It plays an important role in the study of seismic waves. Reflection is observed on surface waves in bodies of water. Reflection is observed with many types of electromagnetic waves, not just visible light. Reflection of VHF and higher frequency radio waves is important for radio transmissions and radar. Even hard X-rays and gamma rays can be reflected at small angles to the surface by specially made mirrors. In medicine, the reflection of ultrasound at the interfaces between tissues and organs is used when performing ultrasound diagnostics.
Story
The law of reflection was first mentioned in Euclid's Catoptrics, dating back to about 200 BC. e.
Laws of reflection. Fresnel formulas
The law of light reflection - establishes a change in the direction of travel of a light ray as a result of a meeting with a reflecting (mirror) surface: the incident and reflected rays lie in the same plane with the normal to the reflecting surface at the point of incidence, and this normal divides the angle between the rays into two equal parts. The widely used but less precise formulation “angle of incidence equals angle of reflection” does not indicate the exact direction of reflection of the beam. However, it looks like this:
This law is a consequence of the application of Fermat's principle to a reflecting surface and, like all laws of geometric optics, is derived from wave optics. The law is valid not only for perfectly reflective surfaces, but also for the boundary of two media that partially reflects light. In this case, like the law of refraction of light, it does not state anything about the intensity of reflected light.
Fedorov shift
Types of reflection
The reflection of light can be mirrored(that is, as observed when using mirrors) or diffuse(in this case, upon reflection, the path of the rays from the object is not preserved, but only the energy component of the light flux) depending on the nature of the surface.
Mirror reflection
Specular reflection of light is distinguished by a certain relationship between the positions of the incident and reflected rays: 1) the reflected ray lies in the plane passing through the incident ray and the normal to the reflecting surface, restored at the point of incidence; 2) the angle of reflection is equal to the angle of incidence. The intensity of reflected light (characterized by the reflection coefficient) depends on the angle of incidence and polarization of the incident beam of rays (see Polarization of Light), as well as on the ratio of the refractive indices n 2 and n 1 of the 2nd and 1st media. This dependence (for a reflecting medium - a dielectric) is expressed quantitatively by the Fresnel formula. From them, in particular, it follows that when light is incident normal to the surface, the reflection coefficient does not depend on the polarization of the incident beam and is equal to
In the important special case of normal incidence from air or glass onto their interface (refractive index of air = 1.0; glass = 1.5), it is 4%.
Total internal reflection
With an increase in the angle of incidence, the angle of refraction also increases, while the intensity of the reflected beam increases, and the refracted beam decreases (their sum is equal to the intensity of the incident beam). At a certain critical value, the intensity of the refracted beam becomes zero and complete reflection of light occurs. The value of the critical angle of incidence can be found by setting the refraction angle equal to 90° in the law of refraction:
Diffuse light reflection
When light is reflected from an uneven surface, the reflected rays diverge in different directions (see Lambert's Law). For this reason, you cannot see your reflection when looking at a rough (matte) surface. Reflection becomes diffuse when surface irregularities are of the order of a wavelength or more. Thus, the same surface can be matte, diffusely reflective for visible or ultraviolet radiation, but smooth and specularly reflective for infrared radiation.
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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.
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; part of it penetrates into another medium, that is, it is absorbed.
Light absorption (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). Another good example of the use of light reflection is mirrors and light 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 effort, fos - “light”), retroreflector, flicker (from the English flick - “blink”) - a device designed to reflect a beam of light towards the source with minimal dispersion.
Every cyclist knows that traveling at night 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.
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.
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
The smooth surface of water, glass and polished metal is approximately mirror-like. 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
A very important example of the application 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 in different directions, let's take two close rays incident on a plane 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 area 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, you can look in the mirror in the bathroom from a certain angle, but if you move away from it to the side, you won’t 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.)
Most likely, today there is not a single house where there is no mirror. It has become so firmly established in our lives that it is difficult for a person to live without it. What is this object, how does the image reflect it? What if you put two mirrors opposite each other? This amazing object has become central to many fairy tales. There are a sufficient number of signs about him. What does science say about the mirror?
A little history
Most modern mirrors are coated glass. As a coating, a thin metal layer is applied to the back of the glass. Literally a thousand years ago, mirrors were carefully polished copper or bronze disks. But not everyone could afford a mirror. It cost a lot of money. Therefore, poor people were forced to look at their own mirrors, which show a person in full height - this is generally a relatively young invention. It is approximately 400 years old.
The mirror surprised people even more when they could see the reflection of the mirror in the mirror - it generally seemed to them something magical. After all, an image is not the truth, but a kind of reflection of it, a kind of illusion. It turns out that we can see truth and illusion at the same time. It is not surprising that people attributed many magical properties to this object and were even afraid of it.
The very first mirrors were made of platinum (surprisingly, this metal was once not valued at all), gold or tin. Scientists have discovered mirrors made back in the Bronze Age. But the mirror that we can see today began its history after glass blowing technology was mastered in Europe.
Scientific view
From the point of view of the science of physics, the reflection of a mirror in a mirror is the multiplied effect of the same reflection. The more such mirrors installed opposite each other, the greater the illusion of being filled with the same image. This effect is often used in attractions for entertainment. For example, in the Disney park there is a so-called endless hall. There, two mirrors were installed opposite each other, and this effect was repeated many times.
The resulting reflection of a mirror in a mirror, multiplied by a relatively infinite number of times, became one of the most popular attractions. Such attractions have long been part of the entertainment industry. At the beginning of the 20th century, an attraction called the “Palace of Illusions” appeared at an international exhibition in Paris. He was extremely popular. The principle of its creation is the reflection of mirrors in mirrors installed in a row, the size of a full human being, in a huge pavilion. People had the impression that they were in a huge crowd.
Law of Reflection
The principle of operation of any mirror is based on the law of propagation and reflection in space. This law is the main one in optics: it will be the same (equal) to the angle of reflection. It's like a falling ball. If you throw it vertically down towards the floor, it will also bounce vertically upward. If you throw it at an angle, it will bounce back at an angle equal to the angle of impact. Light rays are reflected from a surface in a similar way. Moreover, the smoother and smoother this surface is, the more ideally this law works. Reflection in a flat mirror works according to this law, and the more ideal its surface, the better the reflection.
But if we are dealing with matte or rough surfaces, then the rays are scattered chaotically.
Mirrors can reflect light. What we see, all reflected objects, is thanks to rays that are similar to those of the sun. If there is no light, then nothing is visible in the mirror. When light rays fall on an object or any living creature, they are reflected and carry with them information about the object. Thus, the reflection of a person in the mirror is an idea of an object formed on the retina of his eye and transmitted to the brain with all its characteristics (color, size, distance, etc.).
Types of mirror surfaces
Mirrors can be flat or spherical, which, in turn, can be concave or convex. Today there are already smart mirrors: a kind of media carrier designed to demonstrate to the target audience. The principle of its operation is as follows: when a person approaches, the mirror seems to come to life and begins to show a video. Moreover, this video was not chosen by chance. A system is built into the mirror that recognizes and processes the resulting image of a person. She quickly determines his gender, age, emotional mood. Thus, the system in the mirror selects a demo video that can potentially interest a person. This works 85 times out of 100! But scientists don’t stop there and want to achieve 98% accuracy.
Spherical mirror surfaces
What is the basis of the work of a spherical mirror, or, as it is also called, a curved mirror - a mirror with convex and concave surfaces? Such mirrors differ from ordinary ones in that they bend the image. Convex mirror surfaces make it possible to see more objects than flat ones. But at the same time, all these objects seem smaller in size. Such mirrors are installed in cars. Then the driver has the opportunity to see the image on both the left and the right.
A concave curved mirror focuses the resulting image. In this case, you can see the reflected object in as much detail as possible. A simple example: these mirrors are often used for shaving and in medicine. The image of an object in such mirrors is assembled from images of many different and individual points of this object. To construct an image of an object in a concave mirror, it will be enough to construct an image of its two extreme points. The images of the remaining points will be located between them.
Translucency
There is another type of mirror that has translucent surfaces. They are designed in such a way that one side is like an ordinary mirror, and the other is half transparent. From this transparent side, you can see the view behind the mirror, but from the usual side you can see nothing but the reflection. Such mirrors can often be seen in crime films, when police are conducting an investigation and interrogating a suspect, and on the other hand they are watching him or bringing in witnesses for identification, but so that they are not visible.
The Myth of Infinity
There is a belief that by creating a mirror corridor, you can achieve infinity of the light beam in the mirrors. Superstitious people who believe in fortune telling often use this ritual. But science has long proven that this is impossible. It’s interesting that the mirror is never 100% complete. This requires an ideal, 100% smooth surface. And it can be approximately 98-99%. There are always some errors. Therefore, girls who tell fortunes in such mirrored corridors by candlelight risk, at most, simply entering a certain psychological state that can negatively affect them.
If you place two mirrors opposite each other and light a candle between them, you will see many lights lined up in one row. Question: how many lights can you count? At first glance, this is an infinite number. After all, there seems to be no end to this series. But if we carry out certain mathematical calculations, we will see that even with mirrors having 99% reflection, after approximately 70 cycles the light will become half as weak. After 140 reflections it will weaken by another factor of two. Each time the rays of light dim and change color. Thus, there will come a moment when the light goes out completely.
So is infinity still possible?
Infinite reflection of a beam from a mirror is possible only with absolutely ideal mirrors placed strictly parallel. But is it possible to achieve such absoluteness when nothing in the material world is absolute and ideal? If this is possible, it is only from the point of view of religious consciousness, where absolute perfection is God, the Creator of everything omnipresent.
Due to the lack of an ideal surface of the mirrors and their ideal parallelism to each other, a number of reflections will undergo bending, and the image will disappear, as if around a corner. If we also take into account the fact that a person looking at when there are two mirrors, and there is also a candle between them, will also not stand strictly parallel, then the visible row of candles will disappear behind the frame of the mirror quite quickly.
Multiple reflection
At school, students learn to construct images of an object using the law of reflection of light in a mirror, an object and its mirror image are symmetrical. By studying the construction of images using a system of two or more mirrors, students receive the effect of multiple reflection as a result.
If you add a second one located at right angles to the first to a single flat mirror, then not two reflections will appear in the mirror, but three (they are usually designated S1, S2 and S3). The rule works: the image that appears in one mirror is reflected in the second, then the first is reflected in the other, and again. The new one, S2, will be reflected in the first one, creating a third image. All reflections will match.
Symmetry
The question arises: why are the reflections symmetrical in the mirror? The answer is given by geometric science, and in close connection with psychology. What is top and bottom for us changes places for the mirror. The mirror seems to turn inside out what is in front of it. But it’s surprising that in the end the floor, walls, ceiling and everything else look the same in reflection as they do in reality.
How does a person perceive the reflection in the mirror?
Man sees thanks to light. Its quanta (photons) have the properties of a wave and a particle. Based on the theory of primary and secondary light sources, photons from a light beam falling on an opaque object are absorbed by atoms on its surface. Excited atoms immediately return the energy they absorbed. Secondary photons are emitted evenly in all directions. Rough and matte surfaces give diffuse reflection.
If this is the surface of a mirror (or something similar), then the particles emitting light are ordered, and the light exhibits wave characteristics. Secondary waves are compensated in all directions, in addition to the fact that they are subject to the law that the angle of incidence is equal to the angle of reflection.
Photons seem to bounce off the mirror elastically. Their trajectories start from objects that seem to be located behind him. These are what the human eye sees when looking in the mirror. The world behind the mirror is different from the real one. To read the text there, you need to start from right to left, and the clock hands go in the opposite direction. The double in the mirror raises his left hand when the person standing in front of the mirror raises his right.
Reflections in the mirror will be different for people looking into it at the same time, but located at different distances and in different positions.
In ancient times, the best mirrors were those made of carefully polished silver. Today, a layer of metal is applied to the back of the glass. It is protected from damage by several layers of paint. Instead of silver, to save money, a layer of aluminum is often applied (reflection coefficient is approximately 90%). The human eye practically does not notice the difference between silver coating and aluminum.
Issue 2In the second episode of the program “Academy of Entertaining Sciences. Physics" Professor Quark will tell the children about the physics of mirrors. It turns out that the mirror has many interesting features, and with the help of physics you can figure out why this happens. Why does the mirror reflect everything the other way around? Why do objects in the mirror seem further away than they are? How to make a mirror reflect objects correctly? You will learn the answers to these and many other questions by watching a video lesson on the physics of mirrors.
Physics of mirrors
A mirror is a smooth surface designed to reflect light. The invention of the true glass mirror can be traced back to 1279, when the Franciscan John Peckham described a method of coating glass with a thin layer of lead. The physics of a mirror isn't that complicated. The path of rays reflected from the mirror is simple if we apply the laws of geometric optics. A ray of light falls on a mirror surface at an angle alpha to the normal (perpendicular) drawn to the point of incidence of the ray on the mirror. The angle of the reflected beam will be equal to the same alpha value. A ray incident on a mirror at right angles to the plane of the mirror will be reflected back at itself. For the simplest - flat - mirror, the image will be located behind the mirror symmetrically to the object relative to the plane of the mirror; it will be virtual, straight and the same size as the object itself. This is not difficult to establish using the law of light reflection. Reflection is a physical process of interaction of waves or particles with a surface, a change in the direction of the wave front at the boundary of two media with different properties, in which the wave front returns to the medium from which it came. Simultaneously with the reflection of waves at the interface between media, as a rule, refraction of waves occurs (with the exception of cases of total internal reflection). The law of light reflection - establishes a change in the direction of travel of a light ray as a result of a meeting with a reflecting (mirror) surface: the incident and reflected rays lie in the same plane with the normal to the reflecting surface at the point of incidence, and this normal divides the angle between the rays into two equal parts. The widely used but less precise formulation “the angle of reflection is equal to the angle of incidence” does not indicate the exact direction of reflection of the beam. The physics of a mirror allows you to perform various interesting tricks based on optical illusions. Daniil Edisonovich Quark will demonstrate some of these tricks to television viewers in his laboratory.
At the interface between two different media, if this interface significantly exceeds the wavelength, a change in the direction of light propagation occurs: part of the light energy returns to the first medium, that is reflected, and part penetrates into the second environment and at the same time refracted. The AO beam is called incident ray, and ray OD – reflected beam(see Fig. 1.3). The relative position of these rays is determined laws of reflection and refraction of light.
Rice. 1.3. Reflection and refraction of light.
The angle α between the incident ray and the perpendicular to the interface, restored to the surface at the point of incidence of the ray, is called angle of incidence.
The angle γ between the reflected ray and the same perpendicular is called reflection angle.
Each medium to a certain extent (that is, in its own way) reflects and absorbs light radiation. The quantity that characterizes the reflectivity of the surface of a substance is called reflection coefficient. The reflection coefficient shows what part of the energy brought by radiation to the surface of a body is the energy carried away from this surface by reflected radiation. This coefficient depends on many factors, for example, on the composition of the radiation and on the angle of incidence. The light is completely reflected from a thin film of silver or liquid mercury deposited on a sheet of glass.
Laws of light reflection
The laws of light reflection were discovered experimentally in the 3rd century BC by the ancient Greek scientist Euclid. Also, these laws can be obtained as a consequence of Huygens’ principle, according to which every point in the medium to which a disturbance has reached is a source of secondary waves. The wave surface (wave front) at the next moment is a tangent surface to all secondary waves. Huygens' principle is purely geometric.
A plane wave falls on the smooth reflective surface of a CM (Fig. 1.4), that is, a wave whose wave surfaces are stripes.
Rice. 1.4. Huygens' construction.
A 1 A and B 1 B are the rays of the incident wave, AC is the wave surface of this wave (or the wave front).
Bye wave front from point C will move in time t to point B, from point A a secondary wave will spread across the hemisphere to a distance AD = CB, since AD = vt and CB = vt, where v is the speed of wave propagation.
The wave surface of the reflected wave is a straight line BD, tangent to the hemispheres. Further, the wave surface will move parallel to itself in the direction of the reflected rays AA 2 and BB 2.
Right triangles ΔACB and ΔADB have a common hypotenuse AB and equal legs AD = CB. Therefore they are equal.
Angles CAB = = α and DBA = = γ are equal because these are angles with mutually perpendicular sides. And from the equality of triangles it follows that α = γ.
From Huygens' construction it also follows that the incident and reflected rays lie in the same plane with the perpendicular to the surface restored at the point of incidence of the ray.
The laws of reflection are valid when light rays travel in the opposite direction. As a consequence of the reversibility of the path of light rays, we have that a ray propagating along the path of the reflected one is reflected along the path of the incident one.
Most bodies only reflect the radiation incident on them, without being a source of light. Illuminated objects are visible from all sides, since light is reflected from their surface in different directions, scattering. This phenomenon is called diffuse reflection or diffuse reflection. Diffuse reflection of light (Fig. 1.5) occurs from all rough surfaces. To determine the path of the reflected ray of such a surface, a plane tangent to the surface is drawn at the point of incidence of the ray, and the angles of incidence and reflection are constructed in relation to this plane.
Rice. 1.5. Diffuse reflection of light.
For example, 85% of white light is reflected from the surface of snow, 75% from white paper, 0.5% from black velvet. Diffuse reflection of light does not cause unpleasant sensations in the human eye, unlike specular reflection.
- this is when light rays incident on a smooth surface at a certain angle are reflected predominantly in one direction (Fig. 1.6). The reflective surface in this case is called mirror(or mirror surface). Mirror surfaces can be considered optically smooth if the size of irregularities and inhomogeneities on them does not exceed the light wavelength (less than 1 micron). For such surfaces, the law of light reflection is satisfied.
Rice. 1.6. Specular reflection of light.
Flat mirror is a mirror whose reflecting surface is a plane. A flat mirror makes it possible to see objects in front of it, and these objects appear to be located behind the mirror plane. In geometric optics, each point of the light source S is considered the center of a diverging beam of rays (Fig. 1.7). Such a beam of rays is called homocentric. The image of point S in an optical device is the center S’ of a homocentric reflected and refracted beam of rays in various media. If light scattered by the surfaces of various bodies falls on a flat mirror and then, reflected from it, falls into the eye of the observer, then images of these bodies are visible in the mirror.
Rice. 1.7. An image created by a plane mirror.
The image S’ is called real if the reflected (refracted) rays of the beam intersect at point S’. The image S’ is called imaginary if it is not the reflected (refracted) rays themselves that intersect, but their continuations. Light energy does not reach this point. In Fig. Figure 1.7 shows an image of a luminous point S, which appears using a flat mirror.
Beam SO falls on the CM mirror at an angle of 0°, therefore, the angle of reflection is 0°, and this ray, after reflection, follows the path OS. From the entire set of rays falling from point S onto a flat mirror, we select the ray SO 1.
The SO 1 beam falls on the mirror at an angle α and is reflected at an angle γ (α = γ). If we continue the reflected rays behind the mirror, they will converge at point S 1, which is a virtual image of point S in a plane mirror. Thus, it seems to a person that the rays are coming out of point S 1, although in fact there are no rays leaving this point and entering the eye. The image of point S 1 is located symmetrically to the most luminous point S relative to the CM mirror. Let's prove it.
Beam SB incident on the mirror at an angle of 2 (Fig. 1.8), according to the law of light reflection, is reflected at an angle of 1 = 2.
Rice. 1.8. Reflection from a flat mirror.
From Fig. 1.8 you can see that angles 1 and 5 are equal – like vertical ones. The sums of the angles are 2 + 3 = 5 + 4 = 90°. Therefore, angles 3 = 4 and 2 = 5.
Right triangles ΔSOB and ΔS 1 OB have a common leg OB and equal acute angles 3 and 4, therefore, these triangles are equal in side and two angles adjacent to the leg. This means that SO = OS 1, that is, point S 1 is located symmetrically to point S relative to the mirror.
In order to find the image of an object AB in a flat mirror, it is enough to lower perpendiculars from the extreme points of the object onto the mirror and, continuing them beyond the mirror, set aside a distance behind it equal to the distance from the mirror to the extreme point of the object (Fig. 1.9). This image will be virtual and life-size. The dimensions and relative position of the objects are preserved, but at the same time, in the mirror, the left and right sides of the image change places compared to the object itself. The parallelism of light rays incident on a flat mirror after reflection is also not violated.
Rice. 1.9. Image of an object in a plane mirror.
In technology, mirrors with a complex curved reflecting surface, for example, spherical mirrors, are often used. Spherical mirror- this is the surface of the body, having the shape of a spherical segment and specularly reflecting light. The parallelism of rays when reflected from such surfaces is violated. The mirror is called concave, if the rays are reflected from the inner surface of the spherical segment. Parallel light rays, after reflection from such a surface, are collected at one point, which is why a concave mirror is called collecting. If the rays are reflected from the outer surface of the mirror, then it will convex. Parallel light rays are scattered in different directions, so convex mirror called dispersive.