The limiting angle of total reflection is the angle of incidence of light at the interface between two media, corresponding to a refraction angle of 90 degrees.

Fiber optics is a branch of optics that studies the physical phenomena that arise and occur in optical fibers.

4. Wave propagation in an optically inhomogeneous medium. Explanation of ray bending. Mirages. Astronomical refraction. Inhomogeneous medium for radio waves.

Mirage is an optical phenomenon in the atmosphere: the reflection of light by a boundary between layers of air that are sharply different in density. For an observer, such a reflection means that together with a distant object (or part of the sky), its virtual image is visible, shifted relative to the object. Mirages are divided into lower ones, visible under the object, upper ones, above the object, and side ones.

Inferior Mirage

It is observed with a very large vertical temperature gradient (it decreases with height) over an overheated flat surface, often a desert or an asphalt road. The virtual image of the sky creates the illusion of water on the surface. So, the road stretching into the distance on a hot summer day seems wet.

Superior Mirage

Observed above the cold earth's surface with an inverted temperature distribution (increases with its height).

Fata Morgana

Complex mirage phenomena with a sharp distortion of the appearance of objects are called Fata Morgana.

Volume mirage

In the mountains, very rarely, under certain conditions, you can see the “distorted self” at a fairly close distance. This phenomenon is explained by the presence of “standing” water vapor in the air.

Astronomical refraction is the phenomenon of refraction of light rays from celestial bodies when passing through the atmosphere. Since the density of planetary atmospheres always decreases with altitude, the refraction of light occurs in such a way that the convexity of the curved ray in all cases is directed towards the zenith. In this regard, refraction always “raises” the images of celestial bodies above their true position

Refraction causes a number of optical-atmospheric effects on Earth: magnification day length due to the fact that the solar disk, due to refraction, rises above the horizon several minutes earlier than the moment at which the Sun should have risen based on geometric considerations; the oblateness of the visible disks of the Moon and the Sun near the horizon due to the fact that the lower edge of the disks rises higher by refraction than the upper; twinkling of stars, etc. Due to the difference in the magnitude of refraction of light rays with different wavelengths (blue and violet rays deviate more than red ones), an apparent coloring of celestial bodies occurs near the horizon.

5. The concept of a linearly polarized wave. Polarization of natural light. Unpolarized radiation. Dichroic polarizers. Polarizer and light analyzer. Malus's law.

Wave polarization- the phenomenon of breaking the symmetry of the distribution of disturbances in transverse wave (for example, electric and magnetic field strengths in electromagnetic waves) relative to the direction of its propagation. IN longitudinal polarization cannot occur in a wave, since disturbances in this type of wave always coincide with the direction of propagation.

linear - disturbance oscillations occur in one plane. In this case they talk about “ plane-polarized wave";

circular - the end of the amplitude vector describes a circle in the plane of oscillation. Depending on the direction of rotation of the vector, there may be right or left.

Light polarization is the process of ordering the oscillations of the electric field strength vector of a light wave when light passes through certain substances (during refraction) or when the light flux is reflected.

A dichroic polarizer contains a film containing at least one dichroic organic substance, the molecules or fragments of molecules of which have a flat structure. At least part of the film has a crystalline structure. A dichroic substance has at least one maximum of the spectral absorption curve in the spectral ranges of 400 - 700 nm and/or 200 - 400 nm and 0.7 - 13 μm. When manufacturing a polarizer, a film containing a dichroic organic substance is applied to the substrate, an orienting effect is applied to it, and it is dried. In this case, the conditions for applying the film and the type and magnitude of the orienting influence are chosen so that the order parameter of the film, corresponding to at least one maximum on the spectral absorption curve in the spectral range 0.7 - 13 μm, has a value of at least 0.8. The crystal structure of at least part of the film is a three-dimensional crystal lattice formed by molecules of dichroic organic matter. The spectral range of the polarizer is expanded while simultaneously improving its polarization characteristics.

Malus's law is a physical law that expresses the dependence of the intensity of linearly polarized light after it passes through a polarizer on the angle between the polarization planes of the incident light and the polarizer.

Where I 0 - intensity of light incident on the polarizer, I- intensity of light emerging from the polarizer, k a- polarizer transparency coefficient.

6. Brewster phenomenon. Fresnel formulas for the reflection coefficient for waves whose electric vector lies in the plane of incidence, and for waves whose electric vector is perpendicular to the plane of incidence. Dependence of reflection coefficients on the angle of incidence. The degree of polarization of reflected waves.

Brewster's law is a law of optics that expresses the relationship of the refractive index with the angle at which light reflected from the interface will be completely polarized in a plane perpendicular to the plane of incidence, and the refracted beam is partially polarized in the plane of incidence, and the polarization of the refracted beam reaches its greatest value. It is easy to establish that in this case the reflected and refracted rays are mutually perpendicular. The corresponding angle is called the Brewster angle. Brewster's Law: , Where n 21 - refractive index of the second medium relative to the first, θ Br- angle of incidence (Brewster angle). The amplitudes of the incident (U inc) and reflected (U ref) waves in the KBB line are related by the relation:

K bv = (U pad - U neg) / (U pad + U neg)

Through the voltage reflection coefficient (K U), the KVV is expressed as follows:

K bv = (1 - K U) / (1 + K U) With a purely active load, the BV is equal to:

K bv = R / ρ at R< ρ или

K bv = ρ / R for R ≥ ρ

where R is the active load resistance, ρ is the characteristic impedance of the line

7. The concept of light interference. The addition of two incoherent and coherent waves whose polarization lines coincide. Dependence of the intensity of the resulting wave upon addition of two coherent waves on the difference in their phases. The concept of the geometric and optical difference in wave paths. General conditions for observing interference maxima and minima.

Light interference is the nonlinear addition of the intensities of two or more light waves. This phenomenon is accompanied by alternating maxima and minima of intensity in space. Its distribution is called an interference pattern. When light interferes, energy is redistributed in space.

Waves and the sources that excite them are called coherent if the phase difference between the waves does not depend on time. Waves and the sources that excite them are called incoherent if the phase difference between the waves changes over time. Formula for the difference:

, Where , ,

8. Laboratory methods for observing the interference of light: Young’s experiment, Fresnel biprism, Fresnel mirrors. Calculation of the position of interference maxima and minima.

Young's experiment - In the experiment, a beam of light is directed onto an opaque screen screen with two parallel slits, behind which a projection screen is installed. This experiment demonstrates the interference of light, which is proof of the wave theory. The peculiarity of the slits is that their width is approximately equal to the wavelength of the emitted light. The effect of slot width on interference is discussed below.

If we assume that light consists of particles ( corpuscular theory of light), then on the projection screen one could see only two parallel strips of light passing through the slits of the screen. Between them, the projection screen would remain virtually unlit.

Fresnel biprism - in physics - a double prism with very small angles at the vertices.
A Fresnel biprism is an optical device that allows the formation of two coherent waves from one light source, which make it possible to observe a stable interference pattern on the screen.
The Frenkel biprism serves as a means of experimentally proving the wave nature of light.

Fresnel mirrors are an optical device proposed in 1816 by O. J. Fresnel to observe the phenomenon of interference of coherent light beams. The device consists of two flat mirrors I and II, forming a dihedral angle that differs from 180° by only a few angular minutes (see Fig. 1 in the article Interference of Light). When mirrors are illuminated from a source S, beams of rays reflected from the mirrors can be considered as emanating from coherent sources S1 and S2, which are virtual images of S. In the space where the beams overlap, interference occurs. If the source S is linear (slit) and parallel to the edge of the photons, then when illuminated with monochromatic light, an interference pattern in the form of equally spaced dark and light stripes parallel to the slit is observed on the screen M, which can be installed anywhere in the area of ​​beam overlap. The distance between the stripes can be used to determine the wavelength of the light. Experiments conducted with photons were one of the decisive proofs of the wave nature of light.

9. Interference of light in thin films. Conditions for the formation of light and dark stripes in reflected and transmitted light.

10. Strips of equal slope and strips of equal thickness. Newton's interference rings. Radii of dark and light rings.

11. Interference of light in thin films at normal light incidence. Coating of optical instruments.

12. Optical interferometers of Michelson and Jamin. Determination of the refractive index of a substance using two-beam interferometers.

13. The concept of multi-beam interference of light. Fabry-Perot interferometer. The addition of a finite number of waves of equal amplitudes, the phases of which form an arithmetic progression. Dependence of the intensity of the resulting wave on the phase difference of the interfering waves. The condition for the formation of the main maxima and minima of interference. The nature of the multi-beam interference pattern.

14. The concept of wave diffraction. Wave parameter and limits of applicability of the laws of geometric optics. Huygens-Fresnel principle.

15. Fresnel zone method and proof of rectilinear propagation of light.

16. Fresnel diffraction by a round hole. Radii of Fresnel zones for a spherical and plane wave front.

17. Diffraction of light on an opaque disk. Calculation of the area of ​​Fresnel zones.

18. The problem of increasing the amplitude of a wave when passing through a round hole. Amplitude and phase zone plates. Focusing and zone plates. Focusing lens as a limiting case of a stepped phase zone plate. Lens zoning.

LECTURE 23 GEOMETRIC OPTICS

LECTURE 23 GEOMETRIC OPTICS

1. Laws of reflection and refraction of light.

2. Total internal reflection. Fiber optics.

3. Lenses. Optical power of the lens.

4. Lens aberrations.

5. Basic concepts and formulas.

6. Tasks.

When solving many problems related to the propagation of light, you can use the laws of geometric optics, based on the idea of ​​a light ray as a line along which the energy of a light wave propagates. In a homogeneous medium, light rays are rectilinear. Geometric optics is the limiting case of wave optics as the wavelength tends to zero (λ →0).

23.1. Laws of reflection and refraction of light. Total internal reflection, light guides

Laws of reflection

Reflection of light- a phenomenon occurring at the interface between two media, as a result of which a light beam changes the direction of its propagation, remaining in the first medium. The nature of reflection depends on the relationship between the dimensions (h) of the irregularities of the reflecting surface and the wavelength (λ) incident radiation.

Diffuse reflection

When irregularities are randomly located and their sizes are on the order of the wavelength or exceed it, diffuse reflection- scattering of light in all possible directions. It is due to diffuse reflection that non-self-luminous bodies become visible when light is reflected from their surfaces.

Mirror reflection

If the size of the irregularities is small compared to the wavelength (h<< λ), то возникает направленное, или mirror, reflection of light (Fig. 23.1). In this case, the following laws are observed.

The incident ray, the reflected ray, and the normal to the interface between the two media, drawn through the point of incidence of the ray, lie in the same plane.

The angle of reflection is equal to the angle of incidence:β = a.

Rice. 23.1. Path of rays during specular reflection

Laws of refraction

When a light beam falls on the interface between two transparent media, it is divided into two beams: reflected and refracted(Fig. 23.2). The refracted ray propagates in the second medium, changing its direction. The optical characteristic of the medium is absolute

Rice. 23.2. Path of rays during refraction

refractive index, which is equal to the ratio of the speed of light in vacuum to the speed of light in this medium:

The direction of the refracted ray depends on the ratio of the refractive indices of the two media. The following laws of refraction are satisfied.

The incident ray, the refracted ray, and the normal to the interface between the two media, drawn through the point of incidence of the ray, lie in the same plane.

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value equal to the ratio of the absolute refractive indices of the second and first media:

23.2. Total internal reflection. Fiber optics

Let's consider the transition of light from a medium with a higher refractive index n 1 (optically more dense) to a medium with a lower refractive index n 2 (optically less dense). Figure 23.3 shows rays incident on the glass-air interface. For glass, the refractive index n 1 = 1.52; for air n 2 = 1.00.

Rice. 23.3. The occurrence of total internal reflection (n 1 > n 2)

Increasing the angle of incidence leads to an increase in the angle of refraction until the angle of refraction becomes 90°. With a further increase in the angle of incidence, the incident beam is not refracted, but fully reflected from the interface. This phenomenon is called total internal reflection. It is observed when light falls from a denser medium onto the boundary with a less dense medium and consists of the following.

If the angle of incidence exceeds the limiting angle for these media, then refraction at the interface does not occur and the incident light is completely reflected.

The limiting angle of incidence is determined by the relation

The sum of the intensities of the reflected and refracted rays is equal to the intensity of the incident ray. As the angle of incidence increases, the intensity of the reflected beam increases, and the intensity of the refracted beam decreases and becomes equal to zero for the maximum angle of incidence.

Fiber optics

The phenomenon of total internal reflection is used in flexible light guides.

If light is directed at the end of a thin glass fiber surrounded by a cladding with a lower refractive index, the light will propagate along the fiber, experiencing total reflection at the glass-cladding interface. This fiber is called light guide The bends of the light guide do not interfere with the passage of light

In modern optical fibers, light loss due to absorption is very small (about 10% per km), which allows them to be used in fiber-optic communication systems. In medicine, bundles of thin light guides are used to make endoscopes, which are used for visual examination of hollow internal organs (Fig. 23.5). The number of fibers in an endoscope reaches one million.

Using a separate light guide channel placed in a common bundle, laser radiation is transmitted for the purpose of therapeutic effects on internal organs.

Rice. 23.4. Propagation of light rays along a light guide

Rice. 23.5. Endoscope

There are also natural light guides. For example, in herbaceous plants, the stem plays the role of a light guide, supplying light to the underground part of the plant. The stem cells form parallel columns, which resembles the design of industrial light guides. If

If you illuminate such a column by examining it through a microscope, you can see that its walls remain dark, and the inside of each cell is brightly illuminated. The depth to which light is delivered in this way does not exceed 4-5 cm. But even such a short light guide is enough to provide light to the underground part of the herbaceous plant.

23.3. Lenses. Lens power

Lens - a transparent body usually bounded by two spherical surfaces, each of which can be convex or concave. The straight line passing through the centers of these spheres is called main optical axis of the lens(word home usually omitted).

A lens whose maximum thickness is significantly less than the radii of both spherical surfaces is called thin.

Passing through the lens, the light beam changes direction - it is deflected. If the deviation occurs to the side optical axis, then the lens is called collecting, otherwise the lens is called scattering.

Any ray incident on a collecting lens parallel to the optical axis, after refraction, passes through a point on the optical axis (F), called main focus(Fig. 23.6, a). For a diverging lens, passes through the focus continuation refracted ray (Fig. 23.6, b).

Each lens has two focal points located on both sides. The distance from the focus to the center of the lens is called main focal length(f).

Rice. 23.6. Focus of converging (a) and diverging (b) lenses

In the calculation formulas, f is taken with a “+” sign for collecting lenses and with a “-” sign for dispersive lenses.

The reciprocal of the focal length is called optical power of the lens: D = 1/f. Unit of optical power - diopter(dopter). 1 diopter is the optical power of a lens with a focal length of 1 m.

Optical power thin lens and its focal length depend on the radii of the spheres and the refractive index of the lens material relative to the environment:

where R 1, R 2 are the radii of curvature of the lens surfaces; n is the refractive index of the lens material relative to the environment; the “+” sign is taken for convex surfaces, and the “-” sign is for concave. One of the surfaces may be flat. In this case, take R = ∞ , 1/R = 0.

Lenses are used to produce images. Let's consider an object located perpendicular to the optical axis of the collecting lens and construct an image of its top point A. The image of the entire object will also be perpendicular to the axis of the lens. Depending on the position of the object relative to the lens, two cases of refraction of rays are possible, shown in Fig. 23.7.

1. If the distance from the object to the lens exceeds the focal length f, then the rays emitted by point A after passing through the lens intersect at point A", which is called actual image. The actual image is obtained upside down.

2. If the distance from the object to the lens is less than the focal length f, then the rays emitted by point A after passing through the lens dis-

Rice. 23.7. Real (a) and imaginary (b) images given by a collecting lens

are walking and at point A" their continuations intersect. This point is called imaginary image. The virtual image is obtained direct.

A diverging lens gives a virtual image of an object in all its positions (Fig. 23.8).

Rice. 23.8. Virtual image given by a diverging lens

To calculate the image it is used lens formula, which establishes a connection between the provisions points and her Images

where f is the focal length (for a diverging lens it is negative), a 1 - distance from the object to the lens; a 2 is the distance from the image to the lens (the “+” sign is taken for a real image, and the “-” sign for a virtual image).

Rice. 23.9. Lens formula parameters

The ratio of the size of the image to the size of the object is called linear increase:

Linear increase is calculated by the formula k = a 2 / a 1. Lens (even thin) will give the “correct” image, obeying lens formula, only if the following conditions are met:

The refractive index of a lens does not depend on the wavelength of light or the light is sufficient monochromatic.

When obtaining images using lenses real objects, these restrictions, as a rule, are not met: dispersion occurs; some points of the object lie away from the optical axis; the incident light beams are not paraxial, the lens is not thin. All this leads to distortion images. To reduce distortion, lenses of optical instruments are made of several lenses located close to each other. The optical power of such a lens is equal to the sum of the optical powers of the lenses:

23.4. Lens aberrations

Aberrations- a general name for image errors that occur when using lenses. Aberrations (from Latin "aberratio"- deviation), which appear only in non-monochromatic light, are called chromatic. All other types of aberrations are monochromatic, since their manifestation is not related to the complex spectral composition of real light.

1. Spherical aberration- monochromatic aberration caused by the fact that the outer (peripheral) parts of the lens deflect rays coming from a point source more strongly than its central part. As a result of this, the peripheral and central areas of the lens form different images (S 2 and S" 2, respectively) of the point source S 1 (Fig. 23.10). Therefore, at any position of the screen, the image on it appears in the form of a bright spot.

This type of aberration is eliminated by using systems consisting of concave and convex lenses.

Rice. 23.10. Spherical aberration

2. Astigmatism- monochromatic an aberration consisting in the fact that the image of a point has the form of an elliptical spot, which at certain positions of the image plane degenerates into a segment.

Astigmatism of oblique beams appears when the rays emanating from a point make significant angles with the optical axis. In Figure 23.11, and the point source is located on the secondary optical axis. In this case, two images appear in the form of segments of straight lines located perpendicular to each other in planes I and II. The image of the source can only be obtained in the form of a blurry spot between planes I and II.

Astigmatism due to asymmetry optical system. This type of astigmatism occurs when the symmetry of the optical system in relation to the light beam is broken due to the design of the system itself. With this aberration, lenses create an image in which contours and lines oriented in different directions have different sharpness. This is observed in cylindrical lenses (Fig. 23.11, b).

A cylindrical lens forms a linear image of a point object.

Rice. 23.11. Astigmatism: oblique beams (a); due to the cylindricity of the lens (b)

In the eye, astigmatism occurs when there is an asymmetry in the curvature of the lens and cornea systems. To correct astigmatism, glasses are used that have different curvatures in different directions.

3. Distortion(distortion). When the rays emitted by an object make a large angle with the optical axis, another type is detected monochromatic aberrations - distortion In this case, the geometric similarity between the object and the image is violated. The reason is that in reality the linear magnification given by the lens depends on the angle of incidence of the rays. As a result, the square grid image takes either pillow-, or barrel-shaped view (Fig. 23.12).

To combat distortion, a lens system with the opposite distortion is selected.

Rice. 23.12. Distortion: a - pincushion-shaped, b - barrel-shaped

4. Chromatic aberration manifests itself in the fact that a beam of white light emanating from a point gives its image in the form of a rainbow circle, violet rays intersect closer to the lens than red ones (Fig. 23.13).

The cause of chromatic aberration is the dependence of the refractive index of a substance on the wavelength of the incident light (dispersion). To correct this aberration in optics, lenses made from glasses with different dispersions (achromats, apochromats) are used.

Rice. 23.13. Chromatic aberration

23.5. Basic concepts and formulas

Table continuation

End of the table

23.6. Tasks

1. Why do air bubbles shine in water?

Answer: due to the reflection of light at the water-air interface.

2. Why does a spoon seem enlarged in a thin-walled glass of water?

Answer: The water in the glass acts as a cylindrical collecting lens. We see an imaginary enlarged image.

3. The optical power of the lens is 3 diopters. What is the focal length of the lens? Express the answer in cm.

Solution

D = 1/f, f = 1/D = 1/3 = 0.33 m. Answer: f = 33 cm.

4. The focal lengths of the two lenses are equal, respectively: f = +40 cm, f 2 = -40 cm. Find their optical powers.

6. How can you determine the focal length of a converging lens in clear weather?

Solution

The distance from the Sun to the Earth is so great that all the rays incident on the lens are parallel to each other. If you get an image of the Sun on the screen, then the distance from the lens to the screen will be equal to the focal length.

7. For a lens with a focal length of 20 cm, find the distance to the object at which the linear size of the actual image will be: a) twice the size of the object; b) equal to the size of the object; c) half the size of the object.

8. The optical power of the lens for a person with normal vision is 25 diopters. Refractive index 1.4. Calculate the radii of curvature of the lens if it is known that one radius of curvature is 2 times larger than the other.

We pointed out in § 81 that when light falls on the interface between two media, the light energy is divided into two parts: one part is reflected, the other part penetrates through the interface into the second medium. Using the example of the transition of light from air to glass, i.e. from a medium that is optically less dense to a medium that is optically denser, we saw that the proportion of reflected energy depends on the angle of incidence. In this case, the fraction of reflected energy increases greatly as the angle of incidence increases; however, even at very large angles of incidence, close to , when the light beam almost slides along the interface, some of the light energy still passes into the second medium (see §81, tables 4 and 5).

A new interesting phenomenon arises if light propagating in any medium falls on the interface between this medium and a medium that is optically less dense, that is, having a lower absolute refractive index. Here, too, the fraction of reflected energy increases with increasing angle of incidence, but the increase follows a different law: starting from a certain angle of incidence, all light energy is reflected from the interface. This phenomenon is called total internal reflection.

Let us consider again, as in §81, the incidence of light at the interface between glass and air. Let a light beam fall from the glass onto the interface at different angles of incidence (Fig. 186). If we measure the fraction of reflected light energy and the fraction of light energy passing through the interface, we obtain the values ​​given in Table. 7 (glass, like in Table 4, had a refractive index).

Rice. 186. Total internal reflection: the thickness of the rays corresponds to the fraction of light energy charged or passed through the interface

The angle of incidence from which all light energy is reflected from the interface is called the limiting angle of total internal reflection. For the glass for which the table was compiled. 7 (), the limiting angle is approximately .

Table 7. Fractions of reflected energy for various angles of incidence when light passes from glass to air

Angle of incidence

Angle of refraction

Reflected energy percentage (%)

Let us note that when light is incident on the interface at a limiting angle, the angle of refraction is equal to , i.e., in the formula expressing the law of refraction for this case,

when we have to put or . From here we find

At angles of incidence greater than that, there is no refracted ray. Formally, this follows from the fact that at angles of incidence large from the law of refraction for, values ​​larger than unity are obtained, which is obviously impossible.

In table Table 8 shows the limiting angles of total internal reflection for some substances, the refractive indices of which are given in table. 6. It is easy to verify the validity of relation (84.1).

Table 8. Limiting angle of total internal reflection at the boundary with air

Substance Carbon disulfide		Glass (heavy flint)
Glycerol

Total internal reflection can be observed at the boundary of air bubbles in water. They shine because the sunlight falling on them is completely reflected without passing into the bubbles. This is especially noticeable in those air bubbles that are always present on the stems and leaves of underwater plants and which in the sun appear to be made of silver, that is, from a material that reflects light very well.

Total internal reflection finds application in the design of glass rotating and turning prisms, the action of which is clear from Fig. 187. The limiting angle for a prism is depending on the refractive index of a given type of glass; Therefore, the use of such prisms does not encounter any difficulties with regard to the selection of the angles of entry and exit of light rays. Rotating prisms successfully perform the functions of mirrors and are advantageous in that their reflective properties remain unchanged, whereas metal mirrors fade over time due to oxidation of the metal. It should be noted that the wrapping prism is simpler in design than the equivalent rotating system of mirrors. Rotating prisms are used, in particular, in periscopes.

Rice. 187. Path of rays in a glass rotating prism (a), a wrapping prism (b) and in a curved plastic tube - light guide (c)

If n 1 >n 2 then >α, i.e. if light passes from a medium that is optically denser to a medium that is optically less dense, then the angle of refraction is greater than the angle of incidence (Fig. 3)

Limit angle of incidence. If α=α p,=90˚ and the beam will slide along the air-water interface.

If α’>α p, then the light will not pass into the second transparent medium, because will be completely reflected. This phenomenon is called complete reflection of light. The angle of incidence αn, at which the refracted beam slides along the interface between the media, is called the limiting angle of total reflection.

Total reflection can be observed in an isosceles rectangular glass prism (Fig. 4), which is widely used in periscopes, binoculars, refractometers, etc.

a) Light falls perpendicular to the first face and therefore does not undergo refraction here (α=0 and =0). The angle of incidence on the second face is α=45˚, i.e.>α p, (for glass α p =42˚). Therefore, light is completely reflected on this face. This is a rotating prism that rotates the beam 90˚.

b) In this case, the light inside the prism experiences double total reflection. This is also a rotating prism that rotates the beam 180˚.

c) In this case, the prism is already reversed. When the rays exit the prism, they are parallel to the incident ones, but the upper incident ray becomes the lower one, and the lower one becomes the upper one.

The phenomenon of total reflection has found wide technical application in light guides.

The light guide is a large number of thin glass filaments, the diameter of which is about 20 microns, and the length of each is about 1 m. These threads are parallel to each other and located closely (Fig. 5)

Each thread is surrounded by a thin shell of glass, the refractive index of which is lower than the thread itself. The light guide has two ends; the relative positions of the ends of the threads at both ends of the light guide are strictly the same.

If you place an object at one end of the light guide and illuminate it, then an image of this object will appear at the other end of the light guide.

The image is obtained due to the fact that light from some small area of ​​the object enters the end of each of the threads. Experiencing many total reflections, the light emerges from the opposite end of the thread, transmitting the reflection to a given small area of ​​the object.

Because the arrangement of the threads relative to each other is strictly the same, then the corresponding image of the object appears at the other end. The clarity of the image depends on the diameter of the threads. The smaller the diameter of each thread, the clearer the image of the object will be. Losses of light energy along the path of a light beam are usually relatively small in bundles (fibers), since with total reflection the reflection coefficient is relatively high (~0.9999). Energy loss are mainly caused by the absorption of light by the substance inside the fiber.

For example, in the visible part of the spectrum in a 1 m long fiber, 30-70% of the energy is lost (but in a bundle).

Therefore, to transmit large light fluxes and maintain the flexibility of the light-conducting system, individual fibers are collected into bundles (bundles) - light guides

Light guides are widely used in medicine to illuminate internal cavities with cold light and transmit images. Endoscope– a special device for examining internal cavities (stomach, rectum, etc.). Using light guides, laser radiation is transmitted for therapeutic effects on tumors. And the human retina is a highly organized fiber-optic system consisting of ~ 130x10 8 fibers.

The propagation of electromagnetic waves in various media is subject to the laws of reflection and refraction. From these laws, under certain conditions, one interesting effect follows, which in physics is called total internal reflection of light. Let's take a closer look at what this effect is.

Reflection and refraction

Before proceeding directly to the consideration of internal total reflection of light, it is necessary to explain the processes of reflection and refraction.

Reflection refers to the change in direction of movement of a light ray in the same medium when it encounters any interface. For example, if you point a laser pointer at a mirror, you can observe the described effect.

Refraction is, just like reflection, a change in the direction of movement of light, but not in the first, but in the second medium. The result of this phenomenon will be a distortion of the outlines of objects and their spatial arrangement. A common example of refraction is when a pencil or pen breaks when placed in a glass of water.

Refraction and reflection are related to each other. They are almost always present together: part of the beam's energy is reflected, and the other part is refracted.

Both phenomena are the result of the application of Fermat's principle. He states that light moves along the path between two points that will take it the least amount of time.

Since reflection is an effect that occurs in one medium, and refraction occurs in two media, it is important for the latter that both media are transparent to electromagnetic waves.

The concept of refractive index

The refractive index is an important quantity for the mathematical description of the phenomena under consideration. The refractive index of a particular medium is determined as follows:

Where c and v are the speeds of light in vacuum and matter, respectively. The value of v is always less than c, so the exponent n will be greater than one. The dimensionless coefficient n shows how much light in a substance (medium) will lag behind light in a vacuum. The difference between these speeds leads to the occurrence of the phenomenon of refraction.

The speed of light in matter correlates with the density of the latter. The denser the medium, the harder it is for light to move through it. For example, for air n = 1.00029, that is, almost like for a vacuum, for water n = 1.333.

Reflections, refraction and their laws

A prime example of the result of total reflection is the shiny surface of a diamond. The refractive index of a diamond is 2.43, so many rays of light entering a gem experience multiple total reflections before leaving it.

Problem of determining the critical angle θc for diamond

Let's consider a simple problem where we will show how to use the given formulas. It is necessary to calculate how much the critical angle of total reflection will change if a diamond is placed from air into water.

Having looked at the values ​​for the refractive indices of the indicated media in the table, we write them down:

• for air: n 1 = 1.00029;
• for water: n 2 = 1.333;
• for diamond: n 3 = 2.43.

The critical angle for the diamond-air pair is:

θ c1 = arcsin(n 1 /n 3) = arcsin(1.00029/2.43) ≈ 24.31 o.

As you can see, the critical angle for this pair of media is quite small, that is, only those rays can exit the diamond into the air that are closer to the normal than 24.31 o.

For the case of diamond in water we obtain:

θ c2 = arcsin(n 2 /n 3) = arcsin(1.333/2.43) ≈ 33.27 o.

The increase in the critical angle was:

Δθ c = θ c2 - θ c1 ≈ 33.27 o - 24.31 o = 8.96 o.

This slight increase in the critical angle for complete reflection of light in a diamond causes it to shine in water almost the same as in air.