Flat mirror. Constructing images in a plane mirror

We now move on to the problem of finding images when light is reflected from various types of mirrors. The laws for 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 (at ).

The most simple way to solve our problem is to reflect light rays from a flat mirror. 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, discussed in the previous paragraph.

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 with its vertex at point . Let's 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 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 by dashed lines. The intersection point 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 is easy to verify from the equality of triangles and or and .

Due to 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 say that when reflected from a plane 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 point , and this point will be a virtual image of point . The image will be imaginary in the sense indicated above: there are no rays at the point behind the mirror, but the point is the vertex of the beam of rays rotated after reflection from the mirror.

Consideration of the virtual 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 also find the image of an extended object in a flat mirror.

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

This follows from elementary geometric considerations. Since the cap segment was chosen completely arbitrarily, it is possible to construct an image of any object in the same way. Moreover, from the parallelism of all normals to the mirror, it is clear that the dimensions of the virtual image in a plane 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 plane mirror. b) It seems to the observer that a candle is burning in a bottle of water located behind a glass plate where the virtual image of the candle is located in this plate

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

We now turn to consideration of spherical mirrors. In Fig. 205 shows a cross-section of a concave spherical mirror of radius ; - center of the sphere. The midpoint of the existing part of the spherical surface is called the pole of the mirror. 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. The normals to the mirror, drawn at other points on its surface and also, of course, passing through the center of the mirror, are called secondary optical axes. One of them () is shown in Fig. 205. All normals to a spherical surface are, of course, equal, and distinguishing the main optical axis from the secondary ones is not essential. The diameter of the circle enclosing a spherical mirror is called the mirror hole.

Rice. 205. Reflection from a spherical mirror of a ray emerging from 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 ray 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 radius of the mirror. The reflected ray will intersect the axis at a point at a distance from the pole. Let us denote the angle formed by the reflected ray with the axis. 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 us denote by a letter 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 at which the image is located are conjugate with each other, i.e., by placing the source at point , we obtain an image at the point (a consequence of the law reversibility of light rays, see §82).

The formula (91.6) we obtained is the basic formula of a spherical mirror.

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

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 is this so?” you will find in this paragraph.

Rice. 11.1. Without a light source, it is impossible to see anything. If there is a light source, we see not only the source itself, but also objects that reflect the light coming from the source

Find out why we see bodies that are not sources of light

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

What happens if there is some body in the path of the light beam? Some light can pass through a body if it is transparent, some will be absorbed, and some will certainly be reflected from the body. Some 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*. Let's fix a mirror in the center of the washer and direct a narrow beam of light at it so that it produces a light stripe on the surface of the washer. We see that a beam of light reflected from the mirror also produces a light stripe on the surface of the washer (see Fig. 11.2).

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

From point O of incidence of the beam, 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 ray and the perpendicular drawn from the point of incidence is called the angle of incidence; The angle β between the reflected ray and a given perpendicular is called the angle of reflection.

By measuring the angles α and β, you 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 reversibility of light rays: the reflected ray follows the path of the incident ray

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 ray, the reflected ray and the perpendicular to the reflection surface drawn from the point of incidence of the ray 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 back in the 3rd century. BC e.

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

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

Studying the image in a plane mirror

Let's consider how an image is created in a flat mirror (Fig. 11.6).

Let a diverging 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 travel in a diverging 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 hit your eye, it will seem to you that the reflected rays are coming out of point S 1, although in reality there is no light source at point S 1. Therefore, point S 1 is called the virtual image of point S. A plane mirror always gives a virtual image.

Let's find out how the object and its image are located relative to the mirror. To do this, let's turn to geometry. Consider, for example, a beam 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 acute angles (since according to the law of light reflection α = β). From the equality of triangles we have that SO = S 1 O, that is, the point S and its image S 1 are symmetrical relative 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 relative 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 relative 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 a 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 the window glass. But the image disappears if you close the curtains: 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 one is physical phenomenon- reflection of light. For an image to appear, light must be reflected specularly from the surface: after mirror reflection light coming from a point source S, the continuations of the reflected rays will intersect at one point S 1, which will be the image of point S (Fig. 11.8, a). Such reflection is only possible from very smooth surfaces. They are called mirror surfaces. In addition to an ordinary mirror, examples of mirror surfaces are glass, polished furniture, calm surface of water, etc. (Fig. 11.8, b, c).

If light is reflected from a rough surface, such reflection is called scattered (diffuse) (Fig. 11.9). In this case, the reflected rays propagate in different directions (which is why we see an 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, but the black surface absorbs almost all the light falling on it.

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

Task. In Fig. 1 schematically shows an object BC and a mirror NM. Find graphically the area from which the image of the object BC is completely visible.

Analysis of a physical problem. 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 is reflected into the observer’s eye. It is clear that if rays emanating from extreme points object, then rays emanating from all points of the object will be reflected into the eye.

Decision, analysis of results

1. Let's construct point B 1 - the image of point B in a flat mirror (Fig. 2, a). The area limited 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 - enter his eye (Fig. 2, c). This means that 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, look at Fig. again. 2 to the problem and suggest an easier way to find the area of ​​vision of an object in a plane mirror. Test your assumptions by constructing a field of vision for several objects in two ways.

Let's sum it up

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

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

There are specular and diffuse reflections of light. In the case of mirror 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? angle of reflection? 3. Formulate the laws of light reflection. 4. Using what device can you verify the validity of the laws of light reflection? 5. What is the property of reversibility of light rays? 6. In what case is an image called virtual? 7. Describe the image of an object in a flat mirror. 8. How does diffuse reflection of light differ from specular reflection?

Exercise No. 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 him.

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 rice. 1 in your 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 mirror surface, 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 a mirrored display case at a speed of 4 km/h. At what speed is your reflection approaching you? How much will the distance between you and your reflection decrease when you walk 2 m?

7. Sunbeam reflected from the surface of the lake. The angle between the incident ray and the horizon is twice as large as the angle between the incident and reflected rays. 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) Construct the girl’s reflection in the mirror.

2) Find graphically which 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 a car’s headlights, a puddle on the asphalt appears to the driver dark spot against a lighter road background. Why?

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

LABORATORY WORK No. 3

Subject. Study of light reflection using a plane mirror.

Goal: experimentally test the laws of light reflection.

equipment: light source (candle or 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 performing work, remember: 1) safety requirements when working with glass objects; 2) laws of light reflection.

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

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

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

3) install 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 produces 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. Place three points on a sheet of paper: the first - in the middle of the incident beam of light, the second - in the middle of the reflected beam of light, the third - in the place where the light beam falls on the mirror (Fig. 2).

3. Repeat the described steps several more times (for different sheets paper), placing the mirror at different angles to the 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 experiment results

For each experience:

1) construct a ray incident on the mirror and a reflected ray;

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

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

Analysis of the experiment and its results

Analyze the experiment and its results. Draw a conclusion in which you indicate: 1) what relationship you have established between the angle of incidence of the light beam and the angle of its reflection; 2) whether the experimental results turned out to be absolutely accurate, and if not, what were the reasons for the error.

creative task

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

If possible, conduct an experiment.

Assignment with an asterisk

If the reflecting surface of the mirror is flat, then it is a type of 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 ray, the reflected ray, and the normal to the mirror surface at the point of incidence lie in the same plane.

One thing to remember is that a glass mirror has a reflective surface (usually a thin layer of aluminum or silver) placed on its back. It is covered with a protective layer. This means that although the main reflected image is formed on this surface, 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 side 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 when falling on a surface, and at their intersection form an image.

Imaginary (virtual) is obtained when rays, reflected from a surface, form a diverging 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 these points that a virtual image is formed, which cannot be recorded without the use of a flat mirror or other optical instruments (magnifying glass, microscope or binoculars).

Image in a plane mirror: properties and construction algorithm

For a real object, the image obtained using a plane mirror is:

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

Let's construct an image of some object in a plane mirror.

Let's use the properties of a virtual image in a plane 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.

A virtual image is obtained at the intersection of the continuation of reflected rays. Let's depict light rays, going from the imaginary red arrow to the eye. Let us show that the rays are imaginary by drawing them with a dotted line. Continuous lines, coming 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 a periscope, flat telescope, graphic projector, sextant and kaleidoscope. A dental mirror for examining the oral cavity is also flat.

Schoolchildren are able to construct an image of an object in a flat mirror, using the law of light reflection, and know that the object and its image are symmetrical relative to the plane of the mirror. As an individual or group creative assignment(abstract, research project) can be assigned to study the construction of images in a system of two (or more) mirrors - the so-called “multiple reflection”.

A single plane mirror produces one image of an object.

S – object (luminous point), S 1 – image

Let's 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 appearing in one mirror is reflected in another. S 1 is reflected in mirror 2, S 2 is reflected in mirror 1 and these reflections in in this case match up.

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 a reflection of S 1 in mirror 2 and a reflection of S 2 in mirror 1.

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

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

Total quantity visible images object for the case of two perpendicularly located mirrors is equal to 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 ray can experience no more than two reflections, after which it exits the system (see figure). If you decrease the angle between the mirrors, the light will be reflected and “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 device (Germany, 1900) with varying angles between mirrors for studying and demonstrating multiple reflections.

A similar homemade device.

If you put a third mirror to create a straight triangular prism, then the rays of light will be trapped and, reflected, will endlessly run between the mirrors, creating an infinite number of images. This is a kaleidoscopic effect.

But this will only happen in theory. In reality, there are no ideal 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 ones at all.

But let's return to the case of two mirrors. Let two mirrors be located 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 ideal and absorb or scatter some of the light falling on them. In addition, as a result of the phenomenon of perspective, images will become smaller until we can no longer distinguish them. You can also notice that distant images change color (turn green), because A mirror does not reflect and absorb light of different wavelengths equally.

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

How to construct an image of an extended source in a flat mirror (Figure 2.13)? What properties of the image can be identified?

Can a flat mirror be used as a movie screen?

Now, using the law of light reflection, construct an image of a point and an object large sizes in a spherical mirror:

First - in the convex;

- then - in the concave.

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

How do you explain the difference in size and position of images 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 significance of this principle?

Indeed, by applying the Huygens-Fresnel principle and performing simple geometric constructions, it is possible to find the wave surface at any time from 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 new about the material learned in class?

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

Which of your results were surprising or unexpected for you?

What did you learn during the lesson?

Please formulate the main results of the lesson.

Which homework you would assign to consolidate and deepen knowledge on the topic “Huygens' principle. Law of light reflection"?

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

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

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

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

Law of light refraction

Lesson type: explanation of new material.

1) educational 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 light refraction based on the Huygens-Fresnel principle, and the formulation of the law of light refraction; identifying 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, develop students’ analytical abilities.

Visuals and Demonstrations: Optical Disc Demonstration

organizational moment - 3 min

explanation of new material - 30 min

fixing the material - 10 min

homework - 2 min

Introductory word from the teacher. Students are asked to recall what they know about the refraction of light from the geometric optics course.

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

Observing the refraction of light

At the boundary of two media, light changes the direction of its propagation (demonstration using an optical disk). 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.

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Exist various games. Some develop children’s thinking and horizons, others develop dexterity and strength, and others develop design skills. There are games aimed at developing creativity in a child, in which the child shows his creativity, initiative, and independence. Creative expressions children play differently.

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In the history of preschool pedagogy there have been several pedagogical approaches to guide children's story-based games. The first approach is the so-called traditional approach to management role-playing game. This approach has developed in the practice of preschool education based on the results of studies of child development.

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Successful Leadership educational games, first of all, provides for the selection and thinking through of their program content, a clear definition of tasks, determination of the place and role in the whole educational process, interaction and other games and forms of learning. It should be aimed at development.

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

At the moment when the wave reaches point B and the excitation of oscillations begins at this point, the secondary wave with the center at point A will already be a hemisphere with radius r = AD = υΔt = SV. 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 secondary waves is the plane DB, tangent to the spherical surfaces. It represents 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-angled, then ∠DBA = ∠CAB. But α = ∠CAB and γ = ∠DBA are like angles with mutually perpendicular sides. Therefore, the angle reflection is equal to the angle of incidence 1 :

The law of light reflection 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.

When the direction of propagation of light rays is reversed, the reflected ray will become incident, and the incident ray will become reflected. The reversibility of the path of light rays is their important property.

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

Questions for the paragraph

1. How to use the law of reflection to construct an image of a point source of light in a plane mirror?

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

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Law of light reflection. Flat mirror

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In this lesson you will learn about light reflection 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 well known to you; you received it in your 8th grade physics course. We see the world around us due to the reflection of light.

Law of Reflection

First, let's remember the definition.

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

Please note the following: 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 construct an incident ray, a reflected ray 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 (),

– sliding angle.

These laws were first formulated by Euclid in his work Catoptrics. And we have already become acquainted with them as part 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.

The law of light reflection implies the reversibility of light rays. That is, if we swap the places of the incident beam and the reflected one, then nothing will change from the point of view of the trajectory of the light flux.

The range of applications of the law of light reflection is very wide. This is also the fact with which we started the lesson that we see most of the objects around us in reflected light (the moon, a tree, a table). One more good example Uses of light reflection are mirrors and reflectors (reflectors).

Reflectors

Let's understand the principle of operation of a simple reflector.

Reflector (from the ancient Greek kata - a prefix with the meaning of force, 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 a day without reflectors can be dangerous.

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

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

The 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 flat case: two mirrors forming an angle of 90 degrees. A ray 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. Operating principle of the corner 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 ray that hits such a system of mirrors, after reflection from three planes, will go parallel to the arriving ray in the opposite direction (see Fig. 3.).

Rice. 3. Corner reflector

Reflection will occur. It is this simple device with its properties that is called a corner reflector.

Proof of the Law of Reflection

Let's consider the reflection of a plane wave (a wave is called plane if the surfaces of equal phase are planes) (Fig. 1.)

Rice. 4. Plane wave reflection

In the figure - a surface, and - two rays 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, the centers of which lie at the interface between the media.

Different sections of the wave surface do not reach the reflecting boundary at the same time. Excitation of oscillations at a point will begin earlier than at a point for a period of time. At the moment when the wave reaches a point and the excitation of oscillations begins at this point, the secondary wave centered at the point (reflected ray) 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 the 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, using Huygens' principle, we proved the law of light reflection. The same proof can be obtained using Fermat's principle.

Types of reflection

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

Rice. 5. Reflection from a rough, wavy surface

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

A surface is considered uneven if the size of its irregularities is not less than the length of light waves.

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

A surface that disperses light evenly in all directions is called completely matte. In nature, you will not find a completely 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 light wavelength, then such a surface will be called a mirror.

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

Rice. 6. Reflection from a mirror surface

Approximately mirror image is smooth surface water, glass and polished metal. Even a matte surface can turn out to be mirror-like 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 what fraction of the energy of an incident beam is reflected and what is absorbed.

Albedo

Albedo is a coefficient that shows what fraction of the energy of an incident beam is reflected from the surface (from the Latin albedo - “whiteness”) - a characteristic of the diffuse reflectivity of a surface.

Or in other words, this is the share expressed as a percentage of reflected radiation energy from the energy arriving at the surface.

The closer the albedo is to one hundred, 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 reflected much better from a white surface than from a black one.

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

Rice. 7. Albedo value for some surfaces

Flat mirror

Very important example Applications of the law of light reflection are plane mirrors - a flat surface that specularly reflects light. You have such mirrors in your home.

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

Rice. 8. Constructing an image of an object in a plane mirror

- a point source of light emitting rays at different directions, let's take two close rays incident on a flat mirror. The reflected rays will go as if they were coming from a point that is symmetrical to the point relative 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 behind the mirror to the point

It seems to us that the reflected rays come from the 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, which is why this point is called an imaginary image.

The location of the source and the size of the mirror determine the field of vision - the region of space from which the image of the source is visible. The vision area is defined by the edges of the mirror and .

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

In order to construct an image of an arbitrary object in a plane 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 relative to the plane of the mirror, then the image of the object will be symmetrical relative to the plane of the mirror (Fig. 9.)

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

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

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 learned how to construct images of objects in a plane mirror and characterize them.

Analysis of the problem on the law of light reflection

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

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

Rice. 10. Illustration for the problem

Recall that the image in a plane mirror is located symmetrically to the object relative to the mirror plane. This means that if the car moves during the time , then the image, which is located symmetrically, will move during the same time and, therefore, the image moves away from the mirror at a 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 everyone” (Source)

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

3. Internet portal “diplomivanov.narod.ru” (Source)

Homework

1. Construct images AB in a plane mirror

2. Construct an image in a plane mirror

Image in a plane mirror.

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

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

Let's consider how the light source and its virtual image are located relative to the mirror.

We fix a piece of flat glass on a stand in a vertical position. By placing a lit candle in front of the glass, we will see in the glass, as in a mirror, the image of a candle. Now take a second candle of the same kind, but unlit, 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 appear to be lit. This means that the unlit candle is located in the same place where the image of the lit candle is observed. By measuring 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 virtual image of an object in a plane mirror is at the same distance from the mirror as the object itself.
The object and its image in the mirror are not identical, but symmetrical figures. For example, mirror image The right glove is a left glove that can be combined with the right glove only by turning it inside out.

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

The figure shows how the eye perceives the image of point S in the mirror. Rays SO, SO1 and SO2 are reflected from the mirror in accordance with the laws of reflection. The SO ray 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 diverging beam, the eye perceives a luminous point S1 behind the mirror. In fact, at point S1 the extensions of the reflected rays (dotted line), and not the rays themselves, converge (it only seems that the diverging rays entering the eye come from points located in the “looking glass”), therefore such an image is called imaginary (or imaginary), and the point from which, as it seems to us, each beam emanates is the image point. Each point of the object corresponds to an image point.

According to the law of light reflection, the virtual image of an object is located symmetrically relative 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 the mirror. We only think the light is coming from the image because our brain perceives the light entering our eyes as light from a source in front of us. Since the rays do not actually converge in the image, placing a piece of white paper or film in the same place as the image does 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 located. As we will see later, actual images can be formed using lenses and curved mirrors (for example, spherical).

Points S and S’ are symmetrical relative 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 produces a powerful stream of light that brightly illuminates distant objects. There is a lighthouse that sends rays of light tens of kilometers away to guide ships. In all these and many other cases, 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 can be concave or convex. A spherical concave mirror is a highly 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 vertex of the mirror O is called the optical axis of the mirror.

Let us send a beam of light rays from the flashlight onto the mirror, parallel to the optical axis of the mirror. After reflection from the mirror, the rays of this beam will converge at one point F, lying on the optical axis of the mirror. This point is called the focal point of the mirror. If a light source is placed at the focal point of a mirror, 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's bring the light source (a lit candle or electric lamp) closer to the concave mirror so that its image is visible in the mirror. This image - virtual - is located behind the mirror. Compared to the object, it is enlarged and straight.
Let's gradually move the light source away from the mirror. At the same time, its image will move away from the mirror, its size will increase, and then the virtual image will disappear. But now the image of the light source can be obtained on a screen located in front of the mirror, that is, an actual image of the light source can be obtained.
The further we move the light source from the mirror, the closer to the mirror we will have to place the screen in order to obtain an image of the source on it. The size of the image will decrease.
All real images in relation to the object turn out to be reversed (inverted). Their sizes, depending on the distance of the object to the mirror, can be larger, smaller than the object, or equal to the size of the object (light source).

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

Constructing an image in a concave mirror.

A spherical mirror is called concave if the reflecting surface is inner side spherical segment, i.e. if the center of the mirror is located further from the observer than its edges.

If the dimensions of a concave mirror are small in comparison with its radius of curvature, that is, a beam of rays parallel to the main optical axis falls on a concave spherical mirror; after reflection from the mirror, the rays 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 main 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 construct an image of an object in a mirror. In the figure, the luminous point S is located in front of a concave mirror. Let's draw three rays from it to the mirror and construct the reflected rays. These reflected rays will intersect at point S1. Since we took three arbitrary rays emanating from point S, then all other rays falling from this point on the mirror, after reflection, will intersect at point S1. Therefore, point S1 is an image of point S.
For geometric construction To image a point, it is enough to know the direction of propagation of two rays emanating from this point. These rays can be chosen completely arbitrarily. However, it is more convenient to use rays whose course 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. We will pass 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 rays will intersect. This point will be the image of point S; all the rays reflected by the mirror coming from point S will intersect at it.
The image of an object consists of images of many individual points of this object. To construct an image of an object in a concave mirror, it is enough to construct an image of the two extreme points of this object. The images of the remaining points will be located between them. In the figure, the object is depicted as an arrow AB.
By constructing images of points A and B using the above method, we obtain an image of the entire object A1B1. Object AB is located behind the center of the spherical surface of the mirror (behind point C). Its 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 actually 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 falls 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 convex where R is the radius of curvature of the mirror: OF=CF=-R/2.

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 the correct position of the eye. To reduce the reading error, precision measuring instruments are equipped with a mirror scale. Anyone working with such a device sees the scale divisions, a narrow arrow and its image in the mirror. The correct reading on the scale will be such that the eye is positioned so that the arrow covers its image in the mirror.
The “bunny” reflected from the mirror shifts noticeably when the mirror is rotated 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 according to the displacement of the light “bunny” on this scale. The “bunny” is obtained from a small mirror connected to the moving part of the device and illuminated by 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 it is necessary to change the direction of rays, for example in a periscope (picture 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 you take a large concave mirror, you can get a very high temperature at the focus. Here you can place a water tank to obtain hot water, for example, for domestic needs using solar energy.

Using concave mirrors you can direct most light emitted by the source in the desired 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, and spotlights are installed.

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

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