>>Physics: Constructing an image in a mirror

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Flat mirror- This is a flat surface that specularly reflects light.

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). From the source the light goes in all directions. A beam of light falls on the mirror SAB, and the image is created by the entire beam. But to construct an image, it is enough to take any two rays from this beam, for example SO And S.C..  SO Ray falls perpendicular to the mirror surface AB (angle of incidence is 0), so the reflected one will go in the opposite direction OS S.C.. Ray (angle of incidence is 0), so the reflected one will go in the opposite direction And will be reflected at an angle \(~\gamma=\alpha\). Reflected rays SK diverge and do not intersect, but if they fall into a person’s eye, then the person will see the image S 1 which represents the point of intersection continuation

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

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

virtual image Thus, in flat mirror

the image is always virtual. Can be proven (consider triangles SOC SO= S 1 O, i.e. the image of point S 1 is located from the mirror at the same distance as the point S itself. It follows that to construct an image of a point in a plane mirror, it is enough to lower a perpendicular to the plane mirror from this point and extend it to the same distance behind the mirror ( Fig. 16.11).

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

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

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 “Study of the reflection of light from a plane mirror” and a presentation for the lesson.

Target:

2.Develop skills in observing and constructing images in a flat mirror.

3. Foster a creative approach to learning activities and a desire to experiment.

Motivation:

Visual impressions often turn out to be erroneous. Sometimes it is difficult to distinguish apparent light phenomena from reality. One example of a deceptive visual impression is the apparent image of an object in a plane mirror. Our task today is to learn how to construct an image of an object in one or two mirrors located at an angle to each other.

This means that the topic of our lesson will be “Constructing an image in plane mirrors.”

Primary updating of knowledge.

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

a) angle of incidence< 30 0

b) angle of reflection > angle of incidence

c) the reflected ray lies in the plane of the drawing

The angle between the incident ray and the plane mirror is equal to the angle between the incident ray 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 see an object only in the straight-line direction in which the light from the object enters our eyes. When looking at a flat mirror, we are looking 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 we see an imaginary, direct image in the mirror.

Print your name. Read it using a mirror. What happened? It turns out that the image is turned to face the mirror. Tell me which ones printed letters do not change when reflected in a plane mirror?

AND
Thus, we see an imaginary, straight image in the mirror, facing the mirror. For example, raised right hand appears to us to be left and vice versa.

P
A plane mirror is the only optical device in which the image and the object are congruent with each other. This device is widely used in our lives and not only for straightening hair.

Slide No. 5

What conclusion will we draw when constructing? (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 the same times as to the object.)

Slide No. 6

Consolidating new material

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

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

Q3 Construct an image of an acute triangle ABC in a plane mirror.

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

How to construct such an image?

This is the conclusion Anna Spitsova made when drawing up 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 No. 8

TO
how to construct such an image?

Where do you think you can use multiple images of an object in several plane mirrors?

Motivation for tomorrow

Today in the lesson we answered the question of how to construct an image in one flat mirror and in two, located at an angle to each other, and how many other mysteries are stored in an ordinary, familiar thing to all of us: a mirror. This is not the end of our 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 height, 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 search a lot.

D/Z:

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

Video tutorial 2: Flat mirror - Physics in experiments and experiments

Lecture:

Flat mirror- This is a glossy surface. If parallel beams of light fall on such a surface, then they are reflected parallel to each other. By looking at this topic, we can learn why we see ourselves when we look in the mirror.

So, let's first remember the laws of reflection and how to prove them. Take a look at the picture.

Let's pretend that S- some point that glows or reflects light. Consider two arbitrary rays that fall on some glossy surface. Let us move this point symmetrically, relative to the separation of the media. After these two rays are reflected from the surface, they enter our eye. Our brain is designed in such a way that it perceives any reflection as an image that is beyond the boundary of media separation. The most important thing in this explanation is that it really seems to us because of our own perception.

The image we see in the mirror is called imaginary, that is, it does not really exist.

We can even see an image that is not directly above the mirror, or if their sizes are not comparable. The most important thing is that the rays from this object must enter our eyes. This is why we can see the driver’s face on the bus and he is ours, despite the fact that he is not in front of the mirror.

We construct an image of an object in the mirror.

Construction of images in mirrors and their characteristics.

An image of any point A of an object in a spherical mirror can be constructed using any pair of standard rays: To construct an image of any point A of an object, it is necessary to find the point of intersection of any two reflected rays or their extensions; the most convenient are rays going as shown in the figures 2.6 – 2.9

2) a ray passing through the focus, after reflection, will go parallel to the optical axis on which this focus lies;

4) the beam incident on the pole of the mirror, after reflection from the mirror, goes symmetrically to the main optical axis (AB=BM)

Let's look at a few examples of constructing images in concave mirrors:

2) The object is located at a distance that is equal to the radius of curvature of the mirror. The image is real, equal in size to the size of the object, inverted, located strictly under the object (Fig. 2.11).

Rice. 2.12

3) The object is located between the focus and the pole of the mirror. Image – virtual, enlarged, direct (Fig. 2.12)

Mirror formula

Let us find the connection between the optical characteristic and the distances that determine the position of the object and its image.

Let the object be a certain point A located on the optical axis. Using the laws of light reflection, we will construct an image of this point (Fig. 2.13).

Let us denote the distance from the object to the pole of the mirror (AO), and from the pole to the image (OA¢).

Consider the triangle APC, we find that

From triangle APA¢, we obtain that . Let us exclude the angle from these expressions, since it is the only one that does not rely on the OR.

, or

(2.3)

Angles b, q, g rest on OR. Let the beams under consideration be paraxial, then these angles are small and, therefore, their values ​​in radian measure are equal to the tangent of these angles:

; ; , where R=OC, is the radius of curvature of the mirror.

Let us substitute the resulting expressions into equation (2.3)

Since we previously found out that the focal length is related to the radius of curvature of the mirror, then

(2.4)

Expression (2.4) is called the mirror formula, which is used only with the sign rule:

Distances , , are considered positive if they are measured along the path of the ray, and negative otherwise.

Convex mirror.

Let's look at several examples of constructing images in convex mirrors.

2) The object is located at a distance equal to the radius of curvature. Imaginary image, reduced, direct (Fig. 2.15)

The focus of a convex mirror is imaginary. Convex mirror formula

.

The sign rule for d and f remains the same as for a concave mirror.

The linear magnification of an object is determined by the ratio of the height of the image to the height of the object itself

. (2.5)

Thus, regardless of the location of the object relative to the convex mirror, the image always turns out to be virtual, straight, reduced and located behind the mirror. While the images in a concave mirror are more varied, they depend on the location of the object relative to the mirror. Therefore, concave mirrors are used more often.

Having considered the principles of constructing images in various mirrors, we have come to understand the operation of such various instruments as astronomical telescopes and magnifying mirrors in cosmetic devices and medical practice, we are able to design some devices ourselves.