How to determine the angle of refraction of light. Phenomena associated with the refraction of light

The phenomenon of light refraction was known to Aristotle. Ptolemy attempted to establish the law quantitatively by measuring the angles of incidence and refraction of light. However, the scientist made the incorrect conclusion that the angle of refraction is proportional to the angle of incidence. After him, several more attempts were made to establish the law; the attempt of the Dutch scientist Snellius in the 17th century was successful.

The law of light refraction is one of the four fundamental laws of optics, which were empirically discovered even before the nature of light was established. These are the laws:

1. rectilinear propagation of light;
2. independence of light beams;
3. reflection of light from a mirror surface;
4. refraction of light at the boundary of two transparent substances.

All these laws are limited in application and are approximate. Clarifying the boundaries and conditions of applicability of these laws has great importance in establishing the nature of light.

Statement of the law

The incident ray of light, the refracted ray and the perpendicular to the interface between two transparent media lie in the same plane (Fig. 1). In this case, the angle of incidence () and the angle of refraction () are related by the relation:

where is a constant value independent of angles, which is called the refractive index. To be more precise, in expression (1) the relative refractive index of the substance in which the refracted light propagates is used, relative to the medium in which the incident wave of light propagated:

Where - absolute indicator refractive index of the second medium, is the absolute refractive index of the first substance; — phase speed of light propagation in the first medium; — phase speed of light propagation in the second substance. In the event that title="Rendered by QuickLaTeX.com" height="16" width="60" style="vertical-align: -4px;">, то вторая среда считается оптически более плотной, чем первая.!}

Taking into account expression (2), the law of refraction is sometimes written as:

From the symmetry of expression (3) the reversibility of light rays follows. If you reverse the refracted ray (Fig. 1) and make it fall on the interface at an angle , then in medium (1) it will go in reverse direction along the incident beam.

If a light wave propagates from a substance with a higher refractive index into a medium with a lower refractive index, then the angle of refraction will be greater than the angle of incidence.

As the angle of incidence increases, the angle of refraction also increases. This occurs until at a certain angle of incidence, which is called the limiting angle (), the angle of refraction becomes equal to 900. If the angle of incidence is greater than the limiting angle (), then all incident light is reflected from the interface. For the limiting angle of incidence, the expression (1 ) is transformed into the formula:

where equation (4) satisfies the values ​​of the angle at This means that the phenomenon of total reflection is possible when light enters from a substance that is optically denser into a substance that is optically less dense.

Conditions for the applicability of the law of refraction

The law of light refraction is called Snell's law. It is performed for monochromatic light, the wavelength of which is much greater than the intermolecular distances of the medium in which it propagates.

The law of refraction is violated if the size of the surface that separates the two media is small and the phenomenon of diffraction occurs. In addition, Snell's law does not hold true if nonlinear phenomena occur, which can occur at high light intensities.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

The phenomenon of light refraction is a physical phenomenon that occurs whenever a wave travels from one material to another in which its speed of propagation changes. Visually, it manifests itself in the fact that the direction of wave propagation changes.

Physics: refraction of light

If the incident beam hits the interface between two media at an angle of 90°, then nothing happens, it continues its movement in the same direction at right angles to the interface. If the angle of incidence of the beam differs from 90°, the phenomenon of light refraction occurs. This, for example, produces such strange effects as the apparent fracture of an object partially submerged in water or mirages observed in a hot sandy desert.

History of discovery

In the first century AD e. The ancient Greek geographer and astronomer Ptolemy tried to mathematically explain the value of refraction, but the law he proposed later turned out to be unreliable. In the 17th century Dutch mathematician Willebrord Snell developed a law that determined the quantity associated with the ratio of the incident and refracted angles, which was later called the refractive index of a substance. Essentially, the more a substance is able to refract light, the greater this indicator. A pencil in water is “broken” because the rays coming from it change their path at the air-water interface before reaching the eyes. To Snell's disappointment, he was never able to discover the cause of this effect.

In 1678, another Dutch scientist, Christiaan Huygens, developed a mathematical relationship to explain Snell's observations and proposed that the phenomenon of light refraction is the result of the different speed at which a ray passes through two media. Huygens determined that the ratio of the angles of light passing through two materials with different indicators refraction must be equal to the ratio of its speeds in each material. Thus, he postulated that light travels more slowly through media that have a higher refractive index. In other words, the speed of light through a material is inversely proportional to its refractive index. Although the law was subsequently confirmed experimentally, for many researchers of that time this was not obvious, since there were no reliable means of light. It seemed to scientists that its speed did not depend on the material. Only 150 years after Huygens' death was the speed of light measured with sufficient accuracy to prove that he was right.

Absolute refractive index

The absolute refractive index n of a transparent substance or material is defined as the relative speed at which light passes through it relative to the speed in a vacuum: n=c/v, where c is the speed of light in a vacuum and v is the speed of light in the material.

Obviously, there is no refraction of light in a vacuum, devoid of any substance, and in it the absolute index is equal to 1. For other transparent materials, this value is greater than 1. To calculate the indexes of unknown materials, the refraction of light in air (1.0003) can be used.

Snell's laws

Let's introduce some definitions:

• incident ray - a ray that approaches the separation of media;
• point of impact - the point of separation at which it hits;
• the refracted ray leaves the separation of the media;
• normal - a line drawn perpendicular to the division at the point of incidence;
• angle of incidence - the angle between the normal and the incident beam;
• Light can be defined as the angle between the refracted ray and the normal.

According to the laws of refraction:

1. The incident, refracted ray and normal are in the same plane.
2. The ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive coefficients of the second and first medium: sin i/sin r = n r /n i.

Snell's law of refraction of light describes the relationship between the angles of two waves and the refractive indices of two media. When a wave moves from a less refractive medium (such as air) to a more refractive medium (such as water), its speed decreases. On the contrary, when light passes from water to air, the speed increases. in the first medium relative to the normal and the angle of refraction in the second will differ in proportion to the difference in refractive indices between these two substances. If a wave passes from a medium with a low coefficient to a medium with a higher coefficient, then it bends towards the normal. And if it’s the other way around, then it’s deleted.

Relative refractive index

Shows that the ratio of the sines of the incident and refracted angles is equal to a constant, which represents the ratio in both media.

sin i/sin r = n r /n i =(c/v r)/(c/v i)=v i /v r

The ratio n r /n i is called relative coefficient refraction for these substances.

A number of phenomena that result from refraction are often observed in Everyday life. The “broken” pencil effect is one of the most common. The eyes and brain follow the rays back into the water as if they were not being refracted but coming from the object in a straight line, creating a virtual image that appears at a shallower depth.

Dispersion

Careful measurements show that the refraction of light is influenced by the wavelength of the radiation or its color. big influence. In other words, a substance has many that can vary when color or wavelength changes.

This change occurs in all transparent media and is called dispersion. The degree of dispersion of a particular material depends on how much its refractive index changes with wavelength. As the wavelength increases, the phenomenon of light refraction becomes less pronounced. This is confirmed by the fact that violet refracts more than red, since its wavelength is shorter. Thanks to dispersion in ordinary glass, a certain splitting of light into its components occurs.

Decomposition of light

In the late 17th century, Sir Isaac Newton conducted a series of experiments that led to his discovery of the visible spectrum, and showed that white light consists of an ordered array of colors, ranging from violet through blue, green, yellow, orange and ending with red. Working in a darkened room, Newton placed a glass prism into a narrow beam that penetrated through an opening in the window shutters. When passing through a prism, light was refracted - the glass projected it onto the screen in the form of an ordered spectrum.

Newton came to the conclusion that white light consists of a mixture different colors, and also that the prism “scatters” white light, refracting each color at a different angle. Newton was unable to separate the colors by passing them through a second prism. But when he placed the second prism very close to the first in such a way that all the dispersed colors entered the second prism, the scientist found that the colors recombined to form white light again. This discovery convincingly proved the spectrum which can be easily divided and combined.

The phenomenon of dispersion plays a key role in large number various phenomena. Rainbows are created by the refraction of light in raindrops, producing a spectacular display of spectral decomposition similar to that found in a prism.

Critical angle and total internal reflection

When passing through an environment with more high rate refraction into a medium with a lower wave path is determined by the angle of incidence relative to the separation of the two materials. If the angle of incidence exceeds a certain value (depending on the refractive index of the two materials), it reaches a point where light is not refracted into the lower index medium.

The critical (or limiting) angle is defined as the angle of incidence resulting in an angle of refraction equal to 90°. In other words, as long as the angle of incidence is less than the critical angle, refraction occurs, and when it is equal to it, the refracted ray passes along the place where the two materials separate. If the angle of incidence exceeds the critical angle, the light is reflected back. This phenomenon is called complete internal reflection. Examples of its use are diamonds and the diamond cut promotes total internal reflection. Most rays entering through top part diamond will be reflected until they reach the top surface. This is what gives diamonds their brilliant shine. Optical fiber consists of glass “hairs” that are so thin that when light enters at one end, it cannot escape. And only when the beam reaches the other end can it leave the fiber.

Understand and manage

Optical instruments, ranging from microscopes and telescopes to cameras, video projectors, and even human eye rely on the fact that light can be focused, refracted and reflected.

Refraction produces wide range phenomena, including mirages, rainbows, optical illusions. Refraction makes a thick mug of beer appear fuller, and the sun sets a few minutes later than it actually does. Millions of people use the power of refraction to correct vision defects with glasses and contact lenses. By understanding and manipulating these properties of light, we can see details invisible to the naked eye, whether they are on a microscope slide or in a distant galaxy.

The purpose of the lesson

To acquaint students with the laws of light propagation at the interface between two media, to provide an explanation of this phenomenon from the point of view of the wave theory of light.

Homework: § 61, task No. 1035, 1036.

Check of knowledge

Test. Reflection of light

New material

Observation of light refraction.

At the boundary of two media, light changes the direction of its propagation. Part of the light energy returns to the first medium, that is, light is reflected. If the second medium is transparent, then the light can partially pass through the boundary of the media, also changing, as a rule, the direction of propagation. This phenomenon is called refraction of light.

Due to refraction, an apparent change in the shape of objects, their location and size is observed. Simple observations can convince us of this. Place a coin or other small object at the bottom of an empty opaque glass. Let's move the glass so that the center of the coin, the edge of the glass and the eye are on the same straight line. Without changing the position of the head, we will pour water into the glass. As the water level rises, the bottom of the glass with the coin seems to rise. A coin that was previously only partially visible will now be fully visible. Place the pencil at an angle in a container of water. If you look at the vessel from the side, you will notice that the part of the pencil that is in the water seems to be shifted to the side.

These phenomena are explained by a change in the direction of rays at the boundary of two media - the refraction of light.

The law of light refraction determines mutual arrangement the incident ray AB (see figure), the refracted ray DB and the perpendicular CE to the interface, restored at the point of incidence. Angle α is called angle of incidence, and angle β is called refraction angle.

Incident, reflected and refracted rays are easy to observe by making a narrow beam of light visible. The progress of such a beam in the air can be traced by blowing a little smoke into the air or placing a screen at a slight angle to the beam. The refracted beam is also visible in fluorescein-tinted aquarium water.

Let a plane light wave fall on a flat interface between two media (for example, from air to water) (see figure). The wave surface AC is perpendicular to the rays A 1 A and B 1 B. The surface MN will first be reached by the ray A 1 A . Beam B 1 B will reach the surface after time Δt. Therefore, at the moment when the secondary wave at point B just begins to be excited, the wave from point A already has the form of a hemisphere with a radius

The wave surface of a refracted wave can be obtained by drawing a surface tangent to all secondary waves in the second medium, the centers of which lie at the interface between the media. In this case, this is the BD plane. It is the envelope of secondary waves. The angle of incidence α of the beam is equal to CAB in triangle ABC (the sides of one of these angles are perpendicular to the sides of the other). Hence,

The angle of refraction β is equal to the angle ABD of the triangle ABD. That's why

Dividing the resulting equations term by term, we get:

where n is a constant value independent of the angle of incidence.

From the construction (see figure) it is clear that the incident ray, the refracted ray and the perpendicular restored at the point of incidence lie in the same plane. This statement, together with the equation according to which the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media, represents law of light refraction.

You can verify the validity of the law of refraction experimentally by measuring the angles of incidence and refraction and calculating the ratio of their sines at different angles of incidence. This attitude remains unchanged.

Refractive index.
The constant value included in the law of refraction of light is called relative refractive index or refractive index of the second medium relative to the first.

Huygens' principle not only implies the law of refraction. Using this principle, the physical meaning of the refractive index is revealed. It is equal to the ratio of the speeds of light in media at the boundary between which refraction occurs:

If the angle of refraction β is less than the angle of incidence α, then, according to (*), the speed of light in the second medium is less than in the first.

The refractive index of a medium relative to vacuum is called absolute refractive index of this medium. It is equal to the ratio of the sine of the angle of incidence to the sine of the angle of refraction when a light beam passes from a vacuum into a given medium.

Using formula (**), we can express the relative refractive index in terms of the absolute refractive indices n 1 and n 2 of the first and second media.

Indeed, since

where c is the speed of light in vacuum, then

A medium with a lower absolute refractive index is usually called optically less dense medium.

The absolute refractive index is determined by the speed of light propagation in a given medium, which depends on physical condition environment, that is, on the temperature of the substance, its density, the presence of elastic stresses in it. The refractive index also depends on the characteristics of the light itself. Typically, it is less for red light than for green light, and less for green light than for violet light.

Therefore, tables of refractive index values ​​for different substances usually indicate for which light the value is given. given value n and what state the environment is in. If there are no such indications, this means that the dependence on these factors can be neglected.

In most cases, we have to consider the passage of light across the air-air boundary. solid or air - liquid, and not across the vacuum - medium boundary. However, the absolute refractive index n 2 of solid or liquid substance differs slightly from the refractive index of the same substance relative to air. Thus, the absolute refractive index of air at normal conditions for yellow light is approximately 1.000292. Hence,

Worksheet for the lesson

Sample answers
"Light refraction"

Topics of the Unified State Examination codifier: the law of light refraction, total internal reflection.

At the interface between two transparent media, along with the reflection of light, it is observed refraction- light, moving to another medium, changes the direction of its propagation.

The refraction of a light ray occurs when it inclined falling on the interface (though not always - read on about total internal reflection). If the ray falls perpendicular to the surface, then there will be no refraction - in the second medium the ray will retain its direction and will also go perpendicular to the surface.

Law of refraction (special case).

We will start with the special case when one of the media is air. This is exactly the situation that occurs in the vast majority of problems. We will discuss the appropriate special case the law of refraction, and only then we will give its most general formulation.

Suppose that a ray of light traveling in air falls obliquely onto the surface of glass, water or some other transparent medium. When passing into the medium, the beam is refracted, and it further move shown in Fig.

1 . At the point of impact, a perpendicular is drawn (or, as they also say, normal ) to the surface of the medium. The beam, as before, is called incident ray , and the angle between the incident ray and the normal is angle of incidence. Ray is refracted ray refraction angle.

; The angle between the refracted ray and the normal to the surface is called Any transparent medium is characterized by a quantity called refractive index

this environment. The refractive indices of various media can be found in tables. For example, for glass, and for water. In general, in any environment; The refractive index is equal to unity only in a vacuum. In air, therefore, for air we can assume with sufficient accuracy in problems (in optics, air is not very different from vacuum). .

Law of refraction (air-medium transition)
2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the refractive index of the medium:

. (1)

Since from relation (1) it follows that , that is, the angle of refraction is less than the angle of incidence. Remember: passing from air to the medium, the ray, after refraction, goes closer to the normal.

The refractive index is directly related to the speed of light propagation in a given medium. This speed is always less than the speed of light in vacuum: . And it turns out that

. (2)

We will understand why this happens when we study wave optics. For now, let's combine the formulas. (1) and (2) :

. (3)

Since the refractive index of air is very close to unity, we can assume that the speed of light in air is approximately equal to the speed of light in a vacuum. Taking this into account and looking at the formula. (3) , we conclude: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in air to the speed of light in the medium.

Reversibility of light rays.

Now let's consider reverse stroke ray: its refraction when passing from a medium to air. The following useful principle will help us here.

The principle of reversibility of light rays. The beam path does not depend on whether the beam is propagating in the forward or backward direction. Moving in the opposite direction, the beam will follow exactly the same path as in the forward direction.

According to the principle of reversibility, when transitioning from a medium to air, the beam will follow the same trajectory as during the corresponding transition from air to medium (Fig. 2). The only difference in Fig.

2 from fig.

1 is that the direction of the beam has changed to the opposite. Since the geometric picture has not changed, formula (1) will remain the same: the ratio of the sine of the angle to the sine of the angle is still equal to the refractive index of the medium. True, now the angles have changed roles: the angle has become the angle of incidence, and the angle has become the angle of refraction.

In any case, no matter how the beam travels - from air to medium or from medium to air - the following simple rule applies.

We take two angles - the angle of incidence and the angle of refraction; the ratio of the sine of the larger angle to the sine of the smaller angle is equal to the refractive index of the medium.

We are now fully prepared to discuss the law of refraction in the most general case. Law of refraction (general case). Let light pass from medium 1 with a refractive index to medium 2 with a refractive index. A medium with a high refractive index is called optically more dense.

Moving from an optically less dense medium to an optically more dense one, the light beam, after refraction, goes closer to the normal (Fig. 3). In this case, the angle of incidence is greater than the angle of refraction: .

Rice. 3.

On the contrary, moving from an optically denser medium to an optically less dense one, the beam deviates further from the normal (Fig. 4). Here the angle of incidence is less than the angle of refraction:

Rice. 4.

It turns out that both of these cases are covered by one formula - common law refraction, valid for any two transparent media.

Law of refraction.
1) The incident ray, the refracted ray and the normal to the interface between the media, drawn at the point of incidence, lie in the same plane.
2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive index of the second medium to the refractive index of the first medium:

. (4)

It is easy to see that the previously formulated law of refraction for the air-medium transition is a special case of this law. In fact, putting in formula (4) we arrive at formula (1).

Let us now remember that the refractive index is the ratio of the speed of light in a vacuum to the speed of light in a given medium: . Substituting this into (4), we get:

. (5)

Formula (5) naturally generalizes formula (3). The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium.

Total internal reflection.

When light rays pass from an optically denser medium to an optically less dense medium, an interesting phenomenon is observed - complete internal reflection. Let's figure out what it is.

For definiteness, we assume that light comes from water into air. Let us assume that in the depths of the reservoir there is a point source of light emitting rays in all directions. We will look at some of these rays (Fig. 5).

The beam hits the water surface at the smallest angle. This ray is partially refracted (ray) and partially reflected back into the water (ray). Thus, part of the energy of the incident beam is transferred to the refracted beam, and the remaining part of the energy is transferred to the reflected beam.

The angle of incidence of the beam is greater. This beam is also divided into two beams - refracted and reflected. But the energy of the original beam is distributed between them differently: the refracted beam will be dimmer than the beam (that is, it will receive a smaller share of energy), and the reflected beam will be correspondingly brighter than the beam (it will receive a larger share of energy).

As the angle of incidence increases, the same pattern is observed: an increasingly larger share of the energy of the incident beam goes to the reflected beam, and an increasingly smaller share to the refracted beam. The refracted beam becomes dimmer and dimmer, and at some point disappears completely!

This disappearance occurs when the angle of incidence corresponding to the angle of refraction is reached. In this situation, the refracted beam would have to go parallel to the surface of the water, but there is nothing left to go - all the energy of the incident beam went entirely to the reflected beam.

With a further increase in the angle of incidence, the refracted beam will even be absent.

The described phenomenon is complete internal reflection. Water does not release rays with angles of incidence equal to or exceeding a certain value - all such rays are completely reflected back into the water. The angle is called limiting angle of total reflection.

The value is easy to find from the law of refraction. We have:

But, therefore

So, for water the limiting angle of total reflection is equal to:

You can easily observe the phenomenon of total internal reflection at home. Pour water into a glass, lift it and look at the surface of the water slightly below through the wall of the glass. You will see a silvery sheen on the surface - due to total internal reflection, it behaves like a mirror.

The most important technical application total internal reflection is fiber optics. Light rays launched into a fiber optic cable ( light guide) almost parallel to its axis, fall onto the surface at large angles and are completely reflected back into the cable without loss of energy. Repeatedly reflected, the rays travel further and further, transferring energy over a considerable distance. Fiber optic communications are used, for example, in cable television networks and high-speed Internet access.

The phenomenon of refraction of a light wave is understood as a change in the direction of propagation of the front of this wave when it passes from one transparent medium to another. Many optical instruments and the human eye use this phenomenon to perform their functions. The article discusses the laws of light refraction and their use in optical instruments.

Processes of reflection and refraction of light

When considering the issue of the laws of light refraction, mention should also be made of the phenomenon of reflection, since it is closely related to this phenomenon. When light passes from one transparent medium to another, then at the interface between these media two processes occur simultaneously with it:

1. Part of the light beam is reflected back into the first medium at an angle equal to the angle incidence of the initial beam on the interface.
2. The second part of the beam enters the second medium and continues to propagate in it.

The above indicates that the intensity of the initial beam of light will always be greater than that of reflected and refracted light separately. How this intensity is distributed between the beams depends on the properties of the media and on the angle of incidence of light at their interface.

What is the essence of the process of light refraction?

Part of the light beam that falls on the surface between two transparent media continues to propagate in the second medium, but the direction of its propagation will already differ from the original direction in the 1st medium by a certain angle. This is the phenomenon of light refraction. Physical reason This phenomenon lies in the difference in the speed of propagation of a light wave in different media.

Recall that light has maximum speed propagation in a vacuum, it is equal to 299,792,458 m/s. In any material, this speed is always lower, and the greater the density of the medium, the slower the electromagnetic wave propagates in it. For example, in air the speed of light is 299,705,543 m/s, in water at 20 °C it is already 224,844,349 m/s, and in diamond it drops by more than 2 times relative to the speed in vacuum, and is 124,034,943 m /With.

This principle provides a geometric method for finding the wavefront at any given time. Huygens' principle assumes that every point reached by the wave front is a source of electromagnetic secondary waves. They travel in all directions at the same speed and frequency. The resulting wave front is defined as the totality of the fronts of all secondary waves. In other words, the front is a surface that touches the spheres of all secondary waves.

A demonstration of the use of this geometric principle to determine the wavefront is shown in the figure below. As can be seen from this diagram, all radii of the spheres of secondary waves (shown by arrows) are the same, since the wave front propagates in a medium homogeneous from an optical point of view.

Application of Huygens' principle to the process of light refraction

To understand the law of light refraction in physics, you can use Huygens' principle. Let us consider a certain light flux that falls on the interface between two media, and the speed of movement of the electromagnetic wave in the first medium is greater than that for the second.

As soon as part of the front (on the left in the figure below) reaches the interface of the media, secondary spherical waves begin to be excited at each point of the interface, which will already propagate in the second medium. Since the speed of light in the second medium is less than this value for the first medium, the part of the front that has not yet reached the interface between the media (on the right in the figure) will continue to propagate at a higher speed than the part of the front (left) that has already entered the second medium . By drawing circles of secondary waves for each point with a corresponding radius equal to v*t, where t is some specific time of propagation of the secondary wave, and v is the speed of its propagation in the second medium, and then drawing a tangent curve to all surfaces of the secondary waves, one can obtain the front propagation of light in the second medium.

As can be seen from the figure, this front will be deviated by a certain angle from the original direction of its propagation.

Note that if the speeds of the waves were equal in both media, or if the light fell perpendicularly to the interface, then there could be no talk about the process of refraction.

Laws of light refraction

These laws were obtained experimentally. Let 1 and 2 be two transparent media, the speeds of propagation of electromagnetic waves in which are equal to v 1 and v 2, respectively. Let a ray of light fall from medium 1 onto the interface at an angle θ 1 to the normal, and in the second medium it continues to propagate at an angle θ 2 to the normal to the interface. Then the formulation of the laws of light refraction will be as follows:

1. In the same plane there will be two rays (incident and refracted) and a normal restored to the interface between media 1 and 2.
2. The ratio of the velocities of beam propagation in media 1 and 2 will be directly proportional to the ratio of the sines of the angles of incidence and refraction, that is, sin(θ 1)/sin(θ 2) = v 1 /v 2.

The second law is called Snell's law. If we take into account that the index or refractive index of a transparent medium is defined as the ratio of the speed of light in vacuum to this speed in the medium, then the formula for the law of refraction of light can be rewritten as: sin(θ 1)/sin(θ 2) = n 2 /n 1, where n 1 and n 2 are the refractive indices of media 1 and 2, respectively.

Thus, mathematical formula law indicates that the product of the sine of the angle and the refractive index for a particular medium is constant value. Moreover, taking into account the trigonometric properties of the sine, we can say that if v 1 >v 2, then the light will approach the normal when passing through the interface, and vice versa.

A Brief History of the Discovery of the Law

Who discovered the law of light refraction? In fact, it was first formulated by the medieval astrologer and philosopher Ibn Sahl in the 10th century. The second discovery of the law occurred in the 17th century, and this was done by the Dutch astronomer and mathematician Snell van Rooyen, so throughout the world the second law of refraction bears his name.

It is interesting to note that a little later this law was also discovered by the Frenchman Rene Descartes, which is why in French-speaking countries it bears his name.

Sample task

All problems on the law of refraction of light are based on the mathematical formulation of Snell's law. Let us give an example of such a problem: it is necessary to find the angle of propagation of the light front during its transition from diamond to water, provided that this front hits the interface at an angle of 30 o to the normal.

To solve this problem, it is necessary to know either the refractive indices of the media under consideration or the speed of propagation of the electromagnetic wave in them. Referring to the reference data, we can write: n 1 = 2.417 and n 2 = 1.333, where numbers 1 and 2 indicate diamond and water, respectively.

Substituting the obtained values ​​into the formula, we get: sin(30 o)/sin(θ 2) = 1.333/2.417 or sin(θ 2) = 0.39 and θ 2 = 65.04 o, that is, the beam will move significantly away from the normal.

It is interesting to note that if the angle of incidence were greater than 33.5 o, then, in accordance with the formula of the law of light refraction, there would be no refracted ray, and the entire light front would be reflected back into the diamond medium. This effect is known in physics as total internal reflection.

Where does the law of refraction apply?

Practical use The laws of refraction of light are varied. It can be said without exaggeration that the majority of people work on this law. optical instruments. Refraction of light flux in optical lenses used in instruments such as microscopes, telescopes and binoculars. Without the existence of the refraction effect, it would be impossible for a person to see the world, after all vitreous and the lens of the eye are biological lenses that perform the function of focusing the light flux to a point on the sensitive retina of the eye. In addition, the law of total internal reflection finds its application in light fibers.