flat mirror is a flat surface that reflects light specularly.

The construction of an image in mirrors is based on the laws of rectilinear propagation and reflection of light.

Let's build an image of a point source S(Fig. 16.10). Light travels from the source in all directions. A beam of light falls on a mirror SAB, and the image is created by the entire beam. But to build an image, it is enough to take any two rays from this beam, for example SO and SC. Ray SO falls perpendicular to the surface of the mirror AB(the angle of incidence is 0), so the reflected will go in the opposite direction OS. Ray SC reflected at the angle \(~\gamma=\alpha\). reflected beams OS and SC diverge and do not intersect, but if they fall into the human eye, then the person will see the image S 1 which is the intersection point continuation reflected rays.

The image obtained at the intersection of reflected (or refracted) rays is called actual image.

The image obtained by crossing not the reflected (or refracted) rays themselves, but their continuations, is called imaginary image.

Thus, in a flat mirror, the image is always imaginary.

It can be proved (consider the triangles SOC and S 1 OC) that the distance SO= S 1 O, i.e. the image of the point S 1 is located at the same distance from the mirror as the point S itself. It follows that to construct the image of a point in a flat mirror, it is enough to lower the perpendicular from this point onto the flat mirror and continue it at the same distance beyond the mirror ( Fig. 16.11).

When constructing an image of an object, the latter is represented as a set of point light sources. Therefore, it is enough to find the image of the extreme points of the object.

The image A 1 B 1 (Fig. 16.12) of an object AB in a flat mirror is always imaginary, straight, of the same dimensions as the object, and symmetrical with respect to the mirror.

When constructing an image of any point of the source, there is no need to consider many rays. To do this, it is enough to build two beams; their intersection point will determine the location of the image. It is most convenient to construct those rays, the course of which is easy to follow. The path of these rays in the case of reflection from the mirror is shown in Fig. 213.

Rice. 213. Various techniques for constructing an image in a concave spherical mirror

Beam 1 passes through the center of the mirror and is therefore normal to the surface of the mirror. This beam returns after reflection exactly back along the secondary or main optical axis.

Beam 2 is parallel to the main optical axis of the mirror. This beam after reflection passes through the focus of the mirror.

Beam 3, which passes from the point of the object through the focus of the mirror. After reflection from the mirror, it goes parallel to the main optical axis.

Beam 4, incident on the mirror at its pole, will be reflected back symmetrically with respect to the main optical axis. To build an image, you can use any pair of these rays.

Having built images of a sufficient number of points of an extended object, one can get an idea of ​​the position of the image of the entire object. In the case of a simple object shape shown in Fig. 213 (a line segment perpendicular to the main axis), it is enough to build only one point of the image. Some more complicated cases are considered in the exercises.

On fig. 210 were given geometric constructions of images for different positions of the object in front of the mirror. Rice. 210, in - the object is placed between the mirror and the focus - illustrates the construction of a virtual image by continuing the rays behind the mirror.

Rice. 214. Construction of an image in a convex spherical mirror.

On fig. 214 an example of constructing an image in a convex mirror is given. As mentioned earlier, in this case, virtual images are always obtained.

To build an image in a lens of any point of an object, as well as when building an image in a mirror, it is enough to find the intersection point of any two rays emanating from this point. The simplest construction is carried out using the rays shown in Fig. 215.

Rice. 215. Various techniques for constructing an image in a lens

Beam 1 goes along the secondary optical axis without changing direction.

Beam 2 falls on the lens parallel to the main optical axis; refracted, this beam passes through the back focus.

Beam 3 passes through the front focus; refracted, this beam goes parallel to the main optical axis.

The construction of these rays is carried out without any difficulty. Any other ray coming from the point would be much more difficult to construct - one would have to directly use the law of refraction. But this is not necessary, since after the construction is completed, any refracted ray will pass through the point .

It should be noted that when solving the problem of constructing an image of off-axis points, it is not at all necessary that the chosen simplest pairs of rays actually pass through the lens (or mirror). In many cases, for example, when photographing, the object is much larger than the lens, and rays 2 and 3 (Fig. 216) do not pass through the lens. However, these rays can be used to build an image. The real beam u involved in the formation of the image is limited by the frame of the lens (shaded cones), but converge, of course, at the same point , since it is proved that when refraction in the lens, the image of a point source is again a point.

Rice. 216. Building an image in the case when the object is much larger than the lens

Let us consider several typical cases of an image in a lens. We will consider the lens to be converging.

1. The object is from the lens, at a distance greater than twice the focal length. This is usually the position of the subject when photographing.

Rice. 217. Building an image in a lens when the object is behind double the focal length

The construction of the image is given in fig. 217. Since , then by the lens formula (89.6)

,

i.e., the image lies between the back focus and a thin lens located at twice the focal length from the optical center of the lens. The image is inverted (reverse) and reduced, since according to the magnification formula

2. We note an important special case when a beam of rays parallel to some side optical axis falls on the lens. A similar case occurs, for example, when photographing very distant extended objects. The construction of the image is given in fig. 218.

In this case, the image lies on the corresponding secondary optical axis, at the point of its intersection with the rear focal plane (the so-called plane perpendicular to the main axis and passing through the back focus of the lens).

Rice. 218. Image construction in the case when a beam of rays parallel to the side optical axis falls on the lens

The points of the focal plane are often called the foci of the corresponding side axes, leaving the name main focus behind the point corresponding to the main axis.

The focus distance from the main optical axis of the lens and the angle between the secondary axis under consideration and the main axis are obviously related by the formula (Fig. 218)

3. The subject lies between a point at twice the focal length and the front focus - the normal position of the subject when projected by a projection lamp. To study this case, it suffices to use the property of reversibility of the image in a lens. We will consider the source (see Fig. 217), then it will be an image. It is easy to see that in the case under consideration the image is inverse, enlarged and lies at a distance from the lens greater than twice the focal length.

It is useful to note the particular case when the object is at a distance equal to twice the focal length from the lens, i.e. . Then by the lens formula

,

i.e., the image also lies at twice the focal length from the lens. The image in this case is inverted. To increase, we find

i.e. the image has the same dimensions as the subject.

4. Of great importance is the special case when the source is in a plane perpendicular to the main axis of the lens and passing through the front focus.

This plane is also the focal plane; it is called the anterior focal plane. If a point source is located at any of the points of the focal plane, i.e., in one of the front foci, then a parallel beam of rays emerges from the lens, directed along the corresponding optical axis (Fig. 219). The angle between this axis and the main axis and the distance from the source to the axis are related by the formula

5. The subject lies between the front focus and the lens, i.e. . In this case, the image is direct and imaginary.

The construction of the image in this case is given in Fig. 220. Since , to increase we have

i.e. the image is enlarged. We will return to this case when considering the loop.

Rice. 219. Sources and lie in the front focal plane. (Beams of rays emerge from the lens parallel to the side axes passing through the source points)

Rice. 220. Building an image in the case when the object lies between the front focus and the lens

6. Building an image for a diverging lens (Fig. 221).

The image in a diverging lens is always imaginary and direct. Finally, since , the image is always reduced.

Rice. 221. Building an image in a diverging lens

Note that for all constructions of rays passing through a thin lens, we may not consider their path inside the lens itself. It is only important to know the location of the optical center and the main foci. Thus, a thin lens can be represented by a plane passing through the optical center perpendicular to the main optical axis, on which the positions of the main foci should be marked. This plane is called the principal plane. It is obvious that the beam entering the lens and leaving it passes through the same point of the main plane (Fig. 222, a). If we keep the outlines of the lens in the drawings, then only for a visual difference between the converging and diverging lenses; for all constructions, however, these outlines are superfluous. Sometimes, for greater simplicity of the drawing, instead of the outlines of the lens, a symbolic image is used, shown in Fig. 222b.

Rice. 222. a) Replacing the lens with the main plane; b) a symbolic image of a converging (left) and diverging (right) lens; c) replacement of the mirror by the main plane

Similarly, a spherical mirror can be represented by the main plane that touches the surface of the sphere at the pole of the mirror, indicating on the main axis the position of the center of the sphere and the main focus. The position indicates whether we are dealing with a concave (collecting) or a convex (diffusing) mirror (Fig. 222, c).

Construction of images in spherical mirrors

In order to build an image of any point light source in a spherical mirror, it is enough to build a path any two beams emanating from this source and reflected from the mirror. The point of intersection of the reflected rays themselves will give a real image of the source, and the point of intersection of the continuations of the reflected rays will give an imaginary one.

characteristic rays. To construct images in spherical mirrors, it is convenient to use certain characteristic rays, the course of which is easy to construct.

1. Beam 1 , incident on the mirror parallel to the main optical axis, reflected, passes through the main focus of the mirror in a concave mirror (Fig. 3.6, a); in a convex mirror, the main focus is the continuation of the reflected beam 1 ¢ (Fig. 3.6, b).

2. Beam 2 , passing through the main focus of a concave mirror, reflected, goes parallel to the main optical axis - a beam 2 ¢ (Fig. 3.7, a). Ray 2 incident on a convex mirror so that its continuation passes through the main focus of the mirror, being reflected, it also goes parallel to the main optical axis - the beam 2 ¢ (Fig. 3.7, b).

Rice. 3.7

3. Consider a beam 3 passing through Centre concave mirror - point O(Fig. 3.8, a) and beam 3 , falling on a convex mirror so that its continuation passes through the center of the mirror - the point O(Fig. 3.8, b). As we know from geometry, the radius of the circle is perpendicular to the tangent to the circle at the point of contact, so the rays 3 in fig. 3.8 fall on mirrors under right angle, that is, the angles of incidence of these rays are equal to zero. So the reflected rays 3 ¢ in both cases coincide with the falling ones.

Rice. 3.8

4. Beam 4 passing through pole mirrors - dot R, is reflected symmetrically about the main optical axis (rays 4¢ in fig. 3.9), since the angle of incidence is equal to the angle of reflection.

Rice. 3.9

STOP! Decide for yourself: A2, A5.

Reader: Once I took an ordinary tablespoon and tried to see my image in it. I saw the image, but it turned out that if you look at convex part of the spoon, then the image direct, and if on concave then inverted. I wonder why this is so? After all, a spoon, I think, can be considered as some kind of spherical mirror.

Task 3.1. Build images of small vertical segments of the same length in a concave mirror (Fig. 3.10). The focal length is set. It is considered known that the images of small rectilinear segments perpendicular to the main optical axis in a spherical mirror are also small rectilinear segments perpendicular to the main optical axis.

Decision.

1. Case a. Note that in this case all objects are in front of the main focus of the concave mirror.

Rice. 3.11

We will build images only of the upper points of our segments. To do this, draw through all the upper points: BUT, AT and With one common beam 1 , parallel to the main optical axis (Fig. 3.11). reflected beam 1 F 1 .

Now from points BUT, AT and With let the rays 2 , 3 and 4 through the main focus of the mirror. reflected beams 2 ¢, 3 ¢ and 4 ¢ will go parallel to the main optical axis.

Points of intersection of rays 2 ¢, 3 ¢ and 4 ¢ with beam 1 ¢ are images of points BUT, AT and With. These are the dots BUT¢, AT¢ and With¢ in fig. 3.11.

To get images segments enough to drop from the points BUT¢, AT¢ and With¢ perpendicular to the main optical axis.

As can be seen from fig. 3.11, all images turned out valid and inverted.

Reader: And what does it mean - valid?

Author: Picture of items happens valid and imaginary. We already met with the imaginary image when we studied a flat mirror: the imaginary image of a point source is the point at which intersect continuation rays reflected from the mirror. The actual image of a point source is the point where the themselves rays reflected from the mirror.

Note that what farther there was an object from the mirror, the smaller got his image and themes closer this image to mirror focus. Note also that the image of the segment, the lower point of which coincided with center mirrors - dot O, happened symmetrical object relative to the main optical axis.

I hope now you understand why, looking at your reflection in the concave surface of a tablespoon, you saw yourself reduced and turned upside down: after all, the object (your face) was clearly before main focus of a concave mirror.

2. Case b. In this case, the items are between main focus and mirror surface.

The first beam is a beam 1 , as in the case a, let through the upper points of the segments - the points BUT and AT 1 ¢ will pass through the main focus of the mirror - the point F 1 (Fig. 3.12).

Now let's use rays 2 and 3 , emanating from the points BUT and AT and passing through pole mirrors - dot R. reflected beams 2 ¢ and 3 ¢ make the same angles with the main optical axis as the incident rays.

As can be seen from fig. 3.12 reflected beams 2 ¢ and 3 ¢ do not intersect reflected beam 1 ¢. Means, valid images in this case No. But continuation reflected rays 2 ¢ and 3 ¢ intersect with continuation reflected beam 1 ¢ at points BUT¢ and AT¢ behind the mirror, forming imaginary dot images BUT and AT.

Dropping perpendiculars from points BUT¢ and AT¢ to the main optical axis, we get images of our segments.

As can be seen from fig. 3.12, the images of the segments turned out direct and enlarged, and than closer subject to the main focus, topics more his image and themes farther this image is from a mirror.

STOP! Decide for yourself: A3, A4.

Task 3.2. Construct images of two small identical vertical segments in a convex mirror (Fig. 3.13).

Rice. 3.13 Fig. 3.14

Decision. Let's beam 1 through the top points of the segments BUT and AT parallel to the main optical axis. reflected beam 1 ¢ goes so that its continuation crosses the main focus of the mirror - the point F 2 (Fig. 3.14).

Now let's put rays on the mirror 2 and 3 from points BUT and AT so that the continuation of these rays pass through Centre mirrors - dot O. These rays will be reflected in such a way that the reflected rays 2 ¢ and 3 ¢ coincide with the incident rays.

As we see from fig. 3.14 reflected beam 1 ¢ does not intersect with reflected beams 2 ¢ and 3 ¢. Means, valid point images BUT and In no. But continuation reflected beam 1 ¢ intersects with sequels reflected rays 2 ¢ and 3 ¢ at points BUT¢ and AT¢. Therefore, the points BUT¢ and AT¢ – imaginary dot images BUT and AT.

For imaging segments drop perpendiculars from points BUT¢ and AT¢ to the main optical axis. As can be seen from fig. 3.14, the images of the segments turned out direct and reduced. And what closer object to the mirror more his image and themes closer it to the mirror. However, even a very distant object cannot give an image that is far from the mirror. beyond the main focus of the mirror.

I hope now it is clear why, when you looked at your reflection in the convex surface of the spoon, you saw yourself reduced, but not upside down.

STOP! Decide for yourself: A6.

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. It is covered with a 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 generally 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.

Lesson topic: "Flat mirror. Obtaining an image in a flat mirror.

Equipment: two mirrors, a protractor, matches, a project by an 8th grade student on the topic “Investigation of the reflection of light from a flat mirror” and a presentation for the lesson.

Target:

2. To develop the skills of observation and imaging in a flat mirror.

3. To cultivate a creative approach to learning activities, the desire to experiment.

Motivation:

Visual impressions are often wrong. Sometimes it is difficult to distinguish apparent light phenomena from the real. One example of a deceptive visual impression is the apparent image of an object in a flat mirror. Our task today is to learn how to build an image of an object in one and two mirrors located at an angle to each other.

So, the topic of our lesson will be "Building an image in flat mirrors."

Primary updating of knowledge.

In the last lesson, we studied one of the basic laws of the propagation of light - this is the law of reflection of light.

a) angle of incidence< 30 0

b) angle of reflection > angle of incidence

c) the reflected beam lies in the plane of the figure

The angle between the incident beam and the plane mirror is equal to the angle between the incident beam and the reflected one. What is the angle of incidence? (answer 30 0 )

Learning new material.

One of the properties of our vision is that we can only see an object in a rectilinear direction, along which the light from the object enters our eyes. Looking at a flat mirror, we look at an object in front of the mirror, and therefore the light from the object does not directly enter the eyes, but only after reflection. Therefore, we see the object behind the mirror, and not where it actually is. This means that the image in the mirror we see is imaginary, direct.

Write your name in capital letters. Read it with a mirror. What happened? It turns out the image is turned to face the mirror. Tell me, which printed letters do not change when reflected in a flat mirror?

And
so, the image in the mirror we see imaginary, direct, turned to the mirror face. For example, a raised right hand appears to us as a left hand and vice versa.

P
A flat mirror is the only optical device in which the image and object are congruent to each other. This device is widely used in our life and not only for correcting hair.

Slide number 5

What conclusion will we draw during the construction? (The distance from the mirror to the image is the same as from the mirror to the object, the image is located perpendicular to the mirror, the distance to the image changes as much as to the object.)

Slide #6

Fixing new material

IN 1. A person approaches a flat mirror at a speed of 1m/s. How fast is it moving towards its image? (2m/s)

IN 2. A person stands in front of a vertical mirror at a distance of 1m from it. What is the distance from a person to his image? (2m)

B3 Construct an image of an acute-angled triangle ABC in a flat mirror.

It is very interesting to look into two mirrors at once, located at an angle to each other. Place the mirrors at an angle of 90 0 , place a match between them, observe what will happen to the images if the angle between the mirrors is reduced?

How to build such an image?

This is the conclusion that Anna Spitsova made while compiling her project. Do you agree with her? Determine how many images will be in the mirror if the angle between the mirrors is 45 0 , 20 0 ?

Slide #8

To
how to build such an image?

Where do you think it is possible to use multiple images of an object in several flat mirrors?

Motivation for tomorrow

Today in the lesson, we answered the question of how to build an image in one flat mirror and in two, located at an angle to each other, and how many more mysteries are stored in an ordinary, familiar thing to all of us: a mirror. This is not the end of the study of a flat mirror, you may have a desire, for example, to calculate what size the mirror should be in order to see yourself in full growth, how the image depends on the angle of inclination, etc. Remember that new things are discovered not by those who know a lot, but by those who are looking for a lot.

D/W:

§64, exercise 31(1,2), for those who wish: make a kaleidoscope or a periscope.