Reflection of light. Law of Light Reflection

Some laws of physics are difficult to imagine without the use of visual aids. This does not apply to the usual light falling on various objects. Thus, at the boundary separating two media, a change in the direction of light rays occurs if this boundary is much higher. Light occurs when part of its energy returns to the first medium. If some of the rays penetrate into another medium, then they are refracted. In physics, energy falling on the boundary of two different media is called incident, and energy that returns from it to the first medium is called reflected. It is the relative position of these rays that determines the laws of reflection and refraction of light.

Terms

The angle between the incident beam and the perpendicular line to the interface between the two media, restored to the point of incidence of the light energy flow, is called. There is another important indicator. This is the angle of reflection. It occurs between the reflected ray and the perpendicular line restored to the point of its incidence. Light can propagate in a straight line only in a homogeneous medium. Different media absorb and reflect light differently. Reflectance is a quantity that characterizes the reflectivity of a substance. It shows how much energy brought by light radiation to the surface of a medium will be that which is carried away from it by reflected radiation. This coefficient depends on a variety of factors, some of the most important being the angle of incidence and the composition of the radiation. Complete reflection of light occurs when it falls on objects or substances with a reflective surface. For example, this happens when rays hit a thin film of silver and liquid mercury deposited on glass. Total reflection of light occurs quite often in practice.

Laws

The laws of reflection and refraction of light were formulated by Euclid back in the 3rd century. BC e. All of them were established experimentally and are easily confirmed by the purely geometric principle of Huygens. According to him, any point in the medium to which a disturbance reaches is a source of secondary waves.

First light: the incident and reflecting beam, as well as the perpendicular line to the interface, reconstructed at the point of incidence of the light beam, are located in the same plane. A plane wave is incident on a reflective surface, the wave surfaces of which are stripes.

Another law states that the angle of reflection of light is equal to the angle of incidence. This happens because they have mutually perpendicular sides. Based on the principles of equality of triangles, it follows that the angle of incidence is equal to the angle of reflection. It can be easily proven that they lie in the same plane with the perpendicular line restored to the interface at the point of incidence of the beam. These most important laws are also valid for the reverse path of light. Due to the reversibility of energy, a ray propagating along the path of the reflected one will be reflected along the path of the incident one.

Properties of reflecting bodies

The vast majority of objects only reflect the light radiation incident on them. However, they are not a source of light. Well-lit bodies are clearly visible from all sides, since radiation from their surface is reflected and scattered in different directions. This phenomenon is called diffuse (scattered) reflection. It occurs when light hits any rough surface. To determine the path of the beam reflected from the body at the point of its incidence, a plane is drawn that touches the surface. Then the angles of incidence of rays and reflection are constructed in relation to it.

Diffuse reflection

It is only due to the existence of scattered (diffuse) reflection of light energy that we distinguish objects that are not capable of emitting light. Any body will be absolutely invisible to us if the scattering of rays is zero.

Diffuse reflection of light energy does not cause unpleasant sensations in the eyes. This occurs because not all the light returns to the original medium. So about 85% of the radiation is reflected from snow, 75% from white paper, and only 0.5% from black velor. When light is reflected from various rough surfaces, the rays are directed randomly in relation to each other. Depending on the extent to which surfaces reflect light rays, they are called matte or mirror. But still, these concepts are relative. The same surfaces can be mirrored or matte at different wavelengths of incident light. A surface that evenly scatters rays in different directions is considered completely matte. Although there are practically no such objects in nature, unglazed porcelain, snow, and drawing paper are very close to them.

Mirror reflection

Specular reflection of light rays differs from other types in that when energy beams fall on a smooth surface at a certain angle, they are reflected in one direction. This phenomenon is familiar to anyone who has ever used a mirror under rays of light. In this case it is a reflective surface. Other bodies also fall into this category. All optically smooth objects can be classified as mirror (reflective) surfaces if the size of inhomogeneities and irregularities on them is less than 1 micron (does not exceed the wavelength of light). For all such surfaces, the laws of light reflection apply.

Reflection of light from different mirror surfaces

In technology, mirrors with a curved reflective surface (spherical mirrors) are often used. Such objects are bodies shaped like a spherical segment. The parallelism of rays in the case of light reflection from such surfaces is greatly disrupted. There are two types of such mirrors:

Concave - reflect light from the inner surface of a segment of a sphere; they are called collecting, since parallel rays of light, after reflection from them, are collected at one point;

Convex - reflect light from the outer surface, while parallel rays are scattered to the sides, which is why convex mirrors are called scattering.

Options for reflecting light rays

A beam incident almost parallel to the surface touches it only slightly, and then is reflected at a very obtuse angle. Then it continues along a very low trajectory, closest to the surface. A beam falling almost vertically is reflected at an acute angle. In this case, the direction of the already reflected beam will be close to the path of the incident beam, which is fully consistent with physical laws.

Light refraction

Reflection is closely related to other phenomena of geometric optics, such as refraction and total internal reflection. Often light passes through the boundary between two media. Refraction of light is the change in direction of optical radiation. It occurs when it passes from one environment to another. The refraction of light has two patterns:

The beam passing through the boundary between the media is located in a plane that passes through the perpendicular to the surface and the incident beam;

The angle of incidence and refraction are related.

Refraction is always accompanied by reflection of light. The sum of the energies of the reflected and refracted beams of rays is equal to the energy of the incident beam. Their relative intensity depends on the incident beam and the angle of incidence. The design of many optical instruments is based on the laws of light refraction.

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 media 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

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

Edu.glavsprav.ru ().
Nvtc.ee ().
Raal100.narod.ru ().
Optika.ucoz.ru ().

Homework

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

At a certain angle of incidence of light $(\alpha )_(pad)=(\alpha )_(pred)$, which is called limit angle, the angle of refraction is equal to $\frac(\pi )(2),\ $in this case the refracted ray slides along the interface between the media, therefore, there is no refracted ray. 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 refraction angle ($(\alpha )_(pr)$). In this case, $cos((\alpha )_(pr))$ is a purely imaginary quantity. If we turn to the Fresnel Formulas, it is convenient to present them in the form:

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

Note 1

It should be noted that the inhomogeneous wave does not disappear in the second medium. So, if $\alpha =(\alpha )_0=(arcsin \left(n\right),\ then\ )$ $E_(pr\bot )=2E_(pr\bot ).$ Violations of the law of conservation of energy in a given case no. Since Fresnel's formulas are valid for a monochromatic field, that is, for a steady-state 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 penetrates through the interface into the second medium to a small depth of the order of the wavelength and moves 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 medium at a point that is offset relative to the entry point.

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

Total reflection causes mirages to occur when the earth's surface is hot. Thus, the complete reflection of light that comes from clouds leads to the impression that there are puddles on the surface of heated asphalt.

Under ordinary reflection, the relations $\frac(E_(otr\bot ))(E_(pad\bot ))$ and $\frac(E_(otr//))(E_(pad//))$ are always real. At full reflection they are complex. This means that in this case the phase of the wave undergoes 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. Let us equate 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:

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

Applying 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 limiting one. It may happen that it penetrates the air gap as a non-uniform wave. If the thickness of the gap 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 back into a homogeneous one. Such an experiment was carried out by Newton. The scientist pressed another prism, which was ground spherically, to the hypotenuse face of the 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 a place where the thickness of the gap is comparable to the wavelength. If observations were carried out 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, you can change the intensity of the transmitted light. This phenomenon formed the basis of the light telephone, which was patented by Zeiss. In this device, one of the media is a transparent membrane, which vibrates under the influence of sound falling on it. Light that passes through an air gap changes intensity in time with changes in sound intensity. When it hits a photocell, it generates alternating current, which changes in accordance with changes in sound intensity. 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. Prisms are used for this purpose.

Example 1

Exercise: Give an example of the phenomenon of total reflection, which occurs frequently.

Solution:

We can give the following 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 that have a small angle relative to the highway surface are completely reflected. If you concentrate your attention, while driving in a car, on a suitable section of the highway surface, you can see a car driving quite far ahead upside down.

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 a given beam at the air-crystal interface is 400?

Solution:

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

From expression (2.1) we have:

Let's substitute the right side of expression (2.3) into formula (2.2) and express the desired angle:

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

Let's carry out the calculations:

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

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

Class: 11

Presentation for the lesson

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Lesson objectives:

Educational:

Students must repeat and generalize the knowledge acquired while studying the topic “Reflection and refraction of light”: the phenomenon of rectilinear propagation of light in a homogeneous medium, the law of reflection, the law of refraction, the law of total reflection.
Consider the application of laws in science, technology, optical instruments, medicine, transport, construction, everyday life, the world around us,
Be able to apply the acquired knowledge when solving qualitative, computational and experimental problems;

Educational:

broaden students' horizons, develop logical thinking and intelligence;
be able to make comparisons and make inputs;
develop monologue speech, be able to speak in front of an audience.
teach how to obtain information from additional literature and the Internet, and analyze it.

Educational:

instill interest in the subject of physics;
teach independence, responsibility, confidence;
create a situation of success and friendly support during the lesson.

Equipment and visual aids:

Geometric optics device, mirrors, prisms, reflectors, binoculars, fiber optics, experimental instruments.
Computer, video projector, screen, presentation “Practical application of the laws of reflection and refraction of light”

Lesson plan.

I. Topic and purpose of the lesson (2 minutes)

II. Repetition (frontal survey) – 4 minutes

III. Application of straightness of light propagation. Problem (at the board). - 5 minutes

IV. Application of the law of light reflection. - 4 minutes

V. Application of the law of refraction of light:

1) Experience - 4 minutes

2) Task - 5 minutes

VI Application of total internal reflection of light:

a) Optical instruments – 4 minutes.

c) Fiber optics – 4 minutes.

VII Mirages - 4 minutes

VIII.Independent work – 7 min.

IX Summing up the lesson. Homework – 2 min.

Total: 45 min

During the classes

I. Lesson topic, goal, objectives, content . (Slide1-2)

Epigraph. (Slide 3)

A wonderful gift of eternal nature,
A priceless and holy gift,
It has an endless source
Enjoying beauty:
The sky, the sun, the radiance of stars,
The sea in brilliant blue -
The whole picture of the universe
We know only in the light.
I.A.Bunin

II. Repetition

Teacher:

a) Geometric optics. (Slides 4-7)

Light propagates in a straight line in a homogeneous medium. Or in a homogeneous medium, light rays are straight lines

The line along which light energy travels is called a ray. The straightness of light propagation at a speed of 300,000 km/s is used in geometric optics.

Example: It is used when checking the straightness of a planed board using a beam.

The ability to see non-luminous objects is due to the fact that every body partially reflects and partially absorbs the light falling on it. (Moon). A medium in which the speed of light propagation is slower is an optically denser medium. Light refraction is the change in direction of a light ray when crossing a boundary between media. The refraction of light is explained by the difference in the speed of propagation of light when passing from one medium to another

b) Demonstration of the phenomenon of reflection and refraction on the “Optical disk” device

c) Questions for repetition. (Slide 8)

III. Application of straightness of light propagation. Problem (at the board).

a) Formation of shadow and penumbra. (Slide 9).

The straightness of light propagation explains the formation of shadow and penumbra. If the size of the source is small or if the source is located at a distance in comparison with which the size of the source can be neglected, only a shadow is obtained. When the light source is large or if the source is close to the subject, unsharp shadows (umbra and penumbra) are created.

b) Illumination of the Moon. (Slide 10).

The Moon, on its way around the Earth, is illuminated by the Sun; it itself does not glow.

1. new moon, 3. first quarter, 5. full moon, 7. last quarter.

c) Application of straightness of light propagation in construction, in the construction of roads and bridges. (Slides 11-14)

d) Problem No. 1352 (D) (student at the blackboard). The length of the shadow from the Ostankino television tower, illuminated by the sun, at some point in time turned out to be equal to 600 m; the length of the shadow from a person with a height of 1.75 m at the same moment in time was equal to 2 m. What is the height of the tower? (Slide 15-16)

Conclusion: Using this principle, you can determine the height of an inaccessible object: the height of the house; the height of the cliff; the height of a tall tree.

e) Questions for repetition. (Slide 17)

IV. Application of the law of light reflection. (Slides 18-21).

a) Mirrors (Student's message).

Light that meets any object on its way is reflected from its surface. If it is not smooth, then reflection occurs in many directions and the light is scattered. When the surface is smooth, then all the rays depart from it parallel to each other and a specular reflection is obtained. This is how light is usually reflected from the free surface of resting liquids and from mirrors. Mirrors can have different shapes. They are flat, spherical, cyoyndric, parabolic, etc. Light emanating from an object spreads in the form of rays, which, falling on the mirror, are reflected. If after this they again gather at some point, they say that the action of the image of the object arose at that point. If the rays remain separated, but at some point their extensions converge, then it seems to us that the rays emanate from it, and that is where the object is located. This is the so-called virtual image, which is created in the imagination of observation. With the help of concave mirrors, you can project an image onto some surface or collect weak light coming from a distant object at one point, as happens when observing stars using a reflecting telescope. In both cases, the image is real, other mirrors are used to see the object in life-size (ordinary flat mirrors), enlarged (such mirrors are carried in a handbag) or reduced (rear-view mirrors in cars). The resulting images are imaginary (virtual). And with the help of curved, non-spherical mirrors you can make the image distorted.

V. Application of the law of refraction of light. (Slides 22-23).

a) Path of rays in a glass plate .

b) Path of rays in a triangular prism . Construct and explain. (Student at the blackboard)

c) Experience: Application of the law of refraction. (Student's message.) (Slides 24)

Inexperienced bathers are often exposed to great danger simply because they forget about one curious consequence of the law of refraction of light. They do not know that refraction seems to lift all objects immersed in water above their true position. The bottom of a pond, river, or reservoir appears to the eye to be raised by almost a third of its depth. It is especially important to know this for children and short people in general, for whom an error in determining the depth can be fatal. The reason is the refraction of light rays.

Experience: Place a coin at the bottom of the cup in front of the students like this. so that it is not visible to the student. Ask him, without turning his head, to pour water into a cup, then the coin will “float up”. If you remove water from the cup with a syringe, the bottom with the coin will “go down” again. Explain the experience. Carry out the experiment for everyone at home.

G) Task. The true depth of the reservoir area is 2 meters. What is the apparent depth for a person looking at the bottom at an angle of 60° to the surface of the water. The refractive index of water is 1.33. (Slides 25-26).

e) Questions for review . (Slide 27-28).

VI. Total internal reflection. Optical instruments

a) Total internal reflection. Optical instruments . (Student message)

(Slides 29-35)

Total internal reflection occurs when light strikes the boundary between an optically denser medium and a less dense medium. Total internal reflection is used in many optical devices. The limiting angle for glass is 35°-40° depending on the refractive index of a given type of glass. Therefore, in 45° prisms, light will experience total internal reflection.

Question. Why are revolving and rotating prisms better to use than mirrors?

a) They reflect almost 100 light, since the best mirrors reflect less than 100. The image is brighter.

c) Their properties remain unchanged since metal mirrors fade over time due to oxidation of the metal.

Application. Rotating prisms are used in periscopes. Reversible prisms are used in binoculars. In transport, a corner reflector is used - a reflector; it is fixed at the back - red, at the front - white, on the spokes of bicycle wheels - orange. A retroreflector or optical device that reflects light back to the source illuminating it, regardless of the angle of incidence of the light on the surface. All vehicles and dangerous sections of roads are equipped with them. Made from glass or plastic.

b) Questions for repetition. (Slide 36).

c) Fiber optics . (Student message). (Slides 37-42).

Fiber optics is based on total internal reflection of light. The fibers are either glass or plastic. Their diameter is very small - a few micrometers. A bundle of these thin fibers is called a light guide; light moves along it almost without loss, even if the light guide is given a complex shape. This is used in decorative lamps, for illuminating jets in fountains.

Light guides are used to transmit signals in telephone and other types of communications. The signal is a modulated light beam and is transmitted with less loss than when transmitting an electrical signal through copper wires.

Light guides are used in medicine to transmit clear images. By inserting an “endoscope” through the esophagus, the doctor is able to examine the walls of the stomach. Some fibers send light to illuminate the stomach, while others carry reflected light. The more fibers and the thinner they are, the better the image. An endoscope is useful when examining the stomach and other hard-to-reach areas, when preparing a patient for surgery, or when looking for injuries and damage without surgery.

In the light guide, light is completely reflected from the inner surface of the glass or transparent plastic fiber. There are lenses at each end of the light guide. At the end facing the object. the lens turns the rays emanating from it into a parallel beam. At the end facing the observer there is a telescope that allows you to view the image.

VII. Mirages. (Student tells, teacher completes) (Slides 43-46).

Napoleon's French army encountered a mirage in Egypt in the 18th century. The soldiers saw a “lake with trees” ahead. Mirage is a French word that means “to reflect as in a mirror.” The sun's rays pass through the air mirror, giving rise to “miracles”. If the earth is well heated, then the lower layer of air is much warmer than the layers located above.

Mirage is an optical phenomenon in a clear, calm atmosphere with varying temperatures of its individual layers, consisting in the fact that invisible objects located beyond the horizon are reflected in a refracted form in the air.

Therefore, the sun's rays, penetrating the air layer, never travel straight, but are curved. This phenomenon is called refraction.

Mirage has many faces. It can be simple, complex, upper, lower, side.

When the lower layers of air are well heated, an inferior mirage is observed - an imaginary inverted image of objects. This happens most often in steppes and deserts. This type of mirage can be seen in Central Asia, Kazakhstan, and the Volga region.

If the ground layers of air are much colder than the upper ones, then an upper mirage occurs - the image comes off the ground and hangs in the air. Objects appear closer and higher than they really are. This type of mirage is observed in the early morning, when the sun's rays have not yet had time to warm the Earth.

On the surface of the sea on hot days, sailors see ships suspended in the air, and even objects far beyond the horizon.

VIII. Independent work. Test - 5 minutes. (Slides 47-53).

1. The angle between the incident beam and the mirror plane is 30°. What is the angle of reflection?

2. Why is red a danger signal for transport?

a) associated with the color of blood;

b) catches the eye better;

c) has the lowest refractive index;

d) has the least dispersion in the air

3. Why do construction workers wear orange helmets?

a) orange color is clearly visible from a distance;

b) changes little during bad weather;

c) has the least light scattering;

d) according to labor safety requirements.

4. How can we explain the play of light in precious stones?

a) their edges are carefully polished;

b) high refractive index;

c) the stone has the shape of a regular polyhedron;

d) correct placement of the gemstone in relation to the light rays.

5. How will the angle between the rays incident on a flat mirror and reflected rays change if the angle of incidence is increased by 15°?

a) will increase by 30°;

b) will decrease by 30°;

c) will increase by 15°;

d) will increase by 15°;

6. What is the speed of light in diamond if the refractive index is 2.4?

a) approximately 2,000,000 km/s;

b) approximately 125,000 km/s;

c) the speed of light does not depend on the medium, i.e. 300000 km/s;

d) 720000 km/s.

IX. Summing up the lesson. Homework. (Slides 54-56).

Analysis and evaluation of students' activities in the classroom. Students discuss the effectiveness of the lesson with the teacher and evaluate their performance.

1. How many correct answers did you get?

3. Did you learn anything new?

4. Best speaker.

2) Do the experiment with a coin at home.

Literature

Gorodetsky D.N. Test work in physics “Higher School” 1987
Demkovich V.P. Collection of problems in physics “Enlightenment” 2004
Giancole D. Physics. Publishing house “Mir” 1990
Perelman A.I. Entertaining physics Publishing house “Science” 1965
Lansberg G.D. Elementary physics textbook Nauka Publishing House 1972
Internet resources

The phenomenon of total internal reflection is used in fiber optics to transmit light signals over long distances. Using conventional mirror reflection does not give the desired result, since even the highest quality mirror (silver-plated) absorbs up to 3% of light energy. When transmitting light over long distances, the energy of light approaches zero. When entering the light guide, the incident beam is directed at an angle that is obviously greater than the limiting one, which ensures reflection of the beam without loss of energy. Light guides, consisting of individual fibers, reach the diameter of a human hair, with a transmission speed faster than the speed of current flow, which allows for faster information transfer.

Fiber light guides are successfully used in medicine. For example, a light guide is inserted into the stomach or into the heart area to illuminate or observe certain areas of the internal organs. The use of light guides allows you to examine internal organs without introducing a light bulb, that is, eliminating the possibility of overheating.

f) Refractometry (from Latin refractus - refracted and Greek metreo - measure) - an analysis method based on the phenomenon of refraction of light when passing from one medium to another. Refraction of light, that is, a change in its original direction, is due to different speeds of light distribution in different media.

28.Polarization of light. The light is natural and polarized. Optically active substances. Measuring the concentration of a solution by the angle of rotation of the plane of polarization (polarimetry).

a) Polarization of light is the separation of rays with a certain orientation of the electric vector from a beam of natural light.

b ) NATURAL LIGHT(unpolarized light) - a set of incoherent light waves with all possible directions of electric magnetic intensity. fields quickly and randomly replacing each other. The light emitted by the center of radiation (atom, molecule, crystal lattice unit, etc.), is usually polarized linearly and maintains the state of polarization for 10-8 s or less (this follows from experiments on observing the interference of light beams at a large path difference, when, therefore, waves emitted at the beginning and end of the specified time interval may interfere). In the next act of radiation, light may have a different direction of polarization. Usually, radiation from a huge number of centers is observed simultaneously, differently oriented and changing orientation according to the laws of statistics. This radiation is E. s.<Мн. источники света (раскалённые тела, светящиеся газы) испускают свет, близкий к Е. с., но всё же в небольшой степени поляризованный. Это объясняется прохождением света внутри источника от глубинных слоев наружу и прохождением света через среду от источника к наблюдателю (поляризация при отражении, при рассеянии света средой, дихроизм среды и т. п.). Близок к Е. с. прямой солнечный свет.

POLARIZED LIGHT - light waves whose electromagnetic vibrations travel in only one direction. Ordinary LIGHT propagates in all directions perpendicular to the direction of its movement. Depending on the oscillation grid, scientists distinguish three types of polarization: linear (planar), circular and elliptical. In linearly polarized light, electrical vibrations are limited to only one direction, and magnetic vibrations are directed at right angles. Linearly polarized light occurs when REFLECTED, for example, from a sheet of glass or the surface of water, when light passes through certain types of crystals, such as quartz, tourmaline or calcite. Polarizing material is used in polarizing sunglasses to reduce glare by deflecting light that becomes polarized when reflected.

V) Optically active substances- media with natural optical activity. Optical activity is the ability of a medium (crystals, solutions, vapors of a substance) to cause rotation of the plane of polarization of optical radiation (light) passing through it. The method for studying optical activity is polarimetry.

d) The speed and accuracy of determining the concentration of many solutions optically made this method very widespread. It is based on the phenomenon of rotation of the plane of polarization of light.

Substances capable of rotating the plane of polarization of linearly polarized light incident on them are called optically active. Pure liquids (for example, turpentine), solutions of certain substances (an aqueous solution of sugar), and some carbohydrates can be optically active. The direction of rotation of the plane of polarization is not the same for different substances. If you look towards the beam passing through a substance, then one part of the substances rotates the plane of polarization clockwise (dextrorotatory substances), the other part counter-rotates (levorotatory substances). Some substances have two modifications, one of which rotates the plane of polarization clockwise, the other counterclockwise (quartz).

Natural light, passing through polarizer P, turns into plane-polarized light. Light filter F transmits light of a certain frequency to the quartz plate K. The quartz plate is cut perpendicular to the optical axis, therefore, light propagates along this axis without birefringence. If in advance, in the absence of a quartz plate, analyzer A is set to complete darkness (the nicoles are crossed), then when the quartz plate is introduced, the field of view brightens. To completely darken, you now need to rotate the analyzer through a certain angle φ. Thus, polarized light passing through quartz did not acquire elliptical polarization, but remained linearly polarized; when passing through quartz, the plane of polarization only rotated by a certain angle, measured by the rotation of analyzer A, necessary to darken the field in the presence of quartz. By changing the filter, you can find that the angle of rotation of the polarization plane is different for different wavelengths, i.e. rotational dispersion occurs.

For a given wavelength, the angle of rotation of the plane of polarization is proportional to the plate thickness d:

where φ is the angle of rotation of the plane of polarization; d – plate thickness; α – specific rotation.

The specific rotation depends on the wavelength, the nature of the substance and temperature. For example, quartz has α = 21.7 deg/mm for λ = 589 nm and α = 48.9 deg/mm for λ = 405 nm.

When linearly polarized light propagates in a solution of an optically active substance, the angle of rotation of the polarization plane depends on the layer thickness d and on the solution concentration C:

In Fig. 2, and are designated: E1 – light vector of the left component, E2 – light vector of the right component, РР – direction of the total vector E.

If the speeds of propagation of both waves are not the same, then as they pass through the substance, one of the vectors, for example E1, will lag behind vector E2 in its rotation (see Fig. 2, b), i.e. the resulting vector E will rotate towards the “faster” vector E2 and take position QQ. The rotation angle will be equal to φ.

The difference in the speed of propagation of light with different directions of circular polarization is due to the asymmetry of molecules or the asymmetric arrangement of atoms in a crystal. To measure the angles of rotation of the plane of polarization, instruments called polarimeters and saccharimeters are used.

29.Features of radiation and absorption of energy by atoms and molecules. Spectra (emission and absorption) atomic, molecular and crystal spectra. Spectrometry and its application in medicine.

An atom and a molecule can be in stationary energy states. In these states they neither emit nor absorb energy. Energy states are schematically represented as levels. The lowest level of energy - the basic one - corresponds to the ground state.

During quantum transitions, atoms and molecules jump from one stationary state to another, from one energy level to another. The change in the state of atoms is associated with energy transitions of electrons. In molecules, energy can change not only as a result of electronic transitions, but also due to changes in atomic vibrations and transitions between rotational levels. When transitioning from higher energy levels to lower ones, an atom or molecule gives off energy, and during reverse transitions it absorbs. An atom in its ground state can only absorb energy. There are two types of quantum transitions:

1) without radiation or absorption of electromagnetic energy by an atom or molecule. This non-radiative transition occurs when an atom or molecule interacts with other particles, for example during a collision. A distinction is made between an inelastic collision, in which the internal state of the atom changes and a non-radiative transition occurs, and elastic - with a change in the kinetic energy of the atom or molecule, but with the preservation of the internal state;

2) with emission or absorption of a photon. The energy of a photon is equal to the difference between the energies of the initial and final stationary states of an atom or molecule

Depending on the reason that causes a quantum transition with the emission of a photon, two types of radiation are distinguished. If this cause is an internal and excited particle spontaneously moving to a lower energy level, then such radiation is called spontaneous. It is random and chaotic in time, frequency (there may be transitions between different sublevels), direction of propagation and polarization. Conventional light sources emit mostly spontaneous radiation. Another type of radiation is forced, or induced. It occurs when a photon interacts with an excited particle if the energy of the photon is equal to the difference in energy levels. As a result of the forced quantum transition, two identical photons will propagate from the particle in one direction: one is the primary, forcing, and the other is secondary, emitted. The energy emitted by atoms or molecules forms the emission spectrum, and the energy absorbed forms the absorption spectrum.

Quantum transitions do not occur between any energy levels. Rules of selection, or prohibition, are established that formulate the conditions under which transitions are possible and impossible or unlikely.

The energy levels of most atoms and molecules are quite complex. The structure of levels and, consequently, spectra depends not only on the structure of a single atom or molecule, but also on external factors.

Spectra are a source of various information.

First of all, atoms and molecules can be identified by the type of spectrum, which is part of the task of qualitative spectral analysis. The intensity of the spectral lines determines the number of emitting (absorbing) atoms - quantitative spectral analysis. In this case, it is relatively easy to find impurities in concentrations of 10~5-10~6% and determine the composition of samples of very small mass - up to several tens of micrograms.

From the spectra one can judge the structure of an atom or molecule, the structure of their energy levels, the mobility of individual parts of large molecules, etc. Knowing the dependence of the spectra on the fields acting on an atom or molecule, one obtains information about the relative position of particles, since the influence of neighboring atoms (molecules) is carried out through an electromagnetic field.

The study of the spectra of moving bodies makes it possible, based on the optical Doppler effect, to determine the relative velocities of the emitter and receiver of radiation.

If we consider that from the spectrum of a substance it is possible to draw conclusions about its state, temperature, pressure, etc., then we can highly appreciate the use of radiation and absorption of energy by atoms and molecules as a research method.

Depending on the energy (frequency) of the photon emitted or absorbed by an atom (or molecule), the following types of spectroscopy are classified: radio, infrared, visible radiation, ultraviolet and x-ray.

Based on the type of substance (source of the spectrum), atomic, molecular spectra and crystal spectra are distinguished.

MOLECULAR SPECTRA- absorption, emission or scattering spectra arising during quantum transitions of molecules from the same energy. states to another. M. s. determined by the composition of the molecule, its structure, the nature of the chemical. communication and interaction with external fields (and, therefore, with the atoms and molecules surrounding it). Naib. characteristic are M. s. rarefied molecular gases, when there is no broadening of spectral lines by pressure: such a spectrum consists of narrow lines with a Doppler width.

Rice. 1. Diagram of energy levels of a diatomic molecule: a And b-electronic levels; u " and u "" - vibrational quantum numbers; J" And J"" - rotational quantum numbers.

In accordance with three systems of energy levels in a molecule - electronic, vibrational and rotational (Fig. 1), M. s. consist of a set of electronic vibrations. and rotate. spectra and lie in a wide range of el-magn. waves - from radio frequencies to x-rays. areas of the spectrum. Frequencies of transitions between rotations. energy levels usually fall into the microwave region (on a wavenumber scale of 0.03-30 cm -1), the frequencies of transitions between oscillations. levels - in the IR region (400-10,000 cm -1), and the frequencies of transitions between electronic levels - in the visible and UV regions of the spectrum. This division is conditional, because it is often rotated. transitions also fall into the IR region, oscillations. transitions - in the visible region, and electronic transitions - in the IR region. Typically, electronic transitions are accompanied by changes in vibrations. energy of the molecule, and with vibrations. transitions changes and rotates. energy. Therefore, most often the electronic spectrum represents systems of electron vibrations. bands, and with high resolution spectral equipment their rotation is detected. structure. Intensity of lines and stripes in M. s. is determined by the probability of the corresponding quantum transition. Naib. intense lines correspond to the transition allowed by the selection rules. To M. s. also include Auger spectra and X-ray spectra. molecular spectra(not covered in the article; see Auger effect, Auger spectroscopy, X-ray spectra, X-ray spectroscopy).

Spectra of crystals(optical) are varied in structure. Along with narrow lines, they contain wide bands (the ratio of frequency n to the speed of light With from fractions to several thousand. cm -1) and continuous regions of the spectrum extending over tens of thousands of kilometers. cm -1(cm. Optical spectra). In the infrared region of the absorption spectra, bands are observed associated with quantum transitions between energy levels caused by the vibrational movements of crystal particles, which are accompanied by changes in the electric dipole moment: a photon is absorbed and a quantum is born vibrations of the crystal lattice - phonon. Processes accompanied by the production of several phonons “blur” and complicate the observed spectrum. A real crystal usually has structural defects (see Fig. Defects in crystals), local vibrations can occur near them, for example, internal vibrations of an impurity molecule. In this case, additional lines with possible “satellites” appear in the spectrum, caused by the connection of local vibrations with lattice vibrations. IN semiconductors some impurities form centers in which electrons move in hydrogen-like orbits. They give an absorption spectrum in the infrared region, consisting of a series of lines ending in a continuous absorption band (impurity ionization). Absorption of light by conduction electrons and holes in semiconductors and metals also begins in the infrared region (see Metal optics). In the spectra of magnetically ordered crystals, magnons manifest themselves similarly to phonons (see Fig. Spin waves).

In the spectrum of scattered light, due to the interaction of light with lattice vibrations, at which the polarizability of the crystal changes, along with the line of the initial frequency n o, lines appear shifted on both sides of it by the frequency of lattice vibrations, which corresponds to the creation or absorption of phonons (see. Raman scattering of light, rice. 1 ). Acoustic lattice vibrations lead to the fact that when light is scattered on thermal fluctuations, lateral satellites also appear near the central (not shifted) Rayleigh line due to scattering on propagating density fluctuations (see Fig. Light Scattering).

Most non-metallic crystals beyond the infrared region are transparent in a certain frequency range. Absorption occurs again when the photon energy becomes high enough to cause electrons to transfer from the upper filled valence band to the lower part of the conduction band of the crystal. The spectrum of this intense self-absorption of light reflects the structure of the electronic energy bands of the crystal and extends further into the visible range as transitions between other energy bands are “switched on.” The position of the edge of self-absorption determines the color of an ideal crystal (without defects). For semiconductors, the long-wave boundary of the intrinsic absorption region lies in the near-infrared region, for ionic crystals - in the near ultraviolet region. Along with direct transitions of electrons, indirect transitions also contribute to the intrinsic absorption of a crystal, during which phonons are additionally created or absorbed. Transitions of electrons from the conduction band to the valence band can be accompanied by recombination radiation.

A conduction electron and a hole, due to electrostatic attraction, can form a bound state - an exciton. The spectrum of excitons can vary from hydrogen-like series to broad bands. Exciton absorption lines lie at the long-wavelength boundary of the crystal's own absorption. Excitons are responsible for the electronic absorption spectra of molecular crystals. Exciton is also known luminescence.

The energies of electronic transitions between local levels of defect centers usually fall into the transparency region of an ideal crystal, due to which they often determine the color of the crystal. For example, in alkali halide crystals the excitation of an electron localized in the anion vacancies(F-color center), leads to the characteristic color of the crystal. Various impurity ions (for example, Tl in KCl) form luminescence centers in crystallophosphorus. They give electronic vibrational (vibronic) spectra. If the electron-phonon (vibronic) interaction in the defect center is weak, then an intense narrow zero-phonon line appears in the spectrum (an optical analogue of the line Mössbauer effect ), adjacent to which is a “phonon wing” with a structure reflecting the dynamics of a crystal with an impurity ( rice. 3 ). As the vibronic interaction increases, the intensity of the zero-phonon line decreases. Strong vibronic coupling results in broad, structureless bands. Since part of the excitation energy in the process of vibrational relaxation before radiation is dissipated in the rest of the crystal, the maximum of the luminescence band lies on the long-wavelength side of the absorption band (Stokes' rule). Sometimes, by the time the light quantum is emitted, an equilibrium distribution among vibrational sublevels has not yet been established in the center, and “hot” luminescence is possible.

If the crystal contains atoms or ions of transition or rare earth elements as impurities, with unfinished f- or d-shells, then one can observe discrete spectral lines corresponding to transitions between sublevels resulting from the splitting of atomic levels by an intracrystalline electric field

SPECTROMETRY is a set of methods and theory for measuring electromagnetic spectra. radiation and the study of the spectral properties of substances and bodies in optical science. wavelength range (~1 nm - 1 mm). Measurements in S. are carried out using spectral devices.