What is the practical application of total internal reflection of light. Total internal reflection of light: description, conditions and laws. Application of total reflection

At a certain angle of incidence of light $(\alpha )_(pad)=(\alpha )_(pred)$, which is called limiting angle, the angle of refraction is equal to $\frac(\pi )(2),\ $in this case, the refracted beam slides along the interface between the media, therefore, there is no refracted beam. Then, from the law of refraction, we can write that:

Picture 1.

In the case of total reflection, the equation is:

has no solution in the region of real values of the angle of refraction ($(\alpha )_(pr)$). In this case, $cos((\alpha )_(pr))$ is purely imaginary. If we turn to the Fresnel Formulas, then it is convenient to represent them in the form:

where the angle of incidence is denoted by $\alpha $ (for brevity), $n$ is the refractive index of the medium where the light propagates.

Remark 1

It should be noted that the inhomogeneous wave does not disappear in the second medium. Thus, if $\alpha =(\alpha )_0=(arcsin \left(n\right),\ then\ )$ $E_(pr\bot )=2E_(pr\bot ).$ no case. Since the Fresnel formulas are valid for a monochromatic field, that is, for a steady process. In this case, the law of conservation of energy requires that the average change in energy over the period in the second medium be equal to zero. The wave and the corresponding fraction of energy penetrate through the interface into the second medium to a shallow depth of the order of the wavelength and move in it parallel to the interface with a phase velocity that is less than the phase velocity of the wave in the second medium. It returns to the first environment at a point that is offset from the entry point.

The penetration of the wave into the second medium can be observed in the experiment. The intensity of the light wave in the second medium is noticeable only at distances smaller than the wavelength. Near the interface on which the light wave falls, which experiences total reflection, on the side of the second medium, the glow of a thin layer can be seen if there is a fluorescent substance in the second medium.

Total reflection causes mirages to occur when the earth's surface is at a high temperature. So, the total reflection of light that comes from the clouds leads to the impression that there are puddles on the surface of the heated asphalt.

Under normal reflection, the relations $\frac(E_(otr\bot ))(E_(pad\bot ))$ and $\frac(E_(otr//))(E_(pad//))$ are always real. Under total reflection they are complex. This means that in this case the phase of the wave suffers a jump, while it is different from zero or $\pi $. If the wave is polarized perpendicular to the plane of incidence, then we can write:

where $(\delta )_(\bot )$ is the desired phase jump. Equating the real and imaginary parts, we have:

From expressions (5) we obtain:

Accordingly, for a wave that is polarized in the plane of incidence, one can obtain:

Phase jumps $(\delta )_(//)$ and $(\delta )_(\bot )$ are not the same. The reflected wave will be elliptically polarized.

Application of total reflection

Let us assume that two identical media are separated by a thin air gap. A light wave falls on it at an angle that is greater than the limit. It may happen that it will penetrate into the air gap as an inhomogeneous wave. If the gap thickness is small, then this wave will reach the second boundary of the substance and will not be very weakened. Having passed from the air gap into the substance, the wave will turn again into a homogeneous one. Such an experiment was carried out by Newton. The scientist pressed another prism, which was polished spherically, to the hypotenuse face of a rectangular prism. In this case, the light passed into the second prism not only where they touch, but also in a small ring around the contact, in the place where the gap thickness is comparable to the wavelength. If the observations were made in white light, then the edge of the ring had a reddish color. This is as it should be, since the penetration depth is proportional to the wavelength (for red rays it is greater than for blue ones). By changing the thickness of the gap, it is possible to change the intensity of the transmitted light. This phenomenon formed the basis of the light telephone, which was patented by Zeiss. In this device, a transparent membrane acts as one of the media, which oscillates under the action of sound incident on it. Light that passes through the air gap changes intensity in time with changes in the strength of the sound. Getting on the photocell, it generates an alternating current, which changes in accordance with changes in the strength of the sound. The resulting current is amplified and used further.

The phenomena of wave penetration through thin gaps are not specific to optics. This is possible for a wave of any nature, if the phase velocity in the gap is higher than the phase velocity in environment. Importance this phenomenon has in nuclear and atomic physics.

The phenomenon of complete internal reflection used to change the direction of light propagation. For this purpose, prisms are used.

Example 1

Exercise: Give an example of the phenomenon of total reflection, which is often encountered.

Decision:

One can give such an example. If the highway is very hot, then the air temperature is maximum near the asphalt surface and decreases with increasing distance from the road. This means that the refractive index of air is minimal at the surface and increases with increasing distance. As a result of this, rays having a small angle with respect to the highway surface suffer total reflection. If you focus your attention, while driving in a car, on a suitable section of the surface of the highway, you can see a car going upside down quite far ahead.

Example 2

Exercise: What is the Brewster angle for a beam of light that falls on the surface of a crystal if the limiting angle of total reflection for this beam at the air-crystal interface is 400?

Decision:

\[(tg(\alpha )_b)=\frac(n)(n_v)=n\left(2.2\right).\]

From expression (2.1) we have:

We substitute the right side of expression (2.3) into formula (2.2), we express the desired angle:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left((\alpha )_(pred)\right)\ ))\right).\]

Let's do the calculations:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left(40()^\circ \right)\ ))\right)\approx 57()^\circ .\]

Answer:$(\alpha )_b=57()^\circ .$

Some laws of physics are difficult to imagine without the use of visual aids. This does not apply to the usual light falling on various objects. So, at the boundary separating two media, a change in the direction of light rays occurs if this boundary is much greater than when light occurs when part of its energy returns to the first medium. If part of the rays penetrates into another medium, then they are refracted. In energy physics, falling on the boundary of two various environments, is called incident, and the one that returns from it to the first medium is called reflected. Exactly mutual arrangement of these rays determines the laws of reflection and refraction of light.

Terms

The angle between the incident beam and the line perpendicular to the interface between two media, restored to the point of incidence of the light energy flux, is called There is another important indicator. This is the angle of reflection. It occurs between the reflected beam and the perpendicular line restored to the point of its incidence. Light can propagate in a straight line only in a homogeneous medium. Different environments absorb and reflect light differently. The reflection coefficient is a value that characterizes the reflectivity of a substance. It shows how much energy brought by light radiation to the surface of the medium will be that which is carried away from it by reflected radiation. This coefficient depends on a number of factors, one of the most important being the angle of incidence and the composition of the radiation. Total reflection of light occurs when it falls on objects or substances with a reflective surface. So, for example, this happens when rays hit a thin film of silver and liquid mercury deposited on glass. Total reflection of light is quite common in practice.

The laws

The laws of reflection and refraction of light were formulated by Euclid as early as the 3rd century. BC e. All of them have been established experimentally and are easily confirmed by the purely geometric principle of Huygens. According to him, any point of the medium, to which the perturbation reaches, is a source of secondary waves.

First light: the incident and reflecting beams, as well as the perpendicular line to the interface, restored at the point of incidence of the light beam, are located in the same plane. falls on a reflective surface. plane wave, whose wave surfaces are strips.

Another law states that the angle of reflection of light is equal to the angle of incidence. This is because they have mutually perpendicular sides. Based on the principles of equality of triangles, it follows that the angle of incidence is equal to the angle of reflection. It can be easily proved that they lie in the same plane with the perpendicular line restored to the interface between the media at the point of incidence of the beam. These most important laws are also valid for the reverse course of light. Due to the reversibility of energy, a beam propagating along the path of the reflected will be reflected along the path of the incident.

Properties of reflective bodies

The vast majority of objects only reflect the light radiation incident on them. However, they are not a source of light. Well-lit bodies are perfectly visible from all sides, since the radiation from their surface is reflected and scattered in different directions. This phenomenon is called diffuse (scattered) reflection. It occurs when light hits any rough surface. To determine the path of the beam reflected from the body at the point of its incidence, a plane is drawn that touches the surface. Then, in relation to it, the angles of incidence of rays and reflection are built.

diffuse reflection

Only due to the existence of diffuse (diffuse) reflection of light energy do we distinguish between objects that are not capable of emitting light. Any body will be absolutely invisible to us if the scattering of rays is zero.

Diffuse reflection of light energy does not cause discomfort in the eyes of a person. This is due to the fact that not all light returns to its original environment. So about 85% of the radiation is reflected from snow, 75% from white paper, and only 0.5% from black velor. When light is reflected from various rough surfaces, the rays are directed randomly with respect to each other. Depending on the extent to which surfaces reflect light rays, they are called matte or mirror. However, these concepts are relative. The same surfaces can be specular and matte at different wavelengths of incident light. A surface that scatters rays evenly across different sides, is considered absolutely matte. Although there are practically no such objects in nature, unglazed porcelain, snow, and drawing paper are very close to them.

Mirror reflection

Specular reflection of light rays differs from other types in that when beams of energy fall on a smooth surface at a certain angle, they are reflected in one direction. This phenomenon is familiar to anyone who has ever used a mirror under the rays of light. In this case, it is a reflective surface. Other bodies also belong to this category. All optically smooth objects can be classified as mirror (reflective) surfaces if the sizes of inhomogeneities and irregularities on them are less than 1 micron (do not exceed the wavelength of light). For all such surfaces, the laws of light reflection are valid.

Reflection of light from different mirror surfaces

In technology, mirrors with a curved reflective surface (spherical mirrors) are often used. Such objects are bodies having the shape of a spherical segment. The parallelism of the rays in the case of reflection of light from such surfaces is strongly violated. There are two types of such mirrors:

Concave - reflect light from the inner surface of a segment of the sphere, they are called collecting, since parallel rays of light after reflection from them are collected at one point;

Convex - reflect light from the outer surface, while parallel rays are scattered to the sides, which is why convex mirrors are called scattering.

Options for reflecting light rays

A beam incident almost parallel to the surface only slightly touches it, and then is reflected at a very obtuse angle. It then continues on a very low trajectory, as close to the surface as possible. A ray incident almost vertically is reflected under acute angle. In this case, the direction of the already reflected beam will be close to the path of the incident beam, which is fully consistent with physical laws.

Light refraction

Reflection is closely related to other phenomena of geometric optics, such as refraction and total internal reflection. Often, light passes through the boundary between two media. Refraction of light is a change in the direction of optical radiation. It occurs when it passes from one medium to another. The refraction of light has two patterns:

The beam that passed through the boundary between the media is located in a plane that passes through the perpendicular to the surface and the incident beam;

The angle of incidence and refraction are related.

Refraction is always accompanied by reflection of light. The sum of the energies of the reflected and refracted beams of rays is equal to the energy of the incident beam. Their relative intensity depends on the incident beam and the angle of incidence. The structure of many optical devices is based on the laws of light refraction.

Picture 1.

In the case of total reflection, the equation is:

where the angle of incidence is denoted by $\alpha $ (for brevity), $n$ is the refractive index of the medium where the light propagates.

Remark 1

where $(\delta )_(\bot )$ is the desired phase jump. Equating the real and imaginary parts, we have:

From expressions (5) we obtain:

Accordingly, for a wave that is polarized in the plane of incidence, one can obtain:

Phase jumps $(\delta )_(//)$ and $(\delta )_(\bot )$ are not the same. The reflected wave will be elliptically polarized.

Application of total reflection

The phenomena of wave penetration through thin gaps are not specific to optics. This is possible for a wave of any nature, if the phase velocity in the gap is higher than the phase velocity in the environment. This phenomenon is of great importance in nuclear and atomic physics.

The phenomenon of total internal reflection is used to change the direction of light propagation. For this purpose, prisms are used.

Example 1

Exercise: Give an example of the phenomenon of total reflection, which is often encountered.

Decision:

Example 2

Exercise: What is the Brewster angle for a beam of light that falls on the surface of a crystal if the limiting angle of total reflection for this beam at the air-crystal interface is 400?

Decision:

\[(tg(\alpha )_b)=\frac(n)(n_v)=n\left(2.2\right).\]

From expression (2.1) we have:

We substitute the right side of expression (2.3) into formula (2.2), we express the desired angle:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left((\alpha )_(pred)\right)\ ))\right).\]

Let's do the calculations:

\[(\alpha )_b=arctg\left(\frac(1)((sin \left(40()^\circ \right)\ ))\right)\approx 57()^\circ .\]

Answer:$(\alpha )_b=57()^\circ .$

The law of refraction, which is often used in optics, says that:

\[\frac((\sin \alpha \ ))((\sin \gamma \ ))=n_(21)\to \frac((\sin \alpha \ ))(n_(21))=(\sin \gamma \ )\left(1\right),\]

$\alpha $ - angle of incidence; $\gamma $ - angle of refraction; $=\frac(n_2)(n_1)$ - relative refractive index. It is obvious from equation (1) that if $n_(21) 1\ ),$ which does not make sense. A similar case occurs for all values of the angle of incidence ($\alpha $) that satisfy the condition $(\sin \alpha \ )>n_(21)$, which is possible for $n_(21)

Using the phenomenon of total reflection

Angle of incidence ($\alpha $) at which the condition is met:

\[(sin (\alpha )_(kr)\ )=n_(21)(2)\]

called the critical or limiting angle. When condition (2) is met, we cannot observe the refracted wave, the entire light wave is reflected back into the first substance. This phenomenon is called the phenomenon of total internal reflection.

Consider two identical substances separated by a thin layer of air. A beam of light falls on this layer at an angle greater than the critical one. The light wave entering the air gap can be inhomogeneous. Let us assume that the thickness of the air gap is small, while the light wave falls on the second boundary of the substance, which is not strongly weakened. Having propagated from the air gap into the substance, the wave will again become homogeneous. This experiment was carried out by Newton. He applied a long flat face of a rectangular prism to a body with a spherical face. Light entered the second prism not only at the point of contact between the bodies, but also in a small annular space near the point of contact, where the thickness of the air gap is of the order of the wavelength. When conducting experiments with white light, the edge of the ring acquired a reddish color, since the penetration depth is proportional to the wavelength (and for red rays it is greater than for blue ones). By changing the thickness of the air gap, the intensity of the transmitted light will change. This phenomenon became the basis of the light telephone, which was patented by Zeiss. In the developed device, one medium was a transparent membrane, which oscillates when exposed to sound falling on it. The light propagating through the air gap changes its intensity in time with changes in the strength of the sound. Due to the light hitting the photocell, an alternating current is generated, which in turn depends on changes in the strength of the sound. The resulting current is amplified and used further.

Application of the phenomenon of total internal reflection

The device of the device is based on the phenomenon of total internal reflection, with the help of which it is possible to determine the refractive index of a substance - the Abbe-Pulrich refractometer. Total internal reflection occurs at the boundary between glass, whose refractive index is quite large and known, and a thin layer of liquid which is deposited on the surface of the glass. The refractometer consists of a glass prism AA (the liquid under investigation is placed between the prism glasses), a light filter (F), a lever that rotates around the tube T, an arc-shaped scale (D), on which the values of the refractive indices are plotted (Fig. 1). The light beam S passes through the filter and experiences total internal reflection at the drop-prism interface. The error of this refractometer is not more than 0.1%.

Based on the phenomenon of total internal reflection, fiber optics is based, in which images are formed when light propagates through light guides. Light guides are collections of flexible fibers made of transparent substances, for example, from quartz sand melts, coated with a sheath of a transparent material with a refractive index lower than that of glass. As a result of multiple reflections, the light wave in the fiber is directed along the required path. Complexes of optical fibers can be used to study internal organs or transmit information using computers.

The periscope (device for observation from a shelter) is based on the phenomenon of total reflection. In periscopes, mirrors or lens systems are used to change the direction of light propagation.

Examples of problems with a solution

Example 1

Exercise. Explain why the sparkle (“play”) of precious stones occurs during their jewelry processing?

Decision. When gem-cutting a stone, the method of processing it is selected in such a way that a total reflection of light occurs on each of its faces. So, for example, Fig.2

Example 2

Exercise. What will be the limiting angle of total internal reflection for rock salt if its refractive index is $n=1.54$?

Decision. Let's depict the course of rays when light from the air hits a salt crystal in Fig.3.

We write the law of total internal reflection:

\[(sin (\alpha )_(kr)\ )=n_(21)\left(2.1\right),\]

where $n_(21)=\frac(n_1)(n)\ $($n_1=1$ is the refractive index of air), then:

\[(\alpha )_(kr)=(\arcsin (\frac(n_1)(n))\ ).\]

Let's do the calculations:

\[(\alpha )_(kr)=(\arcsin \left(\frac(1)(1.54)\right)\approx 40.5()^\circ \ ).\]

Answer.$(\alpha )_(kr)=40.5()^\circ $

Activity

Digital periscope

Here is a technical innovation.

The traditional optical channel of existing periscopes has been replaced by video cameras high resolution and fiber optics. Information from outdoor surveillance cameras is transmitted in real time to a widescreen display in the central post.

The tests are being carried out aboard the Los Angeles-class submarine SSN 767 Hampton. The new model completely changes the decades-old practice of working with a periscope. Now the watch officer works with the cameras mounted on the boom, adjusting the display on the display using the joystick and keyboard.

In addition to the display in the central post, the image from the periscope can be displayed on an arbitrarily big number displays throughout the boat. Cameras make it possible to simultaneously observe different sectors of the horizon, which significantly increases the speed of the watch’s reaction to changes in the tactical situation on the surface.

How to explain the "play of stones"? In jewelry, stones are cut in such a way that each facet has a total reflection of light.

The phenomenon of a mirage is explained by a complete internal phenomenon.

A mirage is an optical phenomenon in the atmosphere: the reflection of light by a boundary between layers of air that are sharply different in warmth. For an observer, such a reflection consists in the fact that, together with a distant object (or a section of the sky), its imaginary image, displaced relative to the object, is visible.

Mirages are distinguished into lower ones, visible under the object, upper ones, above the object, and side ones. An upper mirage is observed over a cold earth's surface, an inferior mirage over an overheated flat surface, often a desert or an asphalt road. The imaginary image of the sky creates the illusion of water on the surface. So, the road that goes into the distance on a hot summer day seems wet. Lateral mirage is sometimes observed near strongly heated walls or rocks.