New concepts arose in connection with the study of electrical phenomena, but it is easier to introduce them for the first time through mechanics. We know that two particles attract each other and that the strength of their attraction decreases with the square of the distance. We can represent this fact in another way, which we will do, although it is difficult to understand the advantages of the new method. The small circle in Fig. 49 represents an attracting body, say the Sun. In reality, our picture should be presented as a model in space, and not as a drawing on a plane. Then the small circle would become a sphere in space, representing the Sun. The body we will call trial body, placed somewhere in the vicinity of the Sun will be attracted to the Sun, and the force of attraction will be directed along the line connecting the centers of both bodies. Thus, the lines in our figure indicate the direction of the gravitational force of the Sun for various positions of the test body. The arrows on each line show that the force is directed towards the Sun; this means that this force is an attractive force. This gravitational field lines. For now this is just a name, and there is no reason to dwell on it in more detail. Our drawing has one characteristic feature that we will look at later. Lines of force are built in space where there is no matter. While all the lines of force, in short, field, show only how a test body will behave when placed near the spherical body for which the field is constructed.
The lines in our spatial model are always perpendicular to the surface of the sphere. Since they diverge from one point, they are more densely located near the sphere and increasingly diverge from each other as they move away from it. If we increase the distance from the sphere by two or three times, then the density of lines in the spatial model (but not in our drawing!) will be four or nine times less. So the lines serve two purposes. On the one hand, they show the direction of forces acting on a body placed adjacent to the sphere - the Sun; on the other hand, the density of the lines of force shows how the force changes with distance. The field image in the figure, correctly interpreted, characterizes the direction of the gravitational force and its dependence on distance. From such a drawing the law of gravity can be read just as well as from a description of its action in words or in the precise and meager language of mathematics. This representation of the field, as we will call it, may seem clear and interesting, but there is no reason to think that its introduction signifies any real progress. It would be difficult to prove its usefulness in the case of gravity. Maybe someone will find it useful to consider these lines not just a drawing, but something O greater, and imagine the real actions of forces passing along the lines. This can be done, but then the speed of action along the lines of force must be considered infinitely large. The force acting between two bodies, according to Newton's law, depends only on the distance; time is not included in the consideration. It does not take time to transfer force from one body to another. But since motion at infinite speed says nothing to any reasonable person, an attempt to make our drawing something O greater than the model leads to nothing. But we do not intend to discuss the problem of gravity now. It served us only as an introduction to simplify the explanation of similar methods of reasoning in the theory of electricity.
We begin by discussing an experiment that has led to serious difficulties in the mechanistic view. Let us have a current flowing through a conductor shaped like a circle. In the center of this coil there is a magnetic needle. At the moment the current arises, a new force appears, acting on the magnetic pole and perpendicular to the line connecting the wire and the pole. This force, caused by a charge moving in a circle, depends, as Rowland's experiment showed, on the speed of the charge. These experimental facts contradict the usual view, according to which all forces must act along the line connecting the particles and can only depend on distance.
The exact expression for the force with which the current acts on a magnetic pole is very difficult; in fact, it is much more complex than the expression of gravitational forces. But we can try to imagine its actions as clearly as we did in the case of gravity. Our question is this: With what force does a current act on a magnetic pole placed anywhere in the vicinity of a conductor through which the current flows? It would be quite difficult to describe this power in words. Even a mathematical formula would be complex and inconvenient. It is much better to represent everything we know about the action of forces using a drawing, or rather, using a spatial model with lines of force. Some of the difficulties arise from the fact that a magnetic pole exists only in connection with another magnetic pole, forming a dipole. However, we can always imagine a magnetic dipole of such a length that it will be possible to take into account the force acting only on the pole that is placed near the current. The other pole can be considered so distant that the force acting on it can be ignored. For definiteness, we will assume that a magnetic pole placed near a wire through which current flows is positive.
The nature of the force acting on the positive magnetic pole can be seen from Fig. 50. Arrows near the wire show the direction of the current from the highest potential to the lowest.
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All other lines are field lines of this current, lying in a certain plane. If the drawing is done properly, then these lines can give us an idea of both the direction of the vector characterizing the action of the current on the positive magnetic pole, and the length of this vector. Force, as we know, is a vector, and to determine it, we must know the direction of the vector and its length. We are mainly interested in the question of the direction of the force acting on the pole. Our question is: how can we find, based on the figure, the direction of the force at any point in space?
The rule for determining the direction of force for such a model is not as simple as in the previous example, where the force lines were straight. To facilitate reasoning, only one field line is drawn in the following figure (Fig. 51). The force vector lies on the tangent to the force line, as indicated in the figure. The force vector arrow coincides in direction with the arrows on the force lines. Therefore, it is the direction in which the force acts on the magnetic pole at a given point. Nice drawing or rather good model tells us something also about the length of the force vector at any point. This vector should be longer where the lines are more dense, i.e., near the conductor, and shorter where the lines are less dense, i.e., away from the conductor.
In this way, the lines of force or, in other words, the field allows us to determine the forces acting on the magnetic pole at any point in space. For now, this is the only justification for careful field construction. Knowing that O expresses the field, we will consider with deeper interest the lines of force associated with the current. These lines are circles; they surround the conductor and lie in a plane perpendicular to the plane in which the current loop is located. Considering the nature of the force in the figure, we once again come to the conclusion that the force acts in the direction perpendicular to any line connecting the conductor and the pole, because the tangent to the circle is always perpendicular to its radius. We can summarize all our knowledge about the action of forces in the construction of a field. We introduce the concept of field along with the concepts of current and magnetic pole in order to more simply represent the acting forces.
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Every current is associated with magnetic field; in other words, a magnetic pole placed near a conductor through which current flows is always subject to some force. Let us note in passing that this property of current allows us to construct a sensitive device for detecting current. Once we have learned to recognize the nature of magnetic forces from a model of the field associated with a current, we will always draw the field surrounding the conductor through which the current flows in order to represent the action of magnetic forces at any point in space. As a first example, we will look at the so-called solenoid. It is a spiral of wire, as shown in Fig. 52. Our task is to study through experiment everything that can be known about the magnetic field associated with the current flowing through the solenoid, and to combine this knowledge in constructing the field. The picture shows us the result. Curved lines of force are closed; they surround the solenoid, characterizing the magnetic field of the current.
The field generated by a magnetic rod can be represented in the same way as the field of a current. Rice. 53 shows this. The lines of force are directed from the positive pole to the negative. The force vector always lies on the tangent to the field line and is greatest near the pole, because the field lines are most densely located in these places. The force vector expresses the action of a magnet on the positive magnetic pole. In this case, the magnet, and not the current, is the “source” of the field.
The last two figures should be carefully compared. In the first case, we have the magnetic field of the current flowing through the solenoid, in the second - the field of the magnetic rod. We will not pay attention to the solenoid and the rod, but will consider only the external fields created by them. We immediately notice that they have exactly the same character; in both cases, the lines of force run from one end - the solenoid or rod - to the other.
The idea of the field bears its first fruit! It would be very difficult to discern any pronounced similarity between the current flowing through the solenoid and the magnetic rod if this were not revealed in the structure of the field.
The concept of a field can now be put to a much more serious test. We will soon see whether it is more than a new representation of the forces at work. We could say: let us assume for a moment that the field, and only it, characterizes in the same way all actions determined by its source. This is just a guess. It would mean that if the solenoid and magnet have the same field, then all their actions must also be the same. It would mean that two solenoids, through which electric current flows, behave like two magnetic rods; that they attract or repel each other, depending on their relative position, in exactly the same way as is the case with magnetic rods. It would also mean that the solenoid and the rod attract and repel each other in the same way as two rods. In short, it would mean that all the actions of the solenoid through which the current flows and the actions of the corresponding magnetic rod are the same, since only the field is essential, and the field in both cases is of the same character. The experiment completely confirms our assumption!
How difficult it would be to foresee these facts without the concept of field! The expression for the force acting between a current-carrying conductor and a magnetic pole is very complex. In the case of two solenoids, we would have to investigate the forces with which both currents act on each other. But if we do this with the help of a field, we immediately determine the nature of all these actions as soon as the similarity is discovered between the field of the solenoid and the field of the magnetic rod.
We have the right to believe that the field is something much larger than we first thought. The properties of the field itself turn out to be essential for describing the phenomenon. The difference in the field sources is not significant. The significance of the field concept is revealed in the fact that it leads to new experimental facts.
Field turns out to be a very useful concept. It arose as something placed between the source and the magnetic needle in order to describe the acting force. He was thought of as the “agent” of the current, through which all the actions of the current were carried out. But now the agent also acts as a translator, translating the laws into simple, clear, easily understood language.
The first success of description using a field showed that it can be convenient for considering all the actions of currents, magnets and charges, that is, considering not directly, but using the field as a translator. The field can be considered as something always associated with a current. It exists even if there is no magnetic pole with which to detect its presence. Let us try to consistently follow this new guiding thread.
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The field of a charged conductor can be introduced in much the same way as the gravitational field or the field of a current or magnet. Let's take the simplest example again. To draw the field of a positively charged sphere, we must ask the question: what kind of forces act on a small positively charged test body placed near the source of the field, that is, near the charged sphere? The fact that we take a positively rather than a negatively charged test body is a simple convention which determines in which direction the field line arrows should be drawn. This model (Fig. 54) is similar to the gravitational field model due to the similarity of Coulomb's and Newton's laws. The only difference between both models is that the arrows are in opposite directions. In fact, two positive charges repel, and two masses attract. However, the field of a sphere with a negative charge (Fig. 55) will be identical to the gravitational field, since a small positive test charge will be attracted by the field source.
If both the electric charge and the magnetic pole are at rest, then there is no interaction between them - neither attraction nor repulsion. Expressing a similar fact in field language, we can say: the electrostatic field does not affect the magnetostatic one, and vice versa. The words “static field” mean that we are talking about a field that does not change over time. Magnets and charges could remain next to each other forever if no external force disturbed their state. Electrostatic, magnetostatic and gravitational fields are different in nature. They do not mix: each retains its individuality independently of the others.
Let us return to the electric sphere, which until now has been at rest, and assume that it has come into motion due to the action of some external force. The charged sphere moves. In field language, this expression means: the field of an electric charge changes with time. But the movement of this charged sphere is equivalent to a current, as we already know from Rowland's experiment. Further, each current is accompanied by a magnetic field. Thus, our chain of conclusions is as follows:
Charge movement → Electric field change
Current → Magnetic field associated with current.
Therefore we conclude:
Change electric field, produced by the movement of a charge, is always accompanied by a magnetic field.
Our conclusion is based on Oersted's experience, but there is more to it than that. It contains the recognition that the connection of the electric field, changing with time, with the magnetic field is very significant for our further conclusions.
Since the charge remains at rest, only an electrostatic field exists. But as soon as the charge begins to move, a magnetic field arises. We can say more. The magnetic field caused by the movement of a charge will be stronger the larger the charge and the faster it moves. This is also a conclusion from Rowland's experience. Using field language again, we can say that the faster the electric field changes, the stronger the accompanying magnetic field.
We will try here to translate the facts already known to us from the language of fluid theory, developed in accordance with the old mechanistic views, into the new language of the field. Later we will see how clear, instructive and comprehensive our new language is.
Relativity and mechanics
The theory of relativity necessarily arises from serious and deep contradictions in the old theory, from which there seemed to be no way out. Force new theory lies in the consistency and simplicity with which it resolves all these difficulties using only a few very convincing assumptions.
Although the theory arose from the field problem, it must cover all physical laws. The difficulty seems to arise here. The laws of the field, on the one hand, and the laws of mechanics, on the other, are completely different in nature. The electromagnetic field equations are invariant with respect to Lorentz transformations, and the mechanical equations are invariant with respect to classical transformations. But the theory of relativity requires that all laws of nature be invariant under Lorentzian, and not classical, transformations. The latter are only a special, limiting case of Lorentz transformations, when the relative velocities of both coordinate systems are very small. If this is so, then classical mechanics should be modified to accommodate the requirement of invariance under Lorentz transformations. Or, in other words, classical mechanics cannot be valid if speeds approach the speed of light. The transition from one coordinate system to another can be carried out only in one way - through Lorentz transformations.
It was not difficult to change classical mechanics so that it did not contradict either the theory of relativity or the abundance of material obtained by observation and explained by classical mechanics. The old mechanics is valid for low speeds and forms a limiting case of the new mechanics.
It is interesting to consider some example of the change in classical mechanics that the theory of relativity introduces. Perhaps this will lead us to some conclusions that can be confirmed or refuted by experiment.
Suppose that a body having a certain mass moves along a straight line and is exposed to an external force acting in the direction of movement. Force, as we know, is proportional to the change in speed. Or, to put it more clearly, it does not matter whether a given body increases its speed in one second from 100 to 101 meters per second, or from 100 kilometers to 100 kilometers and one meter per second, or from 300,000 kilometers to 300,000 kilometers and one meter per second. The force required to impart to a given body any specific change in speed is always the same.
Is this position correct from the point of view of the theory of relativity? No way! This law is valid only for low speeds. What, according to the theory of relativity, is the law for high speeds approaching the speed of light? If the speed is high, then an extremely large force is needed to increase it. It is not at all the same thing to increase by one meter per second a speed equal to approximately 100 m/s, or a speed approaching light speed. The closer the speed is to the speed of light, the more difficult it is to increase it. When the speed is equal to the speed of light, it is no longer possible to increase it further. Thus, the new things that relativity theory introduces are not surprising. The speed of light is the upper limit for all speeds. No finite force, no matter how great, can cause an increase in speed beyond this limit. In place of the old law of mechanics connecting force and change in speed, a more complex law appears. From our new point of view, classical mechanics is simpler because in almost all observations we are dealing with velocities significantly lower than the speed of light.
A body at rest has a certain mass, the so-called rest mass. We know from mechanics that every body resists a change in its motion; the greater the mass, the stronger the resistance, and the smaller the mass, the weaker the resistance. But in the theory of relativity we have something more. A body resists change more strongly not only in the case when its rest mass is greater, but also in the case when its speed is greater. Bodies whose speeds approached the speed of light would offer very strong resistance to external forces. In classical mechanics, resistance given body there is always something unchanging, characterized only by its mass. In the theory of relativity, it depends on both rest mass and speed. The resistance becomes infinitely greater as the speed approaches the speed of light.
The conclusions just mentioned allow us to subject the theory to experimental testing. Do projectiles moving at speeds close to the speed of light resist the action of an external force in the way that theory predicts? Since these provisions of the theory of relativity are expressed in the form of quantitative relationships, we could confirm or refute the theory if we had projectiles moving at speeds close to the speed of light.
We actually find projectiles moving at such speeds in nature. Atoms of a radioactive substance, such as radium, act like a battery that fires projectiles moving at enormous speeds. Without going into detail, we can only point out one of the most important views of modern physics and chemistry. All matter in the world is made up of elementary particles, the number of varieties of which is small. Similarly, in one city, buildings are different in size, design and architecture, but for the construction of all of them, from a hut to a skyscraper, only a very few types of bricks are used, the same in all buildings. Thus, all the known chemical elements of our material world - from the lightest hydrogen to the heaviest uranium - are built from the same kind of bricks, that is, the same kind of elementary particles. The heaviest elements - the most complex structures - are unstable and they decay, or, as we say, they are radioactive. Some bricks, i.e. elementary particles, which make up radioactive atoms, are sometimes ejected at very high speeds, close to the speed of light. An atom of an element, say radium, according to our modern views, confirmed by numerous experiments, has a complex structure, and radioactive decay is one of those phenomena in which it is revealed that the atom is built from simpler bricks - elementary particles.
Through very ingenious and complex experiments, we can discover how particles resist external forces. Experiments show that the drag exerted by these particles depends on speed, just as predicted by the theory of relativity. In many other cases where it was possible to detect a dependence of resistance on speed, complete agreement was established between the theory of relativity and experiment. Once again we see the essential features of creative work in science: the prediction of certain facts by theory and their confirmation by experiment.
This result leads to a further important generalization. A body at rest has mass, but does not have kinetic energy, i.e., energy of motion. A moving body has both mass and kinetic energy. It resists changes in speed more strongly than a body at rest. It seems that kinetic energy of a moving body seems to increase its resistance. If two bodies have the same rest mass, then the body with greater kinetic energy resists the action of an external force more strongly.
Let's imagine a box filled with balls; let the box and balls be at rest in our coordinate system. It takes some force to move it to increase its speed. But will this force produce the same increase in speed in the same period of time if the balls in the box move rapidly in all directions, like molecules in a gas, with average speeds close to the speed of light? Now it will be necessary O greater force, since the increased kinetic energy of the balls increases the resistance of the box. Energy, at least kinetic energy, resists motion in the same way as solid mass. Is this also true for all types of energy?
The theory of relativity, based on its basic principles, gives a clear and convincing answer to this question, the answer is again of a quantitative nature: all energy resists a change in motion; all energy behaves like matter; a piece of iron weighs more when it is red hot than when it is cold; the radiation emitted by the Sun and passing through space contains energy and therefore has mass; The Sun and all emitting stars lose mass due to radiation. This conclusion, completely general in nature, is an important achievement of the theory of relativity and corresponds to all the facts that were used to verify it.
Classical physics allowed two substances - matter and energy. The first had weight, and the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already raised the question of whether modern physics still retains this view of two substances and two conservation laws. The answer is: no. According to the theory of relativity, there is no significant difference between mass and energy. Energy has mass, and mass represents energy. Instead of two conservation laws, we have only one: the law of conservation of mass-energy. This new perspective proved to be very fruitful in further development physics.
How is it that the fact that energy has mass and mass is energy remained unknown for so long? Does a piece of heated iron weigh more than a piece of cold iron? Now we answer “yes”, but before we answered “no”. The pages lying between these two answers cannot, of course, hide this contradiction.
The difficulties facing us here are of the same order as those we have encountered before. The change in mass predicted by the theory of relativity is immeasurably small and cannot be detected by direct weighing even with the help of very sensitive balances. Proof that energy is not weightless can be obtained in many very convincing but indirect ways.
The reason for this lack of immediate evidence is the very small amount of interchange between matter and energy. Energy in relation to mass is like a devalued currency taken in relation to a currency of high value. One example will make this clear. The amount of heat capable of turning 30 thousand tons of water into steam would weigh about one gram. Energy was considered weightless for so long simply because the mass that corresponds to it is too small.
The old energy-substance is the second victim of the theory of relativity. The first was the medium in which light waves propagated.
The influence of the theory of relativity extends far beyond the problems from which it arose. It removes the difficulties and contradictions of field theory; it formulates more general mechanical laws; it replaces two conservation laws with one; it modifies our classical concept of absolute time. Its value is not limited to the realm of physics; it forms a common framework covering all natural phenomena.
Space-time continuum
"The French Revolution began in Paris on July 14, 1789." This sentence establishes the place and time of the event. To someone who hears this statement for the first time and who does not know what Paris means, one could say: it is a city on our Earth, located at 2° east longitude and 49° north latitude. Two numbers would then characterize the place, and July 14, 1789 - the time at which the event occurred. In physics, the exact specification of when and where an event occurred is extremely important, much more important than in history, since these numbers form the basis of a quantitative description.
For the sake of simplicity, we previously considered only motion along a straight line. Our coordinate system was a solid rod with a beginning but no end. Let's keep this restriction. Mark on the rod various points; the position of each of them can be characterized by only one number - the coordinate of the point. When we say that the coordinate of a point is 7.586 m, we mean that its distance from the origin of the rod is 7.586 m. On the contrary, if someone gives me any number and unit of measurement, I can always find a point on the rod corresponding to that number. We see that each number corresponds to a certain point on the rod, and each point corresponds to a certain number. This fact is expressed by mathematicians in the following sentence:
All points of the rod form a one-dimensional continuum.
Then there exists a point arbitrarily close to the given point of the rod. We can connect two distant points on a rod by a series of segments located one after the other, each of which is arbitrarily small. Thus, the fact that these segments connecting distant points can be taken as small as desired is a characteristic of a continuum.
Let's take another example. Let us have a plane, or, if you prefer something more concrete, the surface of a rectangular table (Fig. 66). The position of a point on this table can be characterized by two numbers, and not one, as before. The two numbers are the distances from two perpendicular edges of the table. Not one number, but a pair of numbers corresponds to each point on the plane; Each pair of numbers corresponds to a specific point. In other words, the plane is a two-dimensional continuum. Then there are points arbitrarily close to a given point on the plane. Two distant points can be connected by a curve divided into segments as small as desired. Thus, the arbitrary smallness of the segments that successively fit on a curve connecting two distant points, each of which can be defined by two numbers, is again a characteristic of a two-dimensional continuum.
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One more example. Let's imagine that you want to consider your room as a coordinate system. This means that you want to determine any position of the body relative to the walls of the room. The position of the center of the lamp, if it is at rest, can be described by three numbers: two of them determine the distance from two perpendicular walls, and the third - the distance from the floor or ceiling. Each point in space corresponds to three specific numbers; each three numbers correspond to a specific point in space (Fig. 67). This is expressed by the sentence:
Our space is a three-dimensional continuum.
There are points very close to any given point in space. And again, the arbitrary smallness of the line segments connecting distant points, each of which is represented by three numbers, is a characteristic of the three-dimensional continuum.
But all this hardly applies to physics. To return to physics, we need to consider the movement of material particles. To study and predict phenomena in nature, it is necessary to consider not only the place, but also the time of physical events. Let's take a simple example again.
A small pebble, which we take to be a particle, falls from the tower. Let's assume that the height of the tower is 80 m. Since the time of Galileo, we have been able to predict the coordinates of a stone at an arbitrary moment in time after the start of its fall. Below is a “schedule” that approximately describes the position of the stone after 1, 2, 3 and 4 seconds.
Our “schedule” contains five events, each of which is represented by two numbers - the time and spatial coordinate of each event. The first event is the beginning of the movement of the stone from a height of 80 m from the ground at a time equal to zero. The second event is the coincidence of the stone with the mark on the rod at a height of 75 m from the ground. This will be noted after one second has elapsed. The last event is the impact of the stone on the ground.
Then draw two perpendicular lines; one of them, say horizontal, will be called temporary O th axis, and the vertical axis - the spatial axis. We immediately see that our “schedule” can be represented by five points in space-time O th plane (Fig. 69).
The distances of points from the spatial axis are the time coordinates indicated in the first column of the “schedule”, and the distances from the time O th axes - their spatial coordinates.
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The same connection is expressed in two ways - using a “schedule” and points on a plane. One can be built from the other. The choice between these two representations is only a matter of taste, for in reality they are both equivalent.
Let's now take one more step. Let's imagine an improved "schedule" that gives positions not for every second, but, say, for every hundredth or thousandth of a second. Then we will have many points in our space-time O th plane. Finally, if the position is given for each instant, or, as mathematicians say, if the spatial coordinate is given as a function of time, then the collection of points becomes a continuous line. Therefore, our next drawing (Fig. 70) does not give fragmentary information, as before, but a complete picture of the movement of the stone.
Movement along a solid rod (tower), i.e. movement in one-dimensional space, is represented here as a curve in two-dimensional space-time O m continuum. Every point in our space-time O m continuum corresponds to a pair of numbers, one of which marks the time at yu, and the other is the spatial coordinate. On the contrary, a certain point in our space-time O m continuum corresponds to a certain pair of numbers characterizing the event. Two adjacent points represent two events that occurred in places close to each other and at times immediately following each other.
You might object to our way of representing it this way: it makes little sense to represent time as segments and mechanically connect it to space, forming a two-dimensional continuum from two one-dimensional continuums. But then you would have to object just as seriously to all graphs representing, for example, the change in temperature in New York over the course of last summer, or against graphs depicting changes in the cost of living over the past few years, since in each of these cases the same method is used. In temperature graphs, a one-dimensional temperature continuum is combined with a one-dimensional time s m continuum into a two-dimensional temperature-time continuum.
Let's return to the particle falling from an 80-meter tower. Our graphical picture of motion is a useful convention, since it allows us to characterize the position of a particle at any arbitrary moment in time. Knowing how the particle moves, we would like to depict its movement again. This can be done in two ways.
Let us recall the image of particles changing their position over time in one-dimensional space. We depict motion as a series of events in a one-dimensional spatial continuum. We do not mix time and space when using dynamic a picture in which the positions change with time.
But you can depict the same movement in a different way. We can form static picture by viewing the curve in two-dimensional space-time O m continuum. Now movement is considered as something given, existing in two-dimensional space-time O m continuum, and not as something changing in a one-dimensional spatial continuum.
Both of these paintings are absolutely equal, and preferring one of them over the other is only a matter of agreement and taste.
What is said here about the two pictures of motion has no relation to the theory of relativity. Both ideas can be used with equal justice, although the classical theory rather preferred the dynamic picture of movement as something happening in space, rather than the static picture of it in space-time. But the theory of relativity changed this view. She clearly preferred the static picture and found in this representation of movement as something that exists in space-time a more convenient and more objective picture of reality. We still have to answer the question why these two pictures are equivalent from the point of view of classical physics and not equivalent from the point of view of the theory of relativity. The answer will be clear if we again consider two coordinate systems moving rectilinearly and uniformly relative to each other.
According to classical physics, observers in both systems moving rectilinearly and uniformly relative to each other will find different spatial coordinates for the same event, but the same time at th coordinate. Thus, in our example, the impact of a stone on the ground is characterized by our choice of coordinate system O th coordinate 4 and spatial coordinate 0. According to classical mechanics, observers moving rectilinearly and uniformly relative to the chosen coordinate system will find that the stone will reach the ground four seconds after it begins to fall. But each observer relates the distance to his own coordinate system, and they will, generally speaking, associate different spatial coordinates with the impact event, although temporally A i coordinate will be the same for all other observers moving rectilinearly and uniformly relative to each other. Classical physics knows only “absolute” time, which flows the same for all observers. For each coordinate system, a two-dimensional continuum can be divided into two one-dimensional continuums - time and space. Due to the “absolute” nature of time, the transition from a “static” to a “dynamic” picture of motion has an objective meaning in classical physics.
But we have already seen that classical transformations cannot be applied in physics in the general case. From a practical point of view, they are still suitable for low speeds, but are not suitable for substantiating fundamental physical questions.
According to the theory of relativity, the moment at which the rock hits the ground will not be the same for all observers. And temporary A i and the spatial coordinate will be different in the two various systems coordinates, and change in time O th coordinates will be very noticeable if the relative speed of the systems approaches the speed of light. A two-dimensional continuum cannot be divided into two one-dimensional continuums, as in classical physics. We cannot consider space and time separately when determining space-time s x coordinates in another coordinate system. From the point of view of the theory of relativity, the division of a two-dimensional continuum into two one-dimensional ones turns out to be an arbitrary process that has no objective meaning.
Everything we have just said can easily be generalized to the case of motion not limited to a straight line. In fact, to describe events in nature, you need to use not two, but four numbers. Physical space, conceived through objects and their movements, has three dimensions, and the positions of objects are characterized by three numbers. The moment of the event is the fourth number. Each event corresponds to four specific numbers; any four numbers correspond to a certain event. Therefore, the world of events forms four-dimensional continuum. There is nothing mystical about this, and the last sentence is equally true for classical physics and the theory of relativity. Again, the difference only becomes apparent when two coordinate systems moving relative to each other are considered. Let the room move, and observers inside and outside it determine the space-time s e coordinates of the same events. A proponent of classical physics will break the four-dimensional continuum into three-dimensional space and one-dimensional time O th continuum. The old physicist only cares about the transformation of space, since time is absolute for him. He finds the division of the four-dimensional world continuum into space and time natural and convenient. But from the point of view of the theory of relativity, time, like space, changes when moving from one coordinate system to another; in this case, the Lorentz transformations express the transformation properties of the four-dimensional space-time O th continuum - our four-dimensional world of events.
The world of events can be described dynamically using a picture that changes over time and is sketched against a background of three-dimensional space. But it can also be described by means of a static picture sketched against the background of a four-dimensional space-time O th continuum. From the point of view of classical physics, both pictures, dynamic and static, are equivalent. But from the point of view of the theory of relativity, the static picture is more convenient and more objective.
Even in the theory of relativity we can still use the dynamic picture if we prefer it. But we must remember that this division between time and space has no objective meaning, since time is no longer “absolute”. In what follows, we will continue to use a “dynamic” rather than a “static” language, but we will always take into account its limitations.
General relativity
One more point remains to be clarified. One of the most fundamental questions has not yet been resolved: does an inertial system exist? We have learned something about the laws of nature, their invariance under Lorentz transformations and their validity in all inertial systems moving rectilinearly and uniformly relative to each other. We have laws, but we do not know the “body of reference” to which they should be attributed.
In order to know more about these difficulties, let's talk with a physicist who stands in the position of classical physics and ask him a few simple questions.
What is an inertial system?
This is a coordinate system in which the laws of mechanics are valid. A body that is not acted upon by external forces moves rectilinearly and uniformly in such a system. This property allows us, therefore, to distinguish an inertial coordinate system from any other.
But what does it mean that no external forces act on the body?
This simply means that the body moves in a straight line and uniformly in an inertial coordinate system.
Here you could once again pose the question: “What is an inertial coordinate system?” But since there is little hope of getting an answer different from the one given above, we will try to get specific information by changing the question.
Is a system rigidly connected to the Earth inertial?
No, because the laws of mechanics are not strictly valid on Earth due to its rotation. A coordinate system rigidly associated with the Sun can be considered inertial for solving many problems, but when we talk about the rotation of the Sun, we again conclude that a coordinate system rigidly associated with it cannot be considered strictly inertial.
Then what exactly is your inertial coordinate system and how should you choose its state of motion?
This is only a useful fiction and I have no idea how to implement it. If only I could isolate myself from all material bodies and free myself from all external influences, then my coordinate system would be inertial.
But what do you mean by a coordinate system free from all external influences?
I mean that the coordinate system is inertial. We are back to our original question again! Our conversation reveals a serious difficulty in classical physics. We have laws, but we do not know what the body of reference is to which they should be attributed, and our entire physical structure turns out to be built on sand.
We can approach the same difficulty from a different point of view. Let's try to imagine that in the entire Universe there is only one body that forms our coordinate system. This body begins to rotate. According to classical mechanics, the physical laws for a rotating body are different from the laws for a non-rotating body. If the principle of inertia is valid in one case, then it is not valid in another. But all this sounds very doubtful. Is it permissible to consider the motion of only one body in the entire Universe? By movement of a body we always mean a change in its position relative to another body. Therefore, talking about the movement of a single body means contradicting common sense. Classical mechanics and common sense differ greatly on this point. Newton's recipe is this: if the principle of inertia is in force, then the coordinate system is either at rest or moves rectilinearly and uniformly. If the principle of inertia does not apply, then the body is not in linear and uniform motion. Thus, our conclusion about motion or rest depends on whether or not all physical laws apply to a given coordinate system.
Let's take two bodies, for example the Sun and the Earth. The movement we are seeing is again relative. It can be described using a coordinate system associated with either the Earth or the Sun. From this point of view, the great achievement of Copernicus is the transfer of the coordinate system from the Earth to the Sun. But since the motion is relative and any reference body can be used, it turns out that there is no reason to prefer one coordinate system to another.
Physics intervenes again and changes our conventional wisdom. The coordinate system associated with the Sun is more similar to the inertial system than the system associated with the Earth. Physical laws are preferable to apply in the Copernican system than in the Ptolemaic system. The greatness of Copernicus's discovery can only be highly appreciated from a physical point of view. Physics shows that for describing the motion of planets, a coordinate system rigidly connected to the Sun has enormous advantages.
In classical physics there is no absolute linear and uniform motion. If two coordinate systems move rectilinearly and uniformly relative to each other, then there is no reason to say: “This system is at rest, and the other is moving.” But if both coordinate systems are in non-rectilinear and uneven motion relative to each other, then there is every reason to say: “This body is moving, and the other is at rest (or moving rectilinearly and uniformly).” Absolute motion has a very definite meaning here. At this point there is a wide gulf between common sense and classical physics. The mentioned difficulties concerning the inertial system, as well as the difficulties concerning absolute motion, are closely related to each other. Absolute motion becomes possible only thanks to the idea of an inertial system for which the laws of nature are valid.
It may seem that there is no way out of these difficulties, that no physical theory can avoid them. Their source lies in the fact that the laws of nature are valid only for a special class of coordinate systems, namely inertial ones. The possibility of resolving these difficulties depends on the answer to the following question. Can we formulate physical laws in such a way that they are valid for all coordinate systems, not only for systems moving rectilinearly and uniformly, but also for systems moving completely arbitrarily in relation to each other? If this can be done, then our difficulties will be solved. Then we will be able to apply the laws of nature in any coordinate system. The struggle between the views of Ptolemy and Copernicus, so fierce in the early days of science, would become completely meaningless. Any coordinate system could be used with equal validity. Two sentences - "The sun is at rest, and the Earth is moving" and "The sun is moving, and the Earth is at rest" - would simply mean two different agreements about two different coordinate systems.
Could we build a real relativistic physics, valid in all coordinate systems, a physics in which not absolute, but only relative motion would take place? This actually turns out to be possible!
We have at least one, albeit very weak, indication of how to build a new physics. Indeed, relativistic physics must be applied in all coordinate systems, and therefore, in a special case - in the inertial system. We already know the laws for this inertial coordinate system. New general laws, valid for all coordinate systems, must in the special case of the inertial system be reduced to the old, known laws.
The problem of formulating physical laws for any coordinate system was resolved by the so-called general relativity; the previous theory, which applies only to inertial frames, is called special theory of relativity. These two theories cannot, of course, contradict each other, since we must always include previously established laws special theory relativity into general laws for a non-inertial system. But if previously the inertial coordinate system was the only one for which physical laws were formulated, now it will represent a special limiting case, since any coordinate systems moving arbitrarily in relation to each other are permissible.
This is the program of the general theory of relativity. But in outlining the way in which it was created, we must be even less specific than we have been so far. New difficulties arising in the process of scientific development force our theory to become more and more abstract. A number of surprises await us. But our constant ultimate goal is a better and better understanding of reality. New links are added to the logical chain connecting theory and observation. In order to clear the path leading from theory to experiment from unnecessary and artificial assumptions, in order to cover an ever-increasing area of facts, we must make the chain longer and longer. The simpler and more fundamental our assumptions become, the more complex the mathematical tool of our reasoning; the path from theory to observation becomes longer, thinner and more complex. Although it sounds paradoxical, we can say: modern physics is simpler than old physics, and therefore it seems more difficult and confusing. The simpler our picture of the external world and the more more facts it embraces, the more strongly it reflects the harmony of the Universe in our minds.
Our new idea is simple: build physics that is valid for all coordinate systems. The implementation of this idea introduces formal complexity and forces us to use mathematical methods different from those hitherto used in physics. We will show here only the connection between the implementation of this program and two fundamental problems - gravitation and geometry.
Continuity–discontinuity
Before us is a map of the city of New York and its surrounding area. We ask: which points on this map can be reached by train? Having looked at these points in the railway schedule, we mark them on the map. We then change the question and ask: what points can a car achieve? If we draw lines on a map representing all the roads starting in New York, then any point lying on these roads can practically be reached by car. In both cases we have a series of points. In the first case, they are distant from each other and represent different railway stations, and in the second they are points along highways. Our next question is about the distance to each of these points from New York or, for greater accuracy, from a specific place in this city. In the first case, certain numbers correspond to points on the map. These numbers change irregularly, but always by a finite amount, abruptly. We say: the distances from New York to places that can be reached by train only change intermittently. However, the distances to places that can be reached by car can vary as little as desired; they can vary continuously. Changes in distances can be made arbitrarily small when traveling by car rather than by train.
The output of coal mines can be varied in a continuous manner. The amount of coal produced can be increased or decreased in arbitrarily small portions. But the number of working coal miners can only be changed intermittently. It would be pure nonsense to say: “The number of people employed has increased by 3,783 since yesterday.”
A person who was asked about the amount of money in his pocket cannot name any amount, no matter how small, but only a value containing only two decimal places. The amount of money can only change in leaps and bounds. In America, the smallest possible change, or, as we will call it, the “elementary quantum” of American money, is one cent. The elementary quantum of English money is one farthing, worth only half of the American elementary quantum. Here we have an example of two elementary quanta, the magnitude of which can be compared with each other. The ratio of their values has a certain meaning, since the cost of one of them is twice the cost of the other.
We can say: some quantities can change continuously, while others can only change discontinuously, in portions that cannot be further reduced. These indivisible portions are called elementary quanta these quantities.
We can weigh huge quantities of sand and consider its mass to be continuous, although its granular structure is obvious. But if sand became very precious, and the scales used were very sensitive, we would have to admit the fact that the mass of sand always varies by a multiple of the mass of one smallest particle. The mass of this smallest particle would be our elementary quantum. From this example we see how the discontinuous nature of a quantity, hitherto considered continuous, is revealed through an increase in the accuracy of our measurements.
If we had to characterize the main ideas of quantum theory in one sentence, we could say: it should be assumed that some physical quantities, previously considered continuous, consist of elementary quanta.
The area of facts covered by quantum theory is extremely large. These facts were discovered thanks to the high development of modern experimental technology. Since we can neither show nor describe even basic experiments, we will often have to present their results dogmatically. Our goal is to explain only the fundamental, basic ideas.
Elementary quanta of matter and electricity
In the picture of the structure of matter drawn by the kinetic theory, all elements are built from molecules. Let's take simplest example the easiest chemical element- hydrogen. We have seen how the study of Brownian motion led to the determination of the mass of the hydrogen molecule. It is equal
0.000 000 000 000 000 000 000 003 3 g.
This means that the mass is discontinuous. The mass of any portion of hydrogen can change only by an integer number of smallest portions, each of which corresponds to the mass of one hydrogen molecule. But chemical processes have shown that the hydrogen molecule can be broken into two parts or, in other words, that the hydrogen molecule consists of two atoms. In a chemical process, the role of an elementary quantum is played by an atom, not a molecule. Dividing the above number by two, we find the mass of the hydrogen atom; it is approximately
0.000 000 000 000 000 000 000 001 7 g.
Mass is a discontinuous quantity. But, of course, we don't have to worry about this in the normal measurement of body weight. Even the most sensitive scales are far from achieving the degree of accuracy that would detect discontinuous changes in body weight.
Wave Theory Terminology
Uniform light has a specific wavelength. The wavelength of the red end of the spectrum is twice the wavelength of the violet end.
Terminology of quantum theory
Homogeneous light consists of photons of a certain energy. The energy of a photon for the red end of the spectrum is half the energy of a photon for the violet end.
Literature
Mala Girnicha Encyclopedia. In 3 volumes / Ed. V. S. Biletsky. - Donetsk: “Donbas”, 2004. - ISBN 966-7804-14-3.
http://znaimo.com.ua
Kasatkin A. S. Basics of electrical engineering. M: Vishcha School, 1986.
Bezsonov L. A. Theoretical foundations of electrical engineering. Electric stake. M: Vishcha School, 1978.
slovari.yandex.ru/dict/bse/article/00061/97100.htm
Sivukhin D.V. Advanced course of physics - M. T. III. Electrician
Evolution of physics. Development of ideas from initial concepts to the theory of relativity and quantum
Albert Einstein, Leopold Infeld ( lane from English S. G. Suvorova)
The phenomena of interference and diffraction of light confirm its wave nature. At the beginning of the 19th century, T. Jung and O. Fresnel, having created the wave theory of light, considered light waves to be longitudinal, i.e. similar sound waves. To do this, they had to introduce a certain hypothetical environment called ether, in which the propagation of longitudinal light waves occurred. At that time it seemed incredible that light is transverse waves, since by analogy with mechanical waves one would have to assume that ether is solid(transverse mechanical waves cannot propagate in a gaseous or liquid medium). However, already at that time there were facts that contradicted the longitudinality of light waves.
Back in the Middle Ages, sailors brought unusual transparent stones from Iceland, which were later called Iceland spar. Their unusual feature was that if a piece of Iceland spar was placed on any inscription, then through it the inscription would be seen as forked.
In 1669, the Danish scientist Bartholin reported interesting results from his experiments with Iceland spar crystals. When passing through such a crystal, the beam splits into two (Fig. 2.6.1). These rays are named ordinary beam And extraordinary ray, and the phenomenon itself - birefringence.
An ordinary ray obeys the ordinary law of refraction, but an extraordinary ray does not obey this law. The rays bifurcated even when falling normally onto an Iceland spar crystal. If the crystal is rotated relative to the direction of the original ray, then both rays that passed through the crystal are rotated. Bartolin also discovered that there is a certain direction in the crystal along which the incident beam does not bifurcate. However, he could not give an explanation for these phenomena.
Several years later, this discovery of Bartholin attracted the attention of Huygens, who introduced the concept crystal optical axis(Bartolin actually discovered it).
Optical axis of the crystal is the selected direction in the crystal along which ordinary and extraordinary rays propagate without being separated.
In 1809, the French engineer E. Malus conducted an experiment with tourmaline crystals (transparent greenish crystals). In this experiment, light was successively passed through two identical tourmaline plates. If the second plate is rotated relative to the first, then the intensity of the light passing through the second plate changes from maximum value to zero (Fig. 2.6.2). Dependence of light intensity I from the corner j between the optical axes of both plates has the form:
(Malus's law ), (2.6.1)
Where I 0 – intensity of incident light.
Rice. 2.6.3 A. Rice. 2.6.3 b.
Neither birefringence nor Malus's law can be explained within the framework of the theory of longitudinal light waves. For longitudinal waves, the direction of beam propagation is the axis of symmetry. In a longitudinal wave, all directions in a plane perpendicular to the beam are equal.
To understand how a transverse wave behaves, consider a wave traveling along a cord in a vertical plane. If you place a box with a vertical slit in the path of this wave (Fig. 2.6.3 A), then the wave passes freely through the slit. If the gap in the box is located horizontally, then the wave no longer passes through it (Fig. 2.6.3 b). This wave is also called plane-polarized, because vibrations in it occur in one (vertical) plane.
Experiments with iceland spar and tourmaline crystals made it possible to prove that the light wave is transverse. The first guess about the transverseness of light waves was made by T. Jung (1816). Fresnel, independently of Young, also put forward the concept of transverse light waves, substantiated it with numerous experiments and created the theory of double refraction of light in crystals.
In the mid-60s of the 19th century, Maxwell came to the conclusion that light is an electromagnetic wave. This conclusion was made based on the coincidence of the propagation speed electromagnetic waves, which is obtained from Maxwell's theory, with known value speed of light. By the time Maxwell concluded about the existence of electromagnetic waves, the transverse nature of light waves had already been proven experimentally. Therefore, Maxwell believed that the transversality of electromagnetic waves is another important proof of the electromagnetic nature of light.
IN electromagnetic theory Light also eliminated the difficulties associated with the need to introduce a special medium for wave propagation - ether, which had to be considered as a solid body.
In an electromagnetic wave, the vectors and are perpendicular to each other and lie in a plane perpendicular to the direction of propagation of the wave. It is customary to call the plane in which the vector oscillates plane of oscillation, and the plane in which the vector oscillates, plane of polarization. Since in all processes of interaction of light with matter the main role is played by the electric field strength vector, it is called light vector. If, during the propagation of an electromagnetic wave, the light vector retains its orientation, such a wave is called linearly polarized or plane-polarized.
Linearly polarized light is emitted by lasers. However, light emitted by conventional sources (e.g. sunlight, radiation from incandescent lamps, etc.), not polarized. This is due to the fact that atoms emit light in separate trains independently of each other. As a result, the vector in the resulting light wave randomly changes its orientation in time, so that on average all directions of oscillations are equal.
A light wave in which the directions of oscillations of the light vector change chaotically in time is called natural or unpolarized light.
Natural light passing through a crystal of Iceland spar or tourmaline becomes polarized. The phenomenon of birefringence of light is explained by the fact that in many crystalline substances The refractive indices for two mutually perpendicularly polarized waves are different. Therefore, the crystal bifurcates the rays passing through it (Fig. 2.6.1). The two beams at the output of the crystal are linearly polarized in mutually perpendicular directions. Crystals in which birefringence occurs are called anisotropic.
Light can become polarized when reflected or scattered. In particular, blue light from the sky is partially or fully polarized. Polarization of reflected light was first observed by Malus when he looked through an Iceland spar crystal at the reflection of the setting sun in the windows of the Luxembourg Palace in Paris. Malus established that the reflected light is polarized to one degree or another. The degree of polarization of the reflected beam depends on the angle of incidence: at normal incidence the reflected light is completely unpolarized, but when incident at an angle called the angle of complete polarization or Brewster's angle, the reflected beam is 100% polarized. When reflected at the Brewster angle, the reflected and refracted rays are perpendicular to each other (Fig. 2.5.4). The reflected beam is plane-polarized parallel to the surface.
Because , and , then the Brewster angle is found by the formula.
Polarized light is widely used in many fields of technology (for example, for smooth adjustment of light, in the study of elastic stresses, etc.). Human eye does not distinguish the polarization of light, but the eyes of some insects, for example, bees, perceive it.
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Ministry of Education of the Nizhny Novgorod Region
GBOU SPO "Lukoyanovsky Agricultural College"
Methodological development By academic discipline"Physics"
Transverseness of light waves.
Polarization of light
Developed by: Smirnov A.V. physics teacher
1 qualification category
Lukoyanov, 2012
Considered at the meeting
methodological commission
mathematical and natural science cycle
Protocol No. _____
"__" ________ 2012
Chairman
__________/ N.N. Alexandrova
Approved by the methodological council of GBOU SPO "Lukoyanovsky Agricultural College"
Protocol No. ______
"__" ________ 2012
Chairman
____________________________
Lesson on the topic “Transverseness of light waves. Polarization of light."
Goals:
Educational:
create conditions for studying the concept of “Polarization of Light”, its practical application, achieve conscious assimilation of the acquired knowledge, and teach to use the acquired knowledge in practice.
continue to cultivate accuracy, thrift, and responsibility;
arouse interest in learning activities;
arouse interest in the material being studied.
develop thinking and educational skills;
continue work on developing the skills to recognize the problem, draw conclusions, and generalize.
Lesson type: combined.
Equipment:
laboratory equipment for each table: 2 polaroids, a piece of cellophane; stack of glass plates.
demonstration equipment: light polarization kit, laptop, laptop monitor, projector, interactive whiteboard, current source, low-voltage lamp on a stand.
During the classes
I) Organizational moment(2 minutes.)
Checking attendance, readiness of the class and students for the lesson.
II) Verification homework, updating previously studied
(10 min.)
Test tasks on the board, self-test based on answers on the board, analysis through selective questioning, closing gaps.
Explain from a physical point of view why grass is green.
Explain from a physical point of view how white surfaces differ from black ones.
Which color of light is refracted most by a glass triangular prism?
What phenomenon explains the rainbow color of soap bubbles?
Sources that have the same phase and frequency are called coherent.
Can two stars in the sky be coherent light sources? Why?
What are vibrations that propagate in space over time called?
What wave is called longitudinal?
What wave is called transverse?
How are the vectors arranged? E And IN in an electromagnetic wave?
Is the electromagnetic wave longitudinal or transverse?
III) Learning new material(15 minutes.)
Problem experiment
Students are given equipment and the task for the experiment is displayed on the board:
1) Look at the lamp connected to the source through a Polaroid;
2) rotate the Polaroid around its axis and observe the illumination of the screen. Draw a conclusion;
3) place another polaroid between the polaroid and the screen and rotate first one, then the other polaroid around the axis.
4) Observe how the screen illumination changes. Draw a conclusion.
Heuristic conversation
First guess: Light is a transverse wave. But in a beam of waves incident from a conventional source, there are oscillations in all possible planes perpendicular to the direction of propagation of the waves;
Second guess: Polaroid has the ability to transmit light waves with vibrations lying in one specific plane.
Teacher's word
Theoretical information
Tourmaline crystal polarizes natural light, i.e. selects (passes) vibrations only in one specific plane. Using the second polaroid (analyzer), you can determine the plane of polarization of the first polaroid.
Problem experiment
The task for the experiment is displayed on the board:
1. Take a Polaroid in your hands and, turning it around its axis, look through it at:
laptop screen;
image on the interactive whiteboard;
incandescent lamp.
Heuristic conversation
Students are asked to explain the results of the experiments.
The light from the laptop screen is polarized;
The image on the interactive whiteboard is polarized; the polarization axes for light of different wavelengths do not coincide.
Incandescent light is not polarized.
Teacher's word
Theoretical information
Explanation of the LCD monitor.
Problem experiment:
Television and radio communications are carried out using electromagnetic waves.
Let's remember one of the properties of electromagnetic waves, and try to explain it from the perspective of the knowledge gained in today's lesson.
Demonstration of experience on the polarization of electromagnetic waves (educational film).
Teacher's word
Explanation of the experiment: if the direction of the metal rods of the lattice coincides with the direction of the electric field strength vector, then currents are excited in the rods, the lattice acts as a conductor and reflects the electromagnetic wave. If the grating is rotated 90°, the signal passes through, since in this case the rods are perpendicular to the electric field vector, and it cannot cause the appearance of currents in the rods.
Problem experiment:
Let's place a crumpled piece of cellophane between the Polaroids crossed at an angle of 90°, rotate the Polaroids one by one around the axis, and observe the effect;
Let's place a special slide from the light polarization kit between polaroids crossed at an angle of 90° to observe chromatic polarization, rotate the polaroids around the axis, and observe the effect on the screen.
Let us observe a stack of glass plates through a Polaroid, rotating them around a vertical axis at a certain angle and rotating the Polaroid.
Teacher's word
C 
ellophan: Cellophane has strong anisotropy. This packaging material is made from viscose, a wood product. During production, cellophane film is greatly stretched, lining up long organic molecules in chains. Polaroid glasses: glasses with one or two layers of polaroid. Glasses with two layers of polaroid are used as darkening filters of variable density: a lever protrudes from the side of the glasses, with which you can simultaneously rotate two polaroids relative to the other two, which are stationary. With parallel Polaroids, the transmission of glasses = 40%, with crossed ones it becomes minimal (= 0.01%).
Glasses with a single layer of polaroid are used either to separate images or to reduce the glare of reflected light. In the first case, the polarization planes of both filters are set mutually perpendicular so that light from only one polarization plane reaches each eye. Such glasses were used in a stereo cinema system in which two frames of a stereo pair were sent to the screen in polarized light: the polarization plane of each frame corresponded to the polarization plane of the Polaroid through which the light had to pass to the corresponding eye. In the second case, polaroid filters have the same directions of polarization planes and do not transmit light polarized in a perpendicular plane. Light reflected at an angle from a dielectric medium is highly polarized. Glasses allow you to greatly attenuate this reflected light, which makes it possible, for example, to look deep into the water.
Polarization systems. With linear polarization, two images are superimposed on the same screen through orthogonal (placed at 90 degrees to each other) polarizing filters in projectors. In this case, it is necessary to use a special silver-plated screen, which avoids depolarization and compensates for the loss of brightness (since only 0.71 of the light emitted by each projector falls on the screen.
The viewer puts on glasses, which also have built-in orthogonal polarizing filters; thus, each filter passes only that portion of light waves whose polarization matches that of the filter, and blocks orthogonally polarized light.
Linearly polarized glasses require the viewer to keep their head level without tilting it, otherwise the effect is lost.
An example of a technology that uses linear polarization is IMAX 3D.
When using circular polarization, two images are also superimposed on each other through filters with opposite polarization. The glasses intended for the viewer have built-in “analyzing” filters (with opposite polarization). Unlike linear polarization, if the viewer tilts their head, the separation of the left and right images is preserved, and accordingly the illusion of a stereo image is preserved.
P 
polarization photo filters. The action of these filters is based on the effect of polarization of electromagnetic waves, as well as on the effects of rotation of the plane of polarization by certain substances.
The photosensitive material in photography does not retain information about the plane of polarization of electromagnetic radiation waves incident on it.
Linear polarization filter. Contains one polarizer that rotates in the frame. Its application is based on the fact that part of the light in the world around us is polarized. All rays incident non-perpendicularly and reflected from dielectric surfaces are partially polarized. The light coming from the sky and clouds is partially polarized. Therefore, using a polarizer when shooting, the photographer gets an additional opportunity to change the brightness and contrast various parts Images. For example, shooting a landscape on a sunny day using such a filter can result in a dark, deep blue sky. When photographing objects behind glass, a polarizer allows you to get rid of the photographer’s reflection in the glass.
For shooting in low light conditions, Low Light Polarizer is produced, which partially polarizes the light and therefore has a low magnification. When two such filters are added perpendicular to their planes of polarization, instead of completely extinguishing the light flux, 2/3 of the flux is obtained.
Circular polarizing filter. In addition to the polarizer, it contains a so-called “quarter-wave plate”, at the output of which linearly polarized light becomes circularly polarized. From the point of view of the effect obtained in the picture, a circular polarizer is no different from a linear one. The appearance of such filters was dictated by the development of TTL camera automation elements, which, unlike photographic material, turned out to be dependent on whether the light falling on them through the lens was polarized. In particular, linearly polarized light partially disrupts the automatic phase focusing in SLR cameras and makes exposure metering difficult.
Composite ND filters. If you put two polarizers together, then when the planes of polarization coincide, such a filter has maximum light transmission (and is equivalent to a 2x neutral gray filter). With perpendicular directions of polarization and ideal polarizers, the filter completely absorbs the color incident on it. By choosing the angle of rotation, you can change the light transmission of such a filter within a very wide range.
Composite color polarizing filters. They consist of two polarizing filters that can be rotated, and between them there is a plate that rotates the plane of polarization of the light. Due to the fact that the rotation angle depends on the wavelength, at each position of the polarizers, part of the spectrum passes through such a system, and part is delayed. Rotating the polarizers relative to each other leads to a change in the spectral characteristics of the filter. For example, red-green filters are produced.
Electronically controlled filters. If a liquid crystal element is used as a second polarizer in the design of composite filters, this allows you to control the properties of the filter directly during the shooting process.
IV) Consolidation(10 min.)
Frontal conversation.
Questions for frontal conversation
What is the difference between ordinary light and polarized light?
What are Polaroids?
How do tourmaline crystals and polaroids transform light?
What property of light does the phenomenon of polarization indicate?
Where can you observe the phenomenon of polarization in everyday life and in technology?
Where and how is the phenomenon of polarization used?
Suggest your application of the polarization phenomenon.
V) Summing up(5 minutes.)
Let's define the main thing that we learned today in class:
concept of polarization of light;
Polaroid and its functions;
manifestation, application of light polarization.
VI) Homework(3 min.)
The purpose of the lesson
To form among schoolchildren the concept of “natural and polarized light”; introduce experimental evidence of the transverse nature of light waves; study the properties of polarized light, show the analogy between the polarization of mechanical, electromagnetic and light waves; report examples of the use of polaroids.
The lesson on polarization of light is the final lesson in the topic “Wave Optics”. In this regard, a lesson using computer modeling can be structured as a general repetition lesson or part of the lesson can be devoted to solving problems on the topics “Interference of Light”, “Diffraction of Light”. We offer a model of a lesson in which new material is studied on the topic “Polarization of Light”, and then the learned material is consolidated on a computer model. On this lesson It is easy to combine a real demonstration with a computer simulation, since polaroids can be placed in children's hands and the light can be shown to go out when one of the polaroids is turned.
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Homework: § 74, task No. 1104, 1105.
Explanation of new material
The phenomena of interference and diffraction leave no doubt that propagating light has the properties of waves. But what kind of waves - longitudinal or transverse?
For a long time, the founders of wave optics, Young and Fresnel, considered light waves to be longitudinal, that is, similar to sound waves. At that time, light waves were considered as elastic waves in the ether, filling space and penetrating into all bodies. Such waves, it seemed, could not be transverse, since transverse waves can only exist in a solid body. But how can bodies move in solid ether without encountering resistance? After all, the ether should not interfere with the movement of bodies. Otherwise, the law of inertia would not apply.
However, gradually more and more experimental facts were accumulated, which could not be interpreted in any way, considering light waves to be longitudinal.
Experiments with tourmaline
Let us consider in detail only one of the experiments, very simple and effective. This is an experiment with tourmaline crystals (transparent green crystals).
Demonstrate to students that the light turns off when two polaroids are rotated. A tourmaline crystal has an axis of symmetry and belongs to the so-called uniaxial crystals. Let's take a rectangular plate of tourmaline, cut so that one of its faces is parallel to the axis of the crystal. If a beam of light from an electric lamp or the sun is directed normally towards such a plate, then rotation of the plate around the beam will not cause any change in the intensity of the light passing through it (see figure). One might think that the light was only partially absorbed in the tourmaline and acquired a greenish color. Nothing else happened. But that's not true. The light wave acquired new properties.
These new properties are revealed if the beam is forced to pass through a second exactly the same tourmaline crystal (see Fig. a), parallel to the first. With identically directed axes of the crystals, again nothing interesting happens: the light beam is simply weakened even more due to absorption in the second crystal. But if the second crystal is rotated, leaving the first one motionless (Fig. b), then an amazing phenomenon will be revealed - the extinction of light. As the angle between the axes increases, the light intensity decreases. And when the axes are perpendicular to each other, light does not pass through at all (Fig. c). It is completely absorbed by the second crystal. How can this be explained?
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Transverse light waves
From the experiments described above, two facts follow: firstly, that the light wave coming from the light source is completely symmetrical with respect to the direction of propagation (when the crystal was rotated around the beam in the first experiment, the intensity did not change) and, secondly, that the wave emerging from the first crystal does not have axial symmetry (depending on the rotation of the second crystal relative to the beam, one or another intensity of transmitted light is obtained).
Longitudinal waves have complete symmetry with respect to the direction of propagation (oscillations occur along this direction, and it is the axis of symmetry of the wave). Therefore, it is impossible to explain the experiment with the rotation of the second plate, considering the light wave to be longitudinal.
A complete explanation of the experiment can be obtained by making two assumptions.
The first assumption concerns the light itself. Light is a transverse wave. But in a beam of waves incident from a conventional source, there are oscillations in all possible directions, perpendicular to the direction of propagation of the waves (see figure).
Demonstrate that natural light contains vibrations in all planes.
According to this assumption, the light wave has axial symmetry, while at the same time being transverse. Waves, for example, on the surface of water do not have such symmetry, since vibrations of water particles occur only in the vertical plane.
A light wave that oscillates in all directions perpendicular to the direction of propagation is called natural. This name is justified, since in normal conditions light sources create just such a wave. This assumption explains the result of the first experiment. Rotation of the tourmaline crystal does not change the intensity of the transmitted light, since the incident wave has axial symmetry (despite the fact that it is transverse).
The second assumption that needs to be made is about the crystal. A tourmaline crystal has the ability to transmit light waves with vibrations lying in one specific plane (plane P in the figure).
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On the computer model "Malus' Law"
Demonstrate that a tourmaline crystal exhibits only one plane of light vibration. By rotating the polarizer and then the analyzer, it can be shown that the intensity of the transmitted light changes from a maximum value to zero. To extinguish the light, the angle between the polaroid axes must be 90°. If the axes of the polaroids are parallel, then the second polaroid transmits all the light that passed through the first.
Such light is called polarized, or, more precisely, plane polarized, in contrast to natural light, which can also be called unpolarized. This assumption fully explains the results of the second experiment. A plane-polarized wave emerges from the first crystal. With crossed crystals (the angle between the axes is 90°), it does not pass through the second crystal. If the axes of the crystals make a certain angle between themselves, different from 90°, then oscillations occur, the amplitude of which is equal to the projection of the amplitude of the wave passing through the first crystal onto the direction of the axis of the second crystal.
So, a tourmaline crystal converts natural light into plane-polarized light.
Mechanical model of experiments with tourmaline
It is not difficult to construct a simple visual mechanical model of the phenomenon under consideration. You can create a transverse wave in a rubber cord so that the vibrations quickly change their direction in space. This is an analogue of a natural light wave. Let us now pass the cord through a narrow wooden box (see figure). From vibrations in all possible directions, the box “selects” vibrations in one specific plane. Therefore, a polarized wave comes out of the box.
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If there is another exactly the same box on its path, but rotated 90° relative to the first one, then the vibrations do not pass through it. The wave is completely extinguished.
If you have a mechanical model of polarization in your office, you can demonstrate it. If there is no such model, then this model can be illustrated with fragments of the video film “Polarization”.
Polaroids
Not only tourmaline crystals are capable of polarizing light. The so-called Polaroids, for example, have the same property. Polaroid is a thin (0.1 mm) film of herapatite crystals applied to celluloid or glass plate. You can do the same experiments with a Polaroid as with a tourmaline crystal. The advantage of polaroids is that they can create large surfaces that polarize light. The disadvantages of Polaroids include the purple tint they give to white light.
Direct experiments have proven that the light wave is transverse. In a polarized light wave, vibrations occur in a strictly defined direction.
In conclusion, we can consider the use of polarization in technology and illustrate this material with fragments of the video film “Polarization.”
