those air bubbles that are always present on the stems and leaves of underwater plants and which in the sun appear to be made of silver, that is, from a material that reflects light very well.

Total internal reflection finds application in the design of glass rotating and turning prisms, the action of which is clear from Fig. 187. The limiting angle for a prism is depending on the refractive index of a given type of glass; Therefore, the use of such prisms does not encounter any difficulties with regard to the selection of the angles of entry and exit of light rays. Rotating prisms successfully perform the functions of mirrors and are advantageous in that their reflective properties remain unchanged, whereas metal mirrors fade over time due to oxidation of the metal. It should be noted that the wrapping prism is simpler in design than the equivalent rotating system of mirrors. Rotating prisms are used, in particular, in periscopes.

Rice. 187. Path of rays in a glass rotating prism (a), a wrapping prism (b) and in a curved plastic tube - light guide (c)

Geometric and wave optics. Conditions for using these approaches (based on the relationship between wavelength and object size). Wave coherence. The concept of spatial and temporal coherence. Stimulated 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 light beam does not propagate in any one direction, but has a finite angular distribution, i.e. diffraction occurs. However, in cases where the characteristic transverse dimensions of light beams are large enough compared to the wavelength, we 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. Wave optics phenomena - interference, diffraction, polarization, etc.

Wave interference is the mutual strengthening or weakening of the amplitude of two or more coherent waves simultaneously propagating in space.

Wave diffraction is a phenomenon that manifests itself as a deviation from the laws of geometric optics during wave propagation.

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 their phase difference is constant over time and when adding the oscillations, an oscillation of the same frequency is obtained.

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

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

Stimulated emission is 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 constant power, or pulsed, reaching extremely high peak powers. In some schemes, the laser working element is used as an optical amplifier for radiation from another source.

The physical basis for laser operation is the phenomenon of forced (induced) radiation. The essence of the phenomenon is that an excited atom is capable of emitting 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 with the photon that caused the radiation (it is its “exact copy”). This way the light is amplified. This phenomenon differs from spontaneous radiation, in which the emitted photons have random propagation directions, 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 amplifier mode).

Each of them ensures that the laser performs 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 when light passes through optical systems without taking into account its wave properties.

Total internal reflection is 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 reflectance of total internal reflection is independent of wavelength.

Limiting angle of total internal reflection

Angle of incidence at which a refracted beam begins to slide along the interface between two media without transitioning to an optically denser medium

Ray path in mirrors, prisms and lenses

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

Fiber optics - this term means

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

products from precision engineering industries that contain 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 imagine a little. Imagine a hot summer day BC, a primitive man uses a spear to hunt fish. He notices its position, takes aim and strikes for some reason in a place not at all where the fish was visible. Missed? No, the fisherman has 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 lowered 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 topic of which is: “Refraction of light. The law of light refraction. Complete internal reflection."

In previous lessons, we talked about the fate of a beam in two cases: what happens if a beam of light propagates in a transparently homogeneous medium? The correct answer is that it will spread in a straight line. What happens 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 look at that part of the light beam that is absorbed by the medium.

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

Rice. 1. Refraction of light

If a 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 into the second medium and, as a rule, changes its direction.

The change in the direction of propagation of light when it passes 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 ray that will set the direction of the refracted beam of light will be called a refracted ray. The angle between the perpendicular to the interface, reconstructed from the point of incidence, and the refracted ray is called the angle of refraction; in the figure it is the angle γ. To complete the picture, we will 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 what medium the beam passed into, what the angle of refraction will be? It turns out it is possible!

We obtain a law that quantitatively describes the relationship between the angle of incidence and the angle of refraction. Let's use Huygens' principle, which regulates the propagation of waves 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, in honor of the Dutch scientist who first formulated it. The reason for refraction is the difference in the speed 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 ratio of the sines of these angles, we will be convinced that the law of refraction is indeed valid.

Proof of the law of refraction using 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 light changes direction when passing from one medium to another is the different speed of light in the two media. The concept of “optical density of the medium” is often used to characterize the optical properties of a medium (Fig. 3).

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

If a ray 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 opposite 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 more dense to a less optically dense medium (from glass to water).

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

Rice. 5. Differences in optical density of media

Notice how the head is displaced relative to the body in the liquid, in an environment with higher optical density.

However, the relative refractive index is not always a convenient characteristic to work with, because it depends on the speed 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 they introduced one absolute medium, in comparison with which the speed of light in other environments is compared. Vacuum was chosen as an absolute and the speed of light was compared with the speed of light in vacuum.

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

The absolute refractive index is more convenient for work, because we always know the speed of light in a 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, therefore 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 air has a refractive index close to unity, so we will take it as unity when solving problems.

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

It is not difficult to obtain a relationship between the absolute and relative refractive index of media.

The relative refractive index, that is, for a ray 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 two media are almost the same, this means that the relative refractive index when passing from one medium to another will be equal to unity, that is, the light ray will actually not be refracted. For example, when passing from anise oil to a beryl gemstone, the light will practically not bend, that is, it will behave the same as when passing through anise oil, since their refractive index is 1.56 and 1.57 respectively, so the gemstone can be as if hidden in a liquid, it simply won’t be visible.

If we pour water into a transparent glass and look through the wall of the glass into the light, we will see a silvery sheen on 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 comes from water into air. Let us assume that in the depths of the reservoir there is a point source of light S, emitting rays in all directions. For example, a diver shines a flashlight.

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

Rice. 7. Total internal reflection

The SO 2 beam, whose angle of incidence is greater, is also divided into two beams: refracted and reflected, but the energy of the original beam is distributed between them differently: the refracted beam O 2 A 2 will be dimmer than the O 1 A 1 beam, that is, it will receive a smaller share of energy, and the reflected beam O 2 B 2, accordingly, will be brighter than the beam O 1 B 1, that is, it will receive a larger share of energy. As the angle of incidence increases, the same pattern is observed - an increasingly larger share of the energy of the incident beam goes to the reflected beam and a smaller and smaller share to the refracted beam. The refracted beam becomes dimmer and dimmer and at some point disappears completely; this disappearance occurs when it reaches the angle of incidence, which corresponds to the angle of refraction of 90 0. In this situation, the refracted beam OA should have gone parallel to the surface of the water, but there was nothing left 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 can be easily found 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 method of sending signals that is used by modern telecommunications companies on the Internet.

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

Let us obtain a proof of the law of light refraction using Huygens' principle. It is important to understand that the cause of refraction is the difference in the speed of light in two different media. Let us denote the speed of light in the first medium as V 1, and in the second medium as 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 AS is perpendicular to the rays and, the interface between the media MN is first reached by the ray, and the ray reaches the same surface after a time interval ∆t, which will be equal to the path of SW divided by the speed of light in the first medium.

Therefore, at the moment of time when the secondary wave at point B just 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 at ∆t: AD = ·∆t, that is, 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 at the interface between the media, in this case this 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. Consequently, SV 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 angle ABD in triangle ABD, therefore:

АD = ∆t = АВ 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 light refraction, the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media and is equal to the ratio of the speeds of light in the two given media.

A cubic vessel with opaque walls is positioned so that the eye of the observer 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 an object F located at a distance b = 10 cm from angle D? Vessel edge α = 40 cm (Fig. 9).

What is very important when 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, 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. Unified State Examination task

The beam falls at point F, this 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 NFK, the tangent of the angle β, the tangent of the angle of refraction, is the ratio of the opposite side 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 optical 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 come out 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 regardless of whether the tube is straight or curved (Figure 10). The first light guides, this is the second name for waveguides, 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 desired place). The main application is medicine, flaw detection of motors, but such waveguides are most widely used in information transmission systems. The carrier frequency when transmitting a signal by a light wave is a million times higher than 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 wealth of information in a simple and inexpensive way. Typically, information is transmitted through 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 the basis of all this is such a simple and ordinary phenomenon as the refraction of light.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemosyne, 2012.
2. Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - 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 the refraction of light.
2. Name the reason for the refraction of light.
3. Name the most popular applications of total internal reflection.

When waves propagate in a medium, including electromagnetic ones, to find a new wave front at any time, use Huygens' principle.

Each point on the wave front is a source of secondary waves.

In a homogeneous isotropic medium, the wave surfaces of secondary waves have the form of spheres of radius v×Dt, where v is the speed of wave propagation in the medium. By drawing the envelope of the wave fronts of the secondary waves, we obtain a new wave front at a given moment in time (Fig. 7.1, a, b).

Law of Reflection

Using Huygens' principle, it is possible to prove the law of reflection of electromagnetic waves at the interface between two dielectrics.

The angle of incidence is equal to the angle of reflection. The incident and reflected rays, together with the perpendicular to the interface between the two dielectrics, lie in the same plane.Ð a = Ð b. (7.1)

Let a plane light wave (rays 1 and 2, Fig. 7.2) fall on a flat LED interface between two media. The angle a between the beam and the perpendicular to the LED is called the angle of incidence. If at a given moment in time the front of the incident OB wave reaches point O, then according to Huygens’ principle this point

Rice. 7.2

begins to emit a secondary wave. During the time Dt = VO 1 /v, the incident beam 2 reaches point O 1. During the same time, the front of the secondary wave, after reflection in point O, propagating in the same medium, reaches points of the hemisphere with radius OA = v Dt = BO 1. The new wave front is depicted by the plane AO ​​1, and the direction of propagation by the ray OA. Angle b is called the angle of reflection. From the equality of triangles OAO 1 and OBO 1, the law of reflection follows: the angle of incidence is equal to the angle of reflection.

Law of refraction

An optically homogeneous medium 1 is characterized by , (7.2)

Ratio n 2 / n 1 = n 21 (7.4)

called

(7.5)

For vacuum n = 1.

Due to dispersion (light frequency n » 10 14 Hz), for example, for water n = 1.33, and not n = 9 (e = 81), as follows from electrodynamics for low frequencies. If the speed of light propagation in the first medium is v 1, and in the second - v 2,

Rice. 7.3

then during the time Dt the incident plane wave travels the distance AO 1 in the first medium AO 1 = v 1 Dt. The front of the secondary wave, excited in the second medium (in accordance with Huygens' principle), reaches points of the hemisphere, the radius of which OB = v 2 Dt. The new front of the wave propagating in the second medium is represented by the BO 1 plane (Fig. 7.3), and the direction of its propagation by the rays OB and O 1 C (perpendicular to the wave front). Angle b between the ray OB and the normal to the interface between two dielectrics at point O called the angle of refraction. From the triangles OAO 1 and OBO 1 it follows that AO 1 = OO 1 sin a, OB = OO 1 sin b.

Their attitude expresses law of refraction(law Snell):

. (7.6)

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the relative refractive index of the two media.

Total internal reflection

Rice. 7.4

According to the law of refraction, at the interface between two media one can observe total internal reflection, if n 1 > n 2, i.e. Ðb > Ða (Fig. 7.4). Consequently, there is a limiting angle of incidence Ða pr when Ðb = 90 0 . Then the law of refraction (7.6) takes the following form:

sin a pr = , (sin 90 0 =1) (7.7)

With a further increase in the angle of incidence Ða > Ða pr, the light is completely reflected from the interface between the two media.

This phenomenon is called total internal reflection and are widely used in optics, for example, to change the direction of light rays (Fig. 7.5, a, b).

It is used in telescopes, binoculars, fiber optics and other optical instruments.

In classical wave processes, such as the phenomenon of total internal reflection of electromagnetic waves, phenomena similar to the tunnel effect in quantum mechanics are observed, which is associated with the wave-corpuscular properties of particles.

Indeed, when light passes from one medium to another, refraction of light is observed, associated with a change in the speed of its propagation in different media. At the interface between two media, a light beam is divided into two: refracted and reflected.

A ray of light falls perpendicularly onto face 1 of a rectangular isosceles glass prism and, without refraction, falls on face 2, total internal reflection is observed, since the angle of incidence (Ða = 45 0) of the beam on face 2 is greater than the limiting angle of total internal reflection (for glass n 2 = 1.5; Ða pr = 42 0).

If the same prism is placed at a certain distance H ~ l/2 from face 2, then a ray of light will pass through face 2 * and exit the prism through face 1 * parallel to the ray incident on face 1. The intensity J of the transmitted light flux decreases exponentially with increasing the gap h between the prisms according to the law:

,

where w is a certain probability of the beam passing into the second medium; d is the coefficient depending on the refractive index of the substance; l is the wavelength of the incident light

Therefore, the penetration of light into the “forbidden” region is an optical analogue of the quantum tunneling effect.

The phenomenon of total internal reflection is truly complete, since in this case all the energy of the incident light is reflected at the interface between two media than when reflected, for example, from the surface of metal mirrors. Using this phenomenon, one can trace another analogy between the refraction and reflection of light, on the one hand, and Vavilov-Cherenkov radiation, on the other hand.

WAVE INTERFERENCE

7.2.1. The role of vectors and

In practice, several waves can propagate simultaneously in real media. As a result of the addition of waves, a number of interesting phenomena are observed: interference, diffraction, reflection and refraction of waves etc.

These wave phenomena are characteristic not only of mechanical waves, but also electrical, magnetic, light, etc. All elementary particles also exhibit wave properties, which has been proven by quantum mechanics.

One of the most interesting wave phenomena, which is observed when two or more waves propagate in a medium, is called interference. An optically homogeneous medium 1 is characterized by absolute refractive index , (7.8)

where c is the speed of light in vacuum; v 1 - speed of light in the first medium.

Medium 2 is characterized by the absolute refractive index

where v 2 is the speed of light in the second medium.

Attitude (7.10)

called the relative refractive index of the second medium relative to the first. For transparent dielectrics in which m = 1, using Maxwell's theory, or

where e 1, e 2 are the dielectric constants of the first and second media.

For vacuum n = 1. Due to dispersion (light frequency n » 10 14 Hz), for example, for water n = 1.33, and not n = 9 (e = 81), as follows from electrodynamics for low frequencies. Light is electromagnetic waves. Therefore, the electromagnetic field is determined by the vectors and , which characterize the strengths of the electric and magnetic fields, respectively. However, in many processes of interaction of light with matter, for example, such as the effect of light on the organs of vision, photocells and other devices, the decisive role belongs to the vector, which in optics is called the light vector.