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.

Fresnel formulas show that the modules $\left|E_(otr\bot )\right|=\left|E_(otr\bot )\right|$, $\left|E_(otr//)\right|=\ left|E_(otr//)\right|$ which means the reflection is "full".

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 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.

Solution:

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?

Solution:

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

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

LECTURE 23 GEOMETRIC OPTICS

LECTURE 23 GEOMETRIC OPTICS

1. Laws of reflection and refraction of light.

2. Total internal reflection. fiber optics.

3. Lenses. The 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, one can use the laws of geometric optics based on the concept of a light beam 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 that occurs at the interface between two media, as a result of which the light beam changes the direction of its propagation, remaining in the first medium. The nature of the reflection depends on the ratio between the dimensions (h) of the irregularities of the reflecting surface and the wavelength (λ) incident radiation.

diffuse reflection

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

Mirror reflection

If the dimensions of the irregularities are 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 fulfilled.

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

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

Rice. 23.1. The course of rays in 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 beam propagates in the second medium, changing its direction. The optical characteristic of the medium is absolute

Rice. 23.2. The path of rays at 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 beam depends on the ratio of the refractive indices of the two media. The following laws of refraction are fulfilled.

The incident beam, the refracted beam and the normal to the interface between two media, drawn through the point of incidence of the beam, 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

Consider the transition of light from a medium with a high refractive index n 1 (optically denser) to a medium with a lower refractive index n 2 (optically less dense). Figure 23.3 shows the 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)

An increase in 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 is incident from a denser medium on the boundary with a less dense medium and consists in the following.

If the angle of incidence exceeds the limiting angle for these media, then there is no refraction at the interface 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 beams is equal to the intensity of the incident beam. As the angle of incidence increases, the intensity of the reflected beam increases, while the intensity of the refracted beam decreases, and for the limiting angle of incidence becomes equal to zero.

fiber optics

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

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

In modern light guides, the loss of light as a result of its absorption is very small (on the order of 10% per km), which makes it possible to use them 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 the endoscope reaches a million.

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

Rice. 23.4. Propagation of light rays through a fiber

Rice. 23.5. endoscope

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

to illuminate such a column, examining it through a microscope, it is clear that its walls remain dark, and the inside of each cell is brightly lit. 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 a herbaceous plant.

23.3. Lenses. Optical power of the lens

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 much 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 is to the side optical axis, then the lens is called collecting otherwise the lens is called scattering.

Any ray incident on a converging 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, through the focus passes continuation refracted beam (Fig. 23.6, b).

Each lens has two foci located on either side of it. 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 the “+” sign for gathering lenses and with a "-" sign for scattering lenses.

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

optical power thin lens and focal length depend on the radii of the spheres and the refractive index of the lens substance relative to the environment:

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

Lenses are used to take images. Consider an object located perpendicular to the optical axis of the converging lens, and construct an image of its upper point A. The image of the entire object will also be perpendicular to the lens axis. 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 race-

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

walk around and at point A" their extensions intersect. This point is called imaginary image. The imaginary 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 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 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 Options

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

The 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 the light, or the light is sufficient monochromatic.

When using imaging lenses real subjects, these restrictions, as a rule, are not met: there is dispersion; 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, the 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 is 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 associated with the complex spectral composition of real light.

1. Spherical aberration- monochromatic aberration due to the fact that the extreme (peripheral) parts of the lens deviate rays coming from a point source more strongly than its central part. As a result, the peripheral and central regions of the lens form different images (S 2 and S "2, respectively) of a point source S 1 (Fig. 23.10). Therefore, at any position of the screen, the image on it is obtained in the form of a bright spot.

This kind of aberration is eliminated by using concave and convex lens systems.

Rice. 23.10. Spherical aberration

2. Astigmatism- monochromatic 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 oblique beams manifests itself when the rays emanating from a point make significant angles with the optical axis. In Figure 23.11, a 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 with respect to the beam of light is broken due to the design of the system itself. With this aberration, the 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 is formed when there is an asymmetry in the curvature of the lens and cornea systems. To correct astigmatism, glasses are used that have different curvature in different directions.

3. Distortion(distortion). When the rays sent by the object make a large angle with the optical axis, another kind is found 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 opposite distortion is selected.

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

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 reason for 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 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 converging lens. We see an imaginary magnified image.

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

Solution

D \u003d 1 / f, f \u003d 1 / D \u003d 1/3 \u003d 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 falling 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 distances to the object at which the linear size of the real image will be: a) twice as large as 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 twice the other.

used in so-called fiber optics. Fiber optics is a branch of optics that deals with the transmission of light radiation through fiber optic light guides. Fiber optic light guides are a system of individual transparent fibers assembled into bundles (bundles). Light, getting inside a transparent fiber surrounded by a substance with a lower refractive index, is reflected many times and propagates along the fiber (see Fig. 5.3).

1) In medicine and veterinary diagnostics, light guides are mainly used for illuminating internal cavities and transmitting images.

One example of the use of fiber optics in medicine is endoscope- a special device for examining internal cavities (stomach, rectum, etc.). One of the varieties of such devices is fiber gastroscope. With its help, you can not only visually examine the stomach, but also take the necessary pictures for the purpose of diagnosis.

2) With the help of light guides, laser radiation is also transmitted to the internal organs for the purpose of therapeutic effects on tumors.

3) Fiber optics has found wide application in technology. In connection with the rapid development of information systems in recent years, there is a need for high-quality and fast transmission of information through communication channels. For this purpose, signal transmission is used along a laser beam propagating through fiber optic light guides.

WAVE PROPERTIES OF LIGHT

INTERFERENCE SVETA.

Interference- one of the brightest manifestations of the wave nature of light. This interesting and beautiful phenomenon is observed under certain conditions when two or more light beams are superimposed. We encounter interference phenomena quite often: the colors of oil stains on asphalt, the color of freezing window panes, the bizarre color patterns on the wings of some butterflies and beetles - all this is a manifestation of light interference.

LIGHT INTERFERENCE- addition in space of two or more coherent light waves, in which at its different points it turns out amplification or attenuation of the amplitude resulting wave.

Coherence.

coherence is called the coordinated flow in time and space of several oscillatory or wave processes, i.e. waves with the same frequency and time-constant phase difference.

Monochromatic waves ( waves of one wavelength ) - are coherent.

Because real sources do not give strictly monochromatic light, then the waves emitted by any independent light sources always incoherent. In the source, light is emitted by atoms, each of which emits light only for a time of ≈ 10 -8 s. Only during this time the waves emitted by the atom have constant amplitude and phase of oscillations. But get coherent waves can be divided by dividing the beam of light emitted by one source into 2 light waves and after passing through different paths, reconnect them. Then the phase difference will be determined by the wave path difference: at constant stroke difference phase difference will also constant .

CONDITION INTERFERENCE MAXIMUM :

If a optical path difference ∆ in vacuum is an even number of half-waves or (an integer number of wavelengths)

(4.5)

then the oscillations excited at the point M will occur in the same phase.

CONDITION INTERFERENCE MINIMUM.

If a optical path difference ∆ is equal to an odd number of half-waves

(4.6)

then and oscillations excited at the point M will occur out of phase.

A typical and common example of light interference is a soap film

Application of interference - optics coating: Part of the light passing through the lens is reflected (up to 50% in complex optical systems). The essence of the antireflection method is that the surfaces of optical systems are covered with thin films that create interference phenomena. Film thickness d=l/4 of the incident light, then the reflected light has a path difference , which corresponds to a minimum of interference

DIFFRACTION OF LIGHT

Diffraction called wave bending around obstacles, encountered on their way, or in a broader sense - any wave propagation deviation near obstacles from rectilinear.

The possibility of observing diffraction depends on the ratio of the wavelength of light and the size of obstacles (inhomogeneities)

Diffraction Fraunhofer on a diffraction grating.

One-dimensional diffraction grating - a system of parallel slots of equal width, lying in the same plane and separated by opaque gaps of equal width.

Overall diffraction pattern is the result of mutual interference of waves coming from all slots - in a diffraction grating, multibeam interference of coherent diffracted light beams coming from all slits occurs.

If a a - width every crack (MN); b - width of opaque areas between cracks (NC), then the value d = a+ b called constant (period) of the diffraction grating.

where N 0 is the number of slots per unit length.

Path difference ∆ of beams (1-2) and (3-4) is equal to СF

1. .MINIMUM CONDITION If the path difference CF = (2n+1)l/2- is equal to an odd number of half-wavelengths, then the oscillations of rays 1-2 and 3-4 will pass in antiphase, and they will cancel each other out illumination:

n=1,2,3,4 … (4.8)

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 have seen that the fraction of reflected energy depends on the angle of incidence. In this case, the fraction of reflected energy increases strongly 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, part of the light energy still passes into the second medium (see §81, Tables 4 and 5).

An interesting new phenomenon arises if light propagating in a medium falls on the interface between this medium and a medium that is optically less dense, i.e., has a lower absolute refractive index. Here, too, the proportion of reflected energy increases with increasing angle of incidence, but the increase proceeds according to 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.

Consider again, as in §81, the incidence of light on 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 that has passed through the interface, then the values ​​given in Table 1 are obtained. 7 (glass, as in Table 4, had a refractive index of ).

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

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

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

Angle of incidence

Refraction angle

Share of reflected energy (in %)

Note that when light falls on the interface at the limiting angle, the angle of refraction is , i.e., in the formula expressing the law of refraction for this case,

when we must put or . From here we find

At angles of incidence, large refracted beam does not exist. Formally, this follows from the fact that at angles of incidence large from the law of refraction for , values ​​greater than unity are obtained, which is obviously impossible.

In 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 through 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 seem to be made of silver, that is, of a material that reflects light very well.

Total internal reflection finds its application in the device of glass rotary and inverting prisms, the operation 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. Rotatable prisms successfully perform the functions of mirrors and are beneficial in that their reflective properties remain unchanged, while metal mirrors fade over time due to metal oxidation. It should be noted that an inverting prism is simpler in terms of the design of an equivalent rotating system of mirrors. Rotary prisms are used, in particular, in periscopes.

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

If n 1 >n 2, then >α, i.e. if light passes from an optically denser medium to an optically less dense medium, 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 fully reflected. This phenomenon is called full reflection of light. The angle of incidence α p, 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 α=45˚, i.e.>α p, (for glass α p =42˚). Therefore, on this face, the light is completely reflected. This is a rotary prism that rotates the beam 90˚.

b) In this case, the light inside the prism experiences already twofold total reflection. This is also a rotary prism that rotates the beam by 180˚.

c) In this case, the prism is already inverted. When the rays leave the prism, they are parallel to the incident ones, but in this case the upper incident beam becomes lower, and the lower one becomes upper.

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 each is about 1 m long. These threads are parallel to each other and are located close (Fig. 5)

Each filament is surrounded by a thin shell of glass, the refractive index of which is less than that of the filament itself. The light guide has two ends, the mutual arrangement of the ends of the threads on both ends of the light guide is strictly the same.

If an object is placed at one end of the light guide and illuminated, 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 exits from the opposite end of the filament, transmitting the reflection of a given small area of ​​the object.

Because the location 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. The loss of light energy along the path of the light beam is usually relatively small in bundles (light guides), since with total reflection the reflection coefficient is relatively high (~0.9999). Energy loss are mainly due to the absorption of light by the substance inside the fiber.

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

Therefore, in order to transmit large light fluxes and maintain the flexibility of the light-guiding system, individual fibers are assembled into bundles (bundles) - light guides.

Light guides are widely used in medicine for illuminating internal cavities with cold light and transmitting images. endoscope- a special device for examining internal cavities (stomach, rectum, etc.). With the help of light guides, laser radiation is transmitted for a therapeutic effect on tumors. Yes, and the human retina is a highly organized fiber-optic system consisting of ~ 130x10 8 fibers.