Most of the objects around you - houses, trees, your classmates, etc. - are not sources of light. But you see them. The answer to the question "Why so?" you will find in this paragraph.

Rice. 11.1. In the absence of a light source, nothing can be seen. If there is a light source, we see not only the source itself, but also objects that reflect the light coming from the source.

Finding out why we see bodies that are not light sources

You already know that light travels in a straight line in a homogeneous transparent medium.

But what happens if there is some body in the path of the light beam? Part of the light can pass through the body if it is transparent, part will be absorbed, and part will be reflected from the body. Some of the reflected rays will hit our eyes, and we will see this body (Fig. 11.1).

Establishing the laws of light reflection

To establish the laws of light reflection, we will use a special device - an optical washer*. We fix a mirror in the center of the washer and direct a narrow beam of light at it so that it gives a light strip on the surface of the washer. We see that the beam of light reflected from the mirror also gives a light strip on the surface of the washer (see Fig. 11.2).

The direction of the incident light beam will be set by the CO beam (Fig. 11.2). This beam is called the incident beam. The direction of the reflected beam of light will be set by the beam OK. This ray is called the reflected ray.

From the point O of incidence of the beam, we draw a perpendicular OB to the surface of the mirror. Let us pay attention to the fact that the incident ray, the reflected ray and the perpendicular lie in the same plane - in the plane of the washer surface.

The angle α between the incident beam and the perpendicular drawn from the point of incidence is called the angle of incidence; the angle β between the reflected ray and the given perpendicular is called the angle of reflection.

By measuring the angles α and β, we can verify that they are equal.

If you move the light source along the edge of the disk, the angle of incidence of the light beam will change and the angle of reflection will change accordingly, and each time the angle of incidence and the angle of reflection of the light will be equal (Fig. 11.3). So, we have established the laws of light reflection:

Rice. 11.3. As the angle of incidence of light changes, the angle of reflection also changes. The angle of reflection is always equal to the angle of incidence

Rice. 11.5. Demonstration of the reversibility of light rays: the reflected beam follows the path of the incident beam

rice. 11.6. Approaching the mirror, we see our “double” in it. Of course, there is no “double” there - we see our reflection in the mirror

1. The incident beam, the reflected beam and the perpendicular to the reflection surface, drawn from the point of incidence of the beam, lie in the same plane.

2. The angle of reflection is equal to the angle of incidence: β = α.

The laws of light reflection were established by the ancient Greek scientist Euclid as early as the 3rd century BC. BC e.

In what direction should the professor turn the mirror in order to " sunbeam»hit the boy (Fig. 11.4)?

Using a mirror on an optical washer, one can also demonstrate the reversibility of light rays: if the incident beam is directed along the path of the reflected one, then the reflected beam will follow the path of the incident one (Fig. 11.5).

We study the image in flat mirror

Consider how an image is created in a flat mirror (Fig. 11.6).

Let a divergent beam of light fall from a point source of light S onto the surface of a flat mirror. From this beam we select the rays SA, SB and SC. Using the laws of light reflection, we construct the reflected rays LL b BB 1 and CC 1 (Fig. 11.7, a). These rays will go in a divergent beam. If you extend them in the opposite direction (behind the mirror), they will all intersect at one point - S 1 located behind the mirror.

If some of the rays reflected from the mirror enter your eye, it will seem to you that the reflected rays come out of the point S 1, although in reality there is no light source at the point S 1. Therefore, the point S 1 is called the imaginary image of the point S. A flat mirror always gives imaginary image.

Find out how the object and its image are located relative to the mirror. To do this, we turn to geometry. Consider, for example, a ray SC that falls on a mirror and is reflected from it (Fig. 11.7, b).

From the figure we see that Δ SOC = Δ S 1 OC - right triangles, having a common side CO and equal to sharp corners(because according to the law of light reflection α = β). From the equality of triangles, we have that SO \u003d S 1 O, that is, the point S and its image S 1 are symmetrical with respect to the surface of a flat mirror.

The same can be said about the image of an extended object: the object and its image are symmetrical with respect to the surface of a flat mirror.

So, we have installed General characteristics images in flat mirrors.

1. A flat mirror gives a virtual image of an object.

2. The image of an object in a flat mirror and the object itself are symmetrical with respect to the surface of the mirror, and this means:

1) the image of the object is equal in size to the object itself;

2) the image of the object is located at the same distance from the surface of the mirror as the object itself;

3) the segment connecting the point on the object and the corresponding point on the image is perpendicular to the surface of the mirror.

Distinguish between specular and diffuse reflection of light

In the evening, when the light is on in the room, we can see our image in window glass. But the image disappears if the curtains are drawn: we will not see our image on the fabric. And why? The answer to this question is related to at least two physical phenomena.

The first such physical phenomenon- Reflection of light. In order for an image to appear, the light must be reflected from the surface in a specular manner: after specular reflection of light coming from a point source S, the continuation of the reflected rays will intersect at one point S 1, which will be the image of the point S (Fig. 11.8, a). Such reflection is possible only from very smooth surfaces. They are called so - mirror surfaces. In addition to the usual mirror, examples of mirror surfaces are glass, polished furniture, calm water surface, etc. (Fig. 11.8, b, c).

If light is reflected from a rough surface, such a reflection is called scattered (diffuse) (Fig. 11.9). In this case, the reflected rays propagate in different directions (which is why we see the illuminated object from any direction). It is clear that there are much more surfaces that scatter light than mirror ones.

Look around and name at least ten surfaces that reflect light diffusely.

Rice. 11.8. Specular reflection of light is the reflection of light from a smooth surface.

Rice. 11.9. Scattered (diffuse) reflection of light is the reflection of light from a rough surface

The second physical phenomenon that affects the ability to see an image is the absorption of light. After all, light is not only reflected from physical bodies, but also absorbed by them. The best light reflectors are mirrors: they can reflect up to 95% of the incident light. Bodies are good reflectors of light. white color, but the black surface absorbs almost all the light falling on it.

When snow falls in autumn, the nights become much lighter. Why? Learning to solve problems

Task. On fig. 1 schematically shows the object BC and the mirror NM. Find graphically the area from which the image of the object BC is completely visible.

Analysis physical problem. In order to see the image of a certain point of an object in a mirror, it is necessary that at least part of the rays falling from this point onto the mirror be reflected into the observer's eye. It is clear that if the rays emanating from the extreme points of the object are reflected into the eye, then the rays emanating from all points of the object are also reflected into the eye.

Solution, analysis of results

1. Let's construct point B 1 - the image of point B in a flat mirror (Fig. 2, a). The area bounded by the surface of the mirror and the rays reflected from the extreme points of the mirror will be the area from which the image B 1 of point B in the mirror is visible.

2. Having similarly constructed the image C 1 of point C, we determine the area of ​​its vision in the mirror (Fig. 2, b).

3. The observer can see the image of the entire object only if the rays that give both images - B 1 and C 1 (Fig. 2, c) enter his eye. Hence, the area highlighted in Fig. 2, in orange, is the area from which the image of the object is completely visible.

Analyze the result obtained, once again consider Fig. 2 to the problem and offer an easier way to find the area of ​​vision of an object in a flat mirror. Check your assumptions by plotting the field of view of several objects in two ways.

Summing up

All visible bodies reflect light. When light is reflected, two laws of light reflection are fulfilled: 1) the incident beam, the reflected beam and the perpendicular to the reflection surface, drawn from the point of incidence of the beam, lie in the same plane; 2) the angle of reflection is equal to the angle of incidence.

The image of an object in a flat mirror is imaginary, equal in size to the object itself and located at the same distance from the mirror as the object itself.

Distinguish between specular and diffuse reflections of light. In the case of specular reflection, we can see a virtual image of an object in a reflective surface; in the case of diffuse reflection, no image appears.

Control questions

1. Why do we see surrounding bodies? 2. What angle is called the angle of incidence? reflection angle? 3. Formulate the laws of light reflection. 4. What device can be used to verify the validity of the laws of light reflection? 5. What is the property of reversibility of light rays? 6. In what case is the image called imaginary? 7. Describe the image of an object in a flat mirror. 8. How is diffuse reflection of light different from specular?

Exercise number 11

1. A girl stands at a distance of 1.5 m from a flat mirror. How far is her reflection from the girl? Describe it.

2. The driver of the car, looking in the rearview mirror, saw a passenger sitting in the back seat. Can the passenger at this moment, looking in the same mirror, see the driver?

3. Transfer the pic. 1 in a notebook, for each case construct an incident (or reflected) ray. Label the angles of incidence and reflection.

4. The angle between the incident and reflected rays is 80°. What is the angle of incidence of the beam?

5. The object was at a distance of 30 cm from a flat mirror. Then the object was moved 10 cm from the mirror in a direction perpendicular to the surface of the mirror, and 15 cm parallel to it. What was the distance between the object and its reflection? What did it become?

6. You are moving towards the mirror shop window at a speed of 4 km/h. How fast is your reflection approaching you? By how much will the distance between you and your reflection decrease when you walk 2 m?

7. A sunbeam is reflected from the surface of the lake. The angle between the incident beam and the horizon is twice the angle between the incident and reflected beams. What is the angle of incidence of the beam?

8. The girl looks into a mirror hanging on the wall at a slight angle (Fig. 2).

1) Build the reflection of the girl in the mirror.

2) Find graphically what part of her body the girl sees; the area from which the girl sees herself completely.

3) What changes will be observed if the mirror is gradually covered with an opaque screen?

9. At night, in the light of car headlights, a puddle on the pavement seems to the driver to be a dark spot against a lighter background of the road. Why?

10. In fig. 3 shows the path of the rays in the periscope - a device whose operation is based on the rectilinear propagation of light. Explain how this device works. Use additional sources of information and find out where it is used.

LAB #3

Subject. Investigation of light reflection using a flat mirror.

Purpose: experimentally check the laws of light reflection.

equipment: a light source (a candle or an electric lamp on a stand), a flat mirror, a screen with a slit, several blank white sheets of paper, a ruler, a protractor, a pencil.

instructions for work

preparation for the experiment

1. Before doing work, remember: 1) safety requirements when working with glass objects; 2) laws of reflection of light.

2. Assemble the experimental setup (Fig. 1). For this:

1) install the screen with a slot on a white sheet of paper;

2) by moving the light source, get a strip of light on paper;

3) place a flat mirror at a certain angle to the strip of light and perpendicular to the sheet of paper so that the reflected beam of light also gives a clearly visible strip on the paper.

Experiment

Strictly follow the safety instructions (see the flyleaf of the textbook).

1. With a well-sharpened pencil, draw a line along the mirror on paper.

2. Put three points on a sheet of paper: the first one is in the middle of the incident light beam, the second one is in the middle of the reflected light beam, the third one is in the place where the light beam hits the mirror (Fig. 2).

3. Repeat the described steps several more times (on different sheets of paper), placing the mirror under different angles to an incident beam of light.

4. By changing the angle between the mirror and the sheet of paper, make sure that in this case you will not see the reflected beam of light.

Processing the results of the experiment

For each experience:

1) build the beam incident on the mirror and the reflected beam;

2) through the point of incidence of the beam, draw a perpendicular to the line drawn along the mirror;

3) Label and measure the angle of incidence (α) and the angle of reflection (β) of the light. Enter the measurement results in the table.

Analysis of the experiment and its results

Analyze the experiment and its results. Make a conclusion in which indicate: 1) what is the ratio between the angle of incidence of the light beam and the angle of its reflection you have set; 2) whether the results of the experiments turned out to be absolutely accurate, and if not, what are the reasons for the error.

creative task

Using fig. 3, think over and write down a plan for conducting an experiment to determine the height of a room using a flat mirror; indicate the required equipment.

Experiment if possible.

Task "with an asterisk"

Who can construct an image of a point in a plane mirror?

And how to build an image of an extended source in a flat mirror (Figure 2.13)? What properties of the image can be revealed in this case?

Can a flat mirror be used as a movie screen?

And now, applying the law of reflection of light, build an image of a point and an object not large sizes in a spherical mirror:

First - in a convex;

- then - in a concave.

Compare the obtained images with each other and with the images obtained using a flat mirror.

How would you explain the difference in image size and position based on the Huygens-Fresnel principle?

Thus, the lesson formulated general principle propagation of waves of any nature - the Huygens-Fresnel principle. What do you see as the meaning of this principle?

Indeed, applying the Huygens-Fresnel principle, and performing simple geometric constructions, it is possible to find the wave surface at any time using the wave surface known at the previous time. In the lesson, using the Huygens-Fresnel principle, the law of wave reflection was derived.

What is the novelty of the material studied in the lesson?

How does it relate to the material you have studied in more than early stages studying physics?

Which of the results were surprising or unexpected for you?

What did you learn during the lesson?

Please state the main results of the lesson.

Which homework you would appoint to consolidate and deepen knowledge on the topic “Huygens' principle. The law of reflection of light?

1. (mandatory) Answer the following questions in writing in your notebook:

How to construct an image of a point source of light in a flat mirror using the law of reflection?

· Why can't a flat mirror be used as a movie screen?

2. (optional) Prepare an essay about the Dutch physicist and mathematician Christian Huygens.

Law of refraction of light

Lesson type: explanation of new material.

1) cognitive goal: to create conditions for students to understand the essence and conditions for observing the phenomenon of light refraction; mastering the derivation of the law of refraction of light based on the principle of Huygens - Fresnel, and the formulation of the law of refraction of light; revealing the condition of total internal reflection;

2) developmental goal: to create conditions for the development of thinking, communicative and mental qualities of students;

3) practical goal: to teach students to correctly formulate the purpose of the work, draw conclusions and conduct self-assessment of the work done;

4) educational goal: to cultivate a sense of collectivism, to develop analytic skills students.

Visual Aids and Demos: Demonstration using an optical disc

organizational moment - 3 min

explanation of new material - 30 min

fixing the material - 10 min

homework - 2 min

Introduction by the teacher. Students are invited to recall what they know about the refraction of light from the course of geometric optics.

Let's remember what is the phenomenon of light refraction?

Observation of the refraction of light

At the boundary of two media, light changes its direction of propagation (demonstration using an optical disc). Part of the light energy returns to the first medium, i.e., light is reflected. If the second medium is transparent, then the light can partially pass through the boundary of the media, as a rule, also changing the direction of propagation.

Game methods as a means of forming a culture of personality
Exist various games. Some develop the thinking and horizons of children, others - dexterity, strength, and others - design skills. There are games aimed at developing creativity in a child, in which the child shows his invention, initiative, and independence. Creative manifestations children in games differently.

Issues of pedagogical leadership story games children preschool age V pedagogical literature
In the history of preschool pedagogy, several pedagogical approaches to the management of children's plot games have developed. The first approach is the so-called traditional leadership approach. role-playing game. This approach has developed in practice preschool education according to the results of developmental studies.

Development in subgroups of the content of didactic games to familiarize preschoolers with the objective world
Successful Leadership didactic games, first of all, provides for the selection and thinking through of their program content, a clear definition of tasks, determining the place and role in a holistic educational process, interaction and other games and forms of learning. It should be directed towards development.

www.alfaeducation.ru

§ 60. Huygens' principle. Law of Reflection of Light (end)

At the moment when the wave reaches point B and at this point the excitation of oscillations begins, the secondary wave centered at point A will already be a hemisphere with a radius r = AD = υΔt = SW. The fronts of secondary waves from sources located between points A and B are shown in Figure 8.5. The envelope of the fronts of the secondary waves is the plane DB, tangent to the spherical surfaces. It is the front of the reflected wave. Beams AA 2 and BB 2 are perpendicular to the front of the reflected wave DB. The angle y between the normal to the reflecting surface and the reflected ray is called reflection angle.

Since AD ​​= CB and triangles ADB and ACB are right triangles, then ∠DBA = ∠CAB. But α = ∠CAB and γ = ∠DBA as angles with mutually perpendicular sides. Therefore, the angle reflection is equal to the angle of incidence 1 :

The law of reflection of light follows from Huygens' theory: the incident beam, the reflected beam and the normal to the reflecting surface at the point of incidence lie in the same plane, and the angle of incidence is equal to the angle of reflection.

With the opposite direction of propagation of light rays, the reflected beam will become incident, and the incident beam will be reflected. The reversibility of the course of light rays is their important property.

The general principle of propagation of waves of any nature, the Huygens principle, is formulated. This principle allows, using simple geometric constructions, to find the wave surface at any time using a known wave surface at the previous moment. The law of reflection of light is derived from the Huygens principle.

Questions for the paragraph

1. How to build an image of a point source of light in a flat mirror using the law of reflection?

2. Why can't a flat mirror be used as a movie screen?

www.xn--24-6kct3an.xn--p1ai

The law of reflection of light. flat mirror

This video tutorial is available by subscription

Do you already have a subscription? To come in

In this lesson, you will learn about the reflection of light and we will formulate the basic laws of light reflection. Let's get acquainted with these concepts not only from the point of view of geometric optics, but also from the point of view of the wave nature of light.

How do we see the vast majority of objects around us, because they are not sources of light? The answer is familiar to you, you received it in the 8th grade physics course. We see the world around us by reflecting light.

Law of reflection

First, let's recall the definition.

When a light beam falls on the interface between two media, it experiences reflection, that is, it returns to the original medium.

Pay attention to the following: the reflection of light is far from the only possible outcome of the further behavior of the incident beam, it partially penetrates into another medium, that is, it is absorbed.

Absorption of light (absorption) is the phenomenon of loss of energy by a light wave passing through a substance.

Let's build an incident beam, a reflected beam and a perpendicular to the point of incidence (Fig. 1.).

Rice. 1. Incident beam

The angle of incidence is the angle between the incident ray and the perpendicular (),

- slip angle.

These laws were first formulated by Euclid in his work "Katoptrik". And we have already got acquainted with them in the framework of the 8th grade physics program.

Laws of light reflection

1. The incident ray, the reflected ray and the perpendicular to the point of incidence lie in the same plane.

2. The angle of incidence is equal to the angle of reflection.

From the law of reflection of light follows the reversibility of light rays. That is, if we swap the incident beam and the reflected one, then nothing will change in terms of the trajectory of the propagation of the light flux.

The spectrum of application of the law of reflection of light is very wide. This is the fact with which we started the lesson that we see most of the objects around us in reflected light (moon, tree, table). Another good example use of light reflection are mirrors and reflectors (reflectors).

Reflectors

We will understand the principle of operation of a simple retroreflector.

Reflector (from the ancient Greek kata - a prefix with the meaning of effort, fos - "light"), retroreflector, flicker (from the English flick - "blink") - a device designed to reflect a beam of light towards the source with minimal dispersion.

Every cyclist knows that traveling in dark time days without the presence of reflectors can be dangerous.

Flickers are also used in the uniforms of road workers, traffic police officers.

Surprisingly, the property of a reflector is based on the simplest geometric facts, in particular, on the law of reflection.

Reflection of a beam from a mirror surface occurs according to the law: the angle of incidence is equal to the angle of reflection. Consider a plane case: two mirrors forming an angle of 90 degrees. A beam traveling in a plane and hitting one of the mirrors, after reflection from the second mirror, will go exactly in the direction in which it came (see Fig. 2).

Rice. 2. The principle of operation of the angular reflector

To obtain such an effect in ordinary three-dimensional space, it is necessary to place three mirrors in mutually perpendicular planes. Take a corner of a cube with an edge in the form of a regular triangle. A beam that hits such a system of mirrors, after reflection from three planes, will go parallel to the incoming beam in the opposite direction (see Fig. 3.).

Rice. 3. Corner reflector

There will be a flashback. It is this simple device with its properties that is called a corner reflector.

Proof of the law of reflection

Consider the reflection of a plane wave (a wave is called plane if the surfaces of equal phase are planes) (Fig. 1.)

Rice. 4. Reflection of a plane wave

In the figure - a surface, and - two beams of an incident plane wave, they are parallel to each other, and the plane is a wave surface. The wave surface of the reflected wave can be obtained by drawing the envelope of secondary waves whose centers lie on the interface between the media.

Different sections of the wave surface do not reach the reflecting boundary at the same time. The excitation of oscillations at the point will begin earlier than at the point for the time interval . At the moment when the wave reaches the point and at this point the excitation of oscillations begins, the secondary wave centered at the point (reflected beam) will already be a hemisphere with a radius . Based on what we just wrote down, this radius will also be equal to the segment.

Now we see: , triangles and are rectangular, which means . And in turn, there is an angle of incidence. A is the angle of reflection. Therefore, we get that the angle of incidence is equal to the angle of reflection.

So, with the help of Huygens' principle, we proved the law of reflection of light. The same proof can be obtained using Fermat's principle.

Types of reflection

As an example (Fig. 5.), a reflection from a wavy, rough surface is shown.

Rice. 5. Reflection from a rough, undulating surface

The figure shows that the reflected rays go in a variety of directions, because the direction of the perpendicular to the point of incidence for a different beam will be different, respectively, and the angle of incidence and the angle of reflection will also be different.

A surface is considered uneven if the dimensions of its irregularities are not less than the wavelength of light waves.

A surface that will reflect rays in all directions evenly is called matte. Thus, the matte surface guarantees us a diffuse or diffuse reflection, which occurs due to irregularities, roughness, scratches.

A surface that scatters light evenly in all directions is called absolutely matte. In nature, you will not find an absolutely matte surface, however, the surface of snow, paper and porcelain is very close to them.

If the size of the surface irregularities is less than the wavelength of the light, then such a surface will be called a mirror.

When reflected from a mirror surface, the parallelism of the beam is preserved (Fig. 6.).

Rice. 6. Reflection from a mirror surface

Approximately mirror is the smooth surface of water, glass and polished metal. Even a matte surface can turn out to be a mirror if you change the angle of incidence of the rays.

At the beginning of the lesson, we talked about the fact that part of the incident beam is reflected, and part is absorbed. In physics, there is a quantity that characterizes how much of the energy of the incident beam is reflected and how much is absorbed.

Albedo

Albedo - a coefficient that shows what proportion of the energy of the incident beam is reflected from the surface, (from the Latin albedo - "whiteness") - a characteristic of the diffuse reflectivity of the surface.

Or otherwise, it is a fraction expressed as a percentage of the reflected radiation of energy from the energy entering the surface.

The closer the albedo is to 100, the more energy is reflected from the surface. It is easy to guess that the albedo coefficient depends on the color of the surface, in particular, energy will be much better reflected from a white surface than from a black one.

Snow has the highest albedo for substances. It is about 70-90%, depending on its novelty and variety. That is why the snow slowly melts while it is fresh, or rather white. Albedo values ​​for other substances, surfaces are shown in Figure 7.

Rice. 7. Albedo value for some surfaces

flat mirror

A very important example of the application of the law of reflection of light are flat mirrors - a flat surface that reflects light specularly. Do you have these mirrors in your house?

Let's figure out how to build an image of objects in a flat mirror (Fig. 8.).

Rice. 8. Building an image of an object in a flat mirror

- a point source of light that emits rays in different directions, take two close beams incident on a flat mirror. The reflected rays will go as if they come from a point , which is symmetrical to the point with respect to the plane of the mirror. The most interesting thing will begin when the reflected rays hit our eye: our brain itself completes the diverging beam, continuing it beyond the mirror to the point

It seems to us that the reflected rays come from a point.

This point serves as an image of the light source. Of course, in reality, nothing glows behind the mirror, it's just an illusion, so this point is called an imaginary image.

The area of ​​vision depends on the location of the source and the size of the mirror - the region of space from which the image of the source is visible. The area of ​​vision is set by the edges of the mirror and .

For example, you can look in the mirror in the bathroom at a certain angle, if you move sideways from it, then you will not see yourself or the object you want to examine.

In order to construct an image of an arbitrary object in a flat mirror, it is necessary to construct an image of each of its points. But if we know that the image of a point is symmetrical with respect to the plane of the mirror, then the image of the object will be symmetrical with respect to the plane of the mirror (Fig. 9.)

Rice. 9. Symmetrical reflection of an object relative to the plane of the mirror

Another use for a mirror is to create a periscope, which is a device for observing from cover.

Conclusion

In this lesson, we not only got acquainted with the law of reflection, but also proved it using the Huygens principle already known to us. In addition, we have learned how to build images of objects in a flat mirror and characterize them.

Analysis of the problem on the law of reflection of light

The students studied the relationship between the speeds of the car and its image in a flat mirror in the frame of reference associated with the mirror. The projection onto the axis of the speed vector with which the image moves in this frame of reference is equal to:

1.; 2.; 3.; 4. (See fig. 10.)

Rice. 10. Illustration for the problem

Recall that the image in a flat mirror is located symmetrically to the object with respect to the mirror plane. This means that if the car moves in time, then the image, which is located symmetrically, will move in the same time and, therefore, the image moves away from the mirror with speed . The projection onto the axis will be equal to .

Bibliography

1. Zhilko V.V., Markovich Ya.G. Physics. Grade 11. – 2011.

2. Myakishev G.Ya., Bukhovtsev B.B., Charugin V.M. Physics. Grade 11. Textbook.

3. Kasyanov V.A. Physics, 11th grade. – 2004.

1. Internet portal "Physics for all" (Source)

2. Internet portal of the Unified Collection of Digital Educational Resources (Source)

3. Internet portal "diplomivanov.narod.ru" (Source)

Homework

1. Construct AB images in a flat mirror

2. Plot an image in a flat mirror

Image in a flat mirror.

The image of an object in a flat mirror is formed behind the mirror, that is, where the object does not actually exist. How does it work?

Let the diverging rays SA and SB fall on the mirror MN from the luminous point S. Reflected by the mirror, they will remain divergent. A divergent beam of light enters the eye, positioned as shown in the figure, as if emanating from point S1. This point is the point of intersection of the reflected rays extended beyond the mirror. The point S1 is called the virtual image of the point S because no light comes from the point S1.

Consider how the light source and its imaginary image are located relative to the mirror.

We fix a piece of flat glass on a stand in a vertical position. Putting a lighted candle in front of the glass, we will see in the glass, as in a mirror, the image of a candle. Now let's take the second same, but unlit candle and place it on the other side of the glass. By moving the second candle, we will find a position in which the second candle will also seem to be lit. This means that the unlit candle is in the same place where the image of the lit candle is observed. Having measured the distances from the candle to the glass and from its image to the glass, we will make sure that these distances are the same.

Thus, the imaginary image of an object in a flat mirror is at the same distance from the mirror as the object itself is.
The object and its image in the mirror are not identical, but symmetrical figures. For example, the mirror image of the right glove is the left glove, which can only be combined with the right glove by turning it inside out.

The image of an object given by a flat mirror is formed by rays reflected from the mirror surface.

The figure shows how the eye perceives the image of point S in the mirror. Beams SO, SO1 and SO2 are reflected from the mirror in accordance with the laws of reflection. The SO beam falls on the mirror perpendicularly (= 0°) and, being reflected (= 0°), does not enter the eye. Rays SO1 and SO2 after reflection enter the eye in a divergent beam, the eye perceives the luminous point S1 behind the mirror. In fact, at the point S1, the continuations of the reflected rays converge (dashed line), and not the rays themselves (it only seems that the divergent rays entering the eye come from points located in the “mirror”), therefore such an image is called imaginary (or imaginary), and the point from which, as it seems to us, each beam comes out, is the point of the image. Each point of the object corresponds to the point of the image.

the law of reflection of light, the imaginary image of an object is located symmetrically with respect to the mirror surface. The size of the image is equal to the size of the object itself.

In reality, light rays do not pass through a mirror. It only seems to us that the light comes from the image, because our brain perceives the light entering our eyes as light from a source in front of us. Since the rays don't really converge in the image, placing a sheet of white paper or film on the spot where the image is will not produce any image. Therefore, such an image is called imaginary. It must be distinguished from the actual image through which the light passes and which can be obtained by placing a sheet of paper or photographic film where it is. As we will see later, real images can be formed using lenses and curved mirrors (for example, spherical ones).

Points S and S' are symmetrical with respect to the mirror: SO = OS'. Their image in a flat mirror is imaginary, direct (not reverse), the same size as the object and located at the same distance from the mirror as the object itself.

In the evening, an oncoming car blinds us bright light headlights The spotlight gives a powerful stream of light, brightly illuminating distant objects. There is a lighthouse that sends rays of light for tens of kilometers to orient ships. In all these and many other cases, the light is directed into space by a concave mirror, in front of which is a light source.

Reflective surfaces do not have to be flat. Curved mirrors are most often spherical, that is, they have the shape of a spherical segment. Spherical mirrors are either concave or convex. A spherical concave mirror is a carefully polished spherical surface. In the figures below, point O is the center of the spherical surface that forms the mirror. In the figure, the letter C marks the center of the spherical mirror surface, point O is the top of the mirror. The straight line CO passing through the center of the mirror surface C and the top of the mirror O is called the optical axis of the mirror.

Let us send a beam of light rays parallel to the optical axis of the mirror from the lantern to the mirror. After reflection from the mirror, the rays of this beam will converge at one point F, which lies on the optical axis of the mirror. This point is called the focus of the mirror. If the light source is placed at the focus of the mirror, then the rays will be reflected from the mirror, as shown in the figure.

The distance OF from the top of the mirror to the focus is called the focal length of the mirror, it is equal to half the radius OS of the spherical surface of the mirror, that is, OF= 0.5 OS.

Let us bring a light source (a lit candle or an electric lamp) close to a concave mirror so that its image can be seen in the mirror. This image - imaginary - is located behind the mirror. Compared to the object, it is enlarged and straight.
Let's gradually remove the light source from the mirror. In this case, its image will also move away from the mirror, its dimensions will increase, and then the virtual image will disappear. But now the image of the light source can be obtained on the screen placed in front of the mirror, that is, the actual image of the light source can be obtained.
The farther we move the light source away from the mirror, the closer the screen will have to be placed to the mirror in order to get an image of the source on it. The size of the image will then be reduced.
All real images in relation to the subject are reversed (inverted). Their dimensions, depending on the distance of the object from the mirror, can be larger, smaller than the object, or equal to the dimensions of the object (light source).

Thus, the location and dimensions of the image obtained using a concave mirror depend on the position of the object relative to the mirror.

Building an image in a concave mirror.

A spherical mirror is called concave if the reflecting surface is the inner side of the spherical segment, that is, if the center of the mirror is farther from the observer than its edges.

If the dimensions of the concave mirror are small compared to its radius of curvature, that is, a beam of rays parallel to the main optical axis falls on the concave spherical mirror, after reflection from the mirror the rays will intersect at one point, which is called the main focus of the mirror F. The distance from the focus to the pole of the mirror is called the focal length and is denoted by the same letter F. A concave spherical mirror has a real focus. It is located in the middle between the center and the pole of the mirror (the center of the spherical surface), which means the focal length: ОF = СF = R/2.

Using the laws of light reflection, you can geometrically build an image of an object in a mirror. In the figure, the luminous point S is located in front of the concave mirror. Let's draw three rays from it to the mirror and build the reflected rays. These reflected rays will intersect at point S1. Since we took three arbitrary rays emanating from the point S, then all other rays incident from this point on the mirror will intersect at the point S1 after reflection. Therefore, the point S1 is the image of the point S.
For geometric construction image of a point, it is enough to know the direction of propagation of two rays emerging from this point. These rays can be chosen quite arbitrarily. However, it is more convenient to use rays whose path after reflection from the mirror is known in advance.

Let's construct an image of point S in a concave mirror. To do this, draw two rays from point S. Beam SA is parallel to the optical axis of the mirror; after reflection, it will pass through the focus of the mirror F. Let's draw another ray SB through the focus of the mirror; reflected from the mirror, it will go parallel to the optical axis. At point S1, both reflected beams will intersect. This point will be the image of the point S, in it all the rays reflected by the mirror coming from the point S will intersect.
The image of an object is made up of images of many individual points of this object. To build an image of an object in a concave mirror, it is enough to build an image of the two extreme points of this object. Images of other points will be located between them. In the figure, the object is depicted as an arrow AB.
Having constructed the images of points A and B in the above way, we will obtain an image of the entire object A1B1. The object AB is located behind the center of the spherical surface of the mirror (behind point C). His image A1B1 turned out to be between the focus F and the center of the spherical surface of the mirror C. In relation to the object, it is reduced and inverted. The image A1B1 is real, since the rays reflected from the mirror really intersect at points A1 and B1. Such an image can be obtained on the screen.

A spherical mirror is called convex if the reflection occurs from the outer surface of the spherical segment, that is, if the center of the mirror is closer to the observer than the edges of the mirror.

If a parallel beam of rays is incident on a convex mirror, then the reflected rays are scattered, but their continuation (dotted line) intersect at the main focus of the convex mirror. That is, the main focus of a convex mirror is imaginary.

The focal lengths of spherical mirrors are assigned a certain sign, for a convex where R is the radius of curvature of the mirror: OF=CF=-R/2.

The use of mirrors.

A flat mirror is widely used both in everyday life and in the construction of various devices.
It is known that the accuracy of reading on any scale depends on correct location eyes. To reduce the reading error, precision measuring instruments are equipped with a mirror scale. A person working with such a device sees the divisions of the scale, a narrow arrow and its image in the mirror. The correct reading will be such a reading on the scale, in which the eye is located so that the arrow closes its image in the mirror.
The "bunny" reflected from the mirror noticeably shifts when the mirror is turned, even at a small angle. This phenomenon is used in measuring instruments, the readings of which are taken on a scale remote from the instrument by the displacement of the light spot on this scale. "Bunny" is obtained from a small mirror connected to the moving part of the device and illuminated from a special light source. Measuring instruments with such a reading device are usually very sensitive.

Flat mirrors are very widely used in everyday life, as well as in devices in which you need to change the direction of the rays, for example, in a periscope (figure on the right).

Concave mirrors are used to make spotlights: the light source is placed at the focus of the mirror, the reflected rays come from the mirror in a parallel beam. If we take a large concave mirror, then a very high temperature can be obtained at the focus. Here you can place a tank with water to get hot water, for example, for domestic needs due to solar energy.

Concave mirrors can be used to direct most light emitted by the source the right direction. To do this, a concave mirror, or, as it is called, a reflector, is placed near the light source. This is how car headlights, projection and flashlights, searchlights are arranged.

The spotlight consists of two main parts: a powerful light source and a large concave mirror. With the location of the source and the mirror indicated in the figure, the rays of light reflected from the mirror travel in an almost parallel beam.

Medical examination when applying for a job When applying for an enterprise, organization, each applicant is required to undergo a medical examination. The list of doctors who need to be examined and receive a conclusion may differ. It all depends on the type [...]

Schoolchildren are able to build an image of an object in a flat mirror, using the law of light reflection, and they know that the object and its image are symmetrical with respect to the plane of the mirror. As an individual or group creative task(abstract, research project) can be instructed to investigate the construction of images in a system of two (or more) mirrors - the so-called "multiple reflection".

A single plane mirror gives one image of an object.

S - object (luminous dot), S 1 - image

Add a second mirror, placing it at right angles to the first. It would seem that, two mirrors should add up two images: S 1 and S 2 .

But a third image appears - S 3 . It is usually said - and this is convenient for constructions - that the image that appears in one mirror is reflected in another. S 1 is reflected in mirror 2, S 2 is reflected in mirror 1 and these reflections coincide in this case.

Comment. When dealing with mirrors, often, as in Everyday life, instead of the expression "image in the mirror" they say: "reflection in the mirror", i.e. replace the word "image" with the word "reflection". "He saw his reflection in the mirror."(The title of our note could have been formulated differently: "Multiple reflections" or "Multiple reflections".)

S 3 is the reflection of S 1 in mirror 2 and the reflection of S 2 in mirror 1.

It is interesting to draw the path of the rays that form the image S 3 .

We see that the image S 3 appears as a result double ray reflections (images S 1 and S 2 are formed as a result of single reflections).

In total, the number of visible images of the object for the case of two perpendicularly arranged mirrors is three. We can say that such a system of mirrors quadruples the object (or the "multiplication factor" is equal to four).

In a system of two perpendicular mirrors, any beam can experience no more than two reflections, after which it leaves the system (see figure). If the angle between the mirrors is reduced, then the light will, being reflected, “run” between them more times, forming more images. So, for the case of an angle between the mirrors of 60 degrees, the number of images obtained is five (six). The smaller the angle, the more difficult it is for the rays to leave the space between the mirrors, the longer it will be reflected, the more images will be obtained.

Antique instrument (Germany, 1900) with variable angle between mirrors for studying and demonstrating multiple reflections.

A similar homemade device.

If a third mirror is placed to form a straight triangular prism, then the rays of light will be trapped and reflected, endlessly running between the mirrors, creating an infinite number of images. It is a kaleidoscopic effect.

But this will only be so in theory. In reality, there are no perfect mirrors - some of the light is absorbed, some is scattered. After three hundred reflections, approximately one ten thousandth of the original light remains. Therefore, more distant reflections will be darker, and we will not see the most distant reflections at all.

But let us return to the case of two mirrors. Let two mirrors be parallel to each other, i.e. the angle between them is zero. It can be seen from the figure that the number of images will be infinite.

Again, in reality, we will not see an infinite number of reflections, because. mirrors are not perfect and absorb or scatter some of the light falling on them. In addition, as a result of the phenomenon of perspective, images will shrink until we can no longer distinguish them. You can also notice that distant images change color (turn green) as they A mirror does not equally reflect and absorb light of different wavelengths.

If the reflective surface of a mirror is flat, then it is a flat mirror. Light is always reflected from a flat mirror without scattering according to the laws of geometric optics:

• The angle of incidence is equal to the angle of reflection.
• The incident beam, the reflected beam and the normal to the mirror surface at the point of incidence lie in the same plane.

It should be remembered that a glass mirror has a reflective surface (usually a thin layer of aluminum or silver) placed on its back side. She is covered protective layer. This means that although the main reflected image is formed on this surface, the light will also be reflected from the front surface of the glass. A secondary image is formed, which is much weaker than the main one. It is usually invisible in everyday life, but creates serious problems in the field of astronomy. For this reason, all astronomical mirrors have a reflective surface applied to the front of the glass.

Image types

There are two types of images: real and imaginary.

The real is formed on the film of a video camera, camera or on the retina of the eye. Light rays pass through a lens or lens, converge, falling on the surface, and form an image at their intersection.

The imaginary (virtual) is obtained when the rays, reflected from the surface, form a divergent system. If you complete the continuation of the rays in the opposite direction, then they will certainly intersect at a certain (imaginary) point. It is from such points that an imaginary image is formed, which cannot be registered without the use of a flat mirror or other optical devices (loupe, microscope or binoculars).

Image in a flat mirror: properties and construction algorithm

For a real object, the image obtained with a flat mirror is:

• imaginary;
• straight (not inverted);
• the dimensions of the image are equal to the dimensions of the object;
• the image is the same distance behind the mirror as the object in front of it.

Let's build an image of some object in a flat mirror.

Let us use the properties of a virtual image in a flat mirror. Let's draw an image of a red arrow on the other side of the mirror. Distance A is equal to distance B, and the image is the same size as the object.

The imaginary image is obtained at the intersection of the continuation of the reflected rays. Let's depict light rays coming from an imaginary red arrow to the eye. We show that the rays are imaginary by drawing them with a dotted line. Continuous lines from the surface of the mirror show the path of the reflected rays.

Let's draw straight lines from the object to the points of reflection of the rays on the surface of the mirror. We take into account that the angle of incidence is equal to the angle of reflection.

Plane mirrors are used in many optical instruments. For example, in the periscope, flat telescope, graphic projector, sextant and kaleidoscope. The dental mirror for examining the oral cavity is also flat.

We now turn to the problem of finding images when light is reflected from various types of mirrors. The laws of the formation of images of luminous points upon reflection in a mirror and upon refraction in a lens are largely similar.

This analogy is, of course, not accidental; it is due to the fact that formally, as we saw in Chap. IX, the law of reflection is a special case of the law of refraction (when ).

The problem posed by us for the reflection of light rays from a flat mirror is solved most simply. At the same time, the reflection of light from a flat mirror is the simplest and most well-known case of the formation of virtual images considered in the previous section.

Rice. 203. Formation of a virtual image of a point in a plane mirror

Let a beam of rays from a point source (Fig. 203) fall on a flat mirror (metal mirror, water surface, etc.). Let's see what happens to this cone of rays, which has a vertex at the point . Take two arbitrary rays and . Each of them will be reflected according to the law of reflection, and the angle of each of them with the normal will remain unchanged after reflection. Consequently, the angle between the rays after reflection will also remain unchanged.

This angle between the reflected rays can be depicted in the figure by extending the reflected rays back beyond the plane of the mirror, which is shown in the drawing with dashed lines. The point of intersection of the continuation of the rays behind the mirror will lie on the same normal to the mirror as the point and at the same distance from the plane of the mirror, which can be easily seen from the equality of triangles and or and .

In view of the fact that the considered rays were completely arbitrary, we have the right to extend the results of reflection from a flat mirror established for them to the entire light beam. Therefore, we can state that when reflected from a flat mirror, a beam of light rays emanating from one point turns into a light beam in which the extensions of all light rays intersect again, at the same point.

As a result, to an observer placed in the path of the reflected rays, they will appear to intersect at the point , and this point will be the imaginary image of the point . The image will be imaginary in the above sense: there are no rays at the point behind the mirror, but the point is the vertex of the ray beam rotated after reflection from the mirror.

Consideration of the imaginary image of a luminous point in a flat mirror and the conclusions drawn about the position of this image “behind the mirror” make it easy to find the image of an extended object in a flat mirror as well.

Let there be a rectilinear luminous segment in front of the mirror (Fig. 204, a). Performing the construction of points according to the found recipe and connecting them with a straight line, we will get an image of all points of the segment.

This follows from elementary geometric considerations. Since the cap segment was chosen completely arbitrarily, then in the same way you can build an image of any object. Moreover, from the parallelism of all normals to the mirror, it is clear that the dimensions of the imaginary image in a flat mirror are equal to the dimensions of the object placed in front of the mirror.

Rice. 204. a) Formation of a virtual image of a rectilinear segment in a flat mirror. b) It seems to the observer that the candle is burning in a bottle of water located behind a glass plate where the imaginary image of a candle is located in this plate

In the solution found for the case of reflection of light beams from flat mirrors, each point of a luminous object is also depicted in a flat mirror as a point (i.e., stigmatically).

We now turn to the consideration of spherical mirrors. On fig. 205 shows a section of a concave spherical mirror of radius ; is the center of the sphere. The midpoint of the existing part of the spherical surface is called mirror pole. The normal to the mirror passing through the center of the mirror and through its pole is called the main optical axis of the mirror. Normals to the mirror, drawn at other points on its surface and also, of course, passing through the center of the mirror, are called side optical axes. One of them () is shown in Fig. 205. All normals to a spherical surface, of course, are equal, and the selection of the main optical axis among the side ones is not essential. The diameter of the circle bounding a spherical mirror is called the aperture of the mirror.

Rice. 205. Reflection from a spherical mirror of a beam coming out of a point on the axis

Everything that follows is a simplified repetition of what was said in §§88, 89 regarding lenses.

Let a point light source be located on the main axis of the mirror at a distance from the pole. Just as in the case of lenses, consider a beam belonging to a narrow beam, i.e., forming a small angle with the axis and incident on the mirror at a point at a height above the axis, so that it is small compared to and with the mirror radius . The reflected beam will cross the axis at a point at a distance from the pole. The angle formed by the reflected beam with the axis will be denoted by . It will also be small.

Obviously, there is a perpendicular to the surface of the mirror at the point of incidence, - the angle of incidence, - the angle of reflection. According to the law of reflection

Let the letter denote the angle formed by the radius with the axis. From the triangle we have

from a triangle

Adding (91.2) and (91.3) and taking into account that , we find where the source is located, and the point where the image is located, are conjugated, i.e., placing the source at the point , we get the image at the point (a consequence of the law reversibility of light rays, see §82).

The formula (91.6) obtained by us is the basic formula for a spherical mirror.

It is easy to prove that formula (91.6) remains valid for a convex spherical mirror.