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.

Geometric and wave optics. Conditions for using these approaches (based on the relationship between wavelength and object size). Wave coherence. The concept of spatial and temporal coherence. Stimulated emission. Features of laser radiation. Structure and principle of operation of the laser.

Due to the fact that light is a wave phenomenon, interference occurs, as a result of which limited the light beam does not propagate in any one direction, but has a finite angular distribution, i.e. diffraction occurs. However, in cases where the characteristic transverse dimensions of light beams are large enough compared to the wavelength, we can neglect the divergence of the light beam and assume that it propagates in one single direction: along the light beam.

Wave optics is a branch of optics that describes the propagation of light, taking into account its wave nature. Wave optics phenomena - interference, diffraction, polarization, etc.

Wave interference is the mutual strengthening or weakening of the amplitude of two or more coherent waves simultaneously propagating in space.

Wave diffraction is a phenomenon that manifests itself as a deviation from the laws of geometric optics during wave propagation.

Polarization - processes and states associated with the separation of any objects, mainly in space.

In physics, coherence is the correlation (consistency) of several oscillatory or wave processes in time, which manifests itself when they are added. Oscillations are coherent if their phase difference is constant over time and when adding the oscillations, an oscillation of the same frequency is obtained.

If the phase difference between two oscillations changes very slowly, then the oscillations are said to remain coherent for some time. This time is called coherence time.

Spatial coherence is the coherence of oscillations that occur at the same moment in time at different points of the plane perpendicular to the direction of wave propagation.

Stimulated emission is the generation of a new photon during the transition of a quantum system (atom, molecule, nucleus, etc.) from an excited state to a stable state (lower energy level) under the influence of an inducing photon, the energy of which was equal to the difference in energy levels. The created photon has the same energy, momentum, phase and polarization as the inducing photon (which is not absorbed).

Laser radiation can be continuous, with constant power, or pulsed, reaching extremely high peak powers. In some schemes, the laser working element is used as an optical amplifier for radiation from another source.

The physical basis for laser operation is the phenomenon of forced (induced) radiation. The essence of the phenomenon is that an excited atom is capable of emitting a photon under the influence of another photon without its absorption, if the energy of the latter is equal to the difference in the energies of the levels of the atom before and after the radiation. In this case, the emitted photon is coherent with the photon that caused the radiation (it is its “exact copy”). This way the light is amplified. This phenomenon differs from spontaneous radiation, in which the emitted photons have random propagation directions, polarization and phase

All lasers consist of three main parts:

active (working) environment;

pumping systems (energy source);

optical resonator (may be absent if the laser operates in amplifier mode).

Each of them ensures that the laser performs its specific functions.

Geometric optics. The phenomenon of total internal reflection. Limiting angle of total reflection. The course of the rays. Fiber optics.

Geometric optics is a branch of optics that studies the laws of light propagation in transparent media and the principles of constructing images when light passes through optical systems without taking into account its wave properties.

Total internal reflection is internal reflection, provided that the angle of incidence exceeds a certain critical angle. In this case, the incident wave is completely reflected, and the value of the reflection coefficient exceeds its highest values ​​for polished surfaces. The reflectance of total internal reflection is independent of wavelength.

Limiting angle of total internal reflection

Angle of incidence at which a refracted beam begins to slide along the interface between two media without transitioning to an optically denser medium

Path of rays in mirrors, prisms and lenses

Light rays from a point source travel in all directions. In optical systems, bending back and reflecting from the interfaces between media, some of the rays can intersect again at some point. A point is called a point image. When a ray is reflected from mirrors, the law is fulfilled: “the reflected ray always lies in the same plane as the incident ray and the normal to the impact surface, which passes through the point of incidence, and the angle of incidence subtracted from this normal is equal to the angle of impact.”

Fiber optics - this term means

a branch of optics that studies physical phenomena that arise and occur in optical fibers, or

products from precision engineering industries that contain components based on optical fibers.

Fiber optic devices include lasers, amplifiers, multiplexers, demultiplexers and a number of others. Fiber-optic components include insulators, mirrors, connectors, splitters, etc. The basis of a fiber-optic device is its optical circuit - a set of fiber-optic components connected in a certain sequence. Optical circuits can be closed or open, with or without feedback.

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 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 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.

On the image Ashows a normal ray that passes through the air-Plexiglas interface and exits the Plexiglas plate without undergoing any deflection as it passes through the two boundaries between the Plexiglas and the air. On the image b shows a ray of light entering a semicircular plate normally without deflection, but making an angle y with the normal at point O inside the plexiglass plate. When the beam leaves a denser medium (plexiglass), its speed of propagation in a less dense medium (air) increases. Therefore, it is refracted, making an angle x with respect to the normal in air, which is greater than y.

Based on the fact that n = sin (the angle that the beam makes with the normal in the air) / sin (the angle that the beam makes with the normal in the medium), plexiglass n n = sin x/sin y. If multiple measurements of x and y are made, the refractive index of the plexiglass can be calculated by averaging the results for each pair of values. Angle y can be increased by moving the light source in an arc of a circle centered at point O.

The effect of this is to increase the angle x until the position shown in the figure is reached V, i.e. until x becomes equal to 90 o. It is clear that the angle x cannot be greater. The angle that the ray now makes with the normal inside the plexiglass is called critical or limiting angle with(this is the angle of incidence on the boundary from a denser medium to a less dense one, when the angle of refraction in the less dense medium is 90°).

A weak reflected beam is usually observed, as is a bright beam that is refracted along the straight edge of the plate. This is a consequence of partial internal reflection. Note also that when white light is used, the light appearing along the straight edge is split into the colors of the spectrum. If the light source is moved further around the arc, as in the figure G, so that I inside the plexiglass becomes greater than the critical angle c and refraction does not occur at the boundary of the two media. Instead, the beam experiences total internal reflection at an angle r with respect to the normal, where r = i.

To make it happen total internal reflection, the angle of incidence i must be measured inside a denser medium (plexiglass) and it must be greater than the critical angle c. Note that the law of reflection is also valid for all angles of incidence greater than the critical angle.

Diamond critical angle is only 24°38". Its "flare" therefore depends on the ease with which multiple total internal reflection occurs when it is illuminated by light, which depends largely on the skillful cutting and polishing which enhances this effect. Previously it was it is determined that n = 1 /sin c, so an accurate measurement of the critical angle c will determine n.

Study 1. Determine n for plexiglass by finding the critical angle

Place a half-circle piece of plexiglass in the center of a large piece of white paper and carefully trace its outline. Find the midpoint O of the straight edge of the plate. Using a protractor, construct a normal NO perpendicular to this straight edge at point O. Place the plate again in its outline. Move the light source around the arc to the left of NO, all the time directing the incident ray to point O. When the refracted ray goes along the straight edge, as shown in the figure, mark the path of the incident ray with three points P 1, P 2, and P 3.

Temporarily remove the plate and connect these three points with a straight line that should pass through O. Using a protractor, measure the critical angle c between the drawn incident ray and the normal. Carefully place the plate again in its outline and repeat what was done before, but this time move the light source around the arc to the right of NO, continuously directing the beam to point O. Record the two measured values ​​of c in the results table and determine the average value of the critical angle c. Then determine the refractive index n n for plexiglass using the formula n n = 1 /sin s.


The apparatus for Study 1 can also be used to show that for light rays propagating in a denser medium (Plexiglas) and incident on the Plexiglas-air interface at angles greater than the critical angle c, the angle of incidence i is equal to the angle reflections r.

Study 2. Check the law of light reflection for angles of incidence greater than the critical angle

Place the semi-circular plexiglass plate on a large piece of white paper and carefully trace its outline. As in the first case, find the midpoint O and construct the normal NO. For plexiglass, the critical angle c = 42°, therefore, angles of incidence i > 42° are greater than the critical angle. Using a protractor, construct rays at angles of 45°, 50°, 60°, 70° and 80° to the normal NO.

Carefully place the plexiglass plate back into its outline and direct the light beam from the light source along the 45° line. The beam will go to point O, be reflected and appear on the arcuate side of the plate on the other side of the normal. Mark three points P 1, P 2 and P 3 on the reflected ray. Temporarily remove the plate and connect the three points with a straight line that should pass through point O.

Using a protractor, measure the angle of reflection r between and the reflected ray, recording the results in a table. Carefully place the plate into its outline and repeat for angles of 50°, 60°, 70° and 80° to the normal. Record the value of r in the appropriate space in the results table. Plot a graph of the angle of reflection r versus the angle of incidence i. A straight line graph drawn over the range of incidence angles from 45° to 80° will be sufficient to show that angle i is equal to angle r.

First, let's imagine a little. Imagine a hot summer day BC, a primitive man uses a spear to hunt fish. He notices its position, takes aim and strikes for some reason in a place not at all where the fish was visible. Missed? No, the fisherman has prey in his hands! The thing is that our ancestor intuitively understood the topic that we will study now. In everyday life, we see that a spoon lowered into a glass of water appears crooked; when we look through a glass jar, objects appear crooked. We will consider all these questions in the lesson, the topic of which is: “Refraction of light. The law of light refraction. Complete internal reflection."

In previous lessons, we talked about the fate of a beam in two cases: what happens if a beam of light propagates in a transparently homogeneous medium? The correct answer is that it will spread in a straight line. What happens when a beam of light falls on the interface between two media? In the last lesson we talked about the reflected beam, today we will look at that part of the light beam that is absorbed by the medium.

What will be the fate of the ray that penetrated from the first optically transparent medium into the second optically transparent medium?

Rice. 1. Refraction of light

If a beam falls on the interface between two transparent media, then part of the light energy returns to the first medium, creating a reflected beam, and the other part passes inward into the second medium and, as a rule, changes its direction.

The change in the direction of propagation of light when it passes through the interface between two media is called refraction of light(Fig. 1).

Rice. 2. Angles of incidence, refraction and reflection

In Figure 2 we see an incident beam; the angle of incidence will be denoted by α. The ray that will set the direction of the refracted beam of light will be called a refracted ray. The angle between the perpendicular to the interface, reconstructed from the point of incidence, and the refracted ray is called the angle of refraction; in the figure it is the angle γ. To complete the picture, we will also give an image of the reflected beam and, accordingly, the reflection angle β. What is the relationship between the angle of incidence and the angle of refraction? Is it possible to predict, knowing the angle of incidence and what medium the beam passed into, what the angle of refraction will be? It turns out it is possible!

We obtain a law that quantitatively describes the relationship between the angle of incidence and the angle of refraction. Let's use Huygens' principle, which regulates the propagation of waves in a medium. The law consists of two parts.

The incident ray, the refracted ray and the perpendicular restored to the point of incidence 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 for two given media and is equal to the ratio of the speeds of light in these media.

This law is called Snell's law, in honor of the Dutch scientist who first formulated it. The reason for refraction is the difference in the speed of light in different media. You can verify the validity of the law of refraction by experimentally directing a beam of light at different angles to the interface between two media and measuring the angles of incidence and refraction. If we change these angles, measure the sines and find the ratio of the sines of these angles, we will be convinced that the law of refraction is indeed valid.

Proof of the law of refraction using Huygens' principle is another confirmation of the wave nature of light.

The relative refractive index n 21 shows how many times the speed of light V 1 in the first medium differs from the speed of light V 2 in the second medium.

The relative refractive index is a clear demonstration of the fact that the reason light changes direction when passing from one medium to another is the different speed of light in the two media. The concept of “optical density of the medium” is often used to characterize the optical properties of a medium (Fig. 3).

Rice. 3. Optical density of the medium (α > γ)

If a ray passes from a medium with a higher speed of light to a medium with a lower speed of light, then, as can be seen from Figure 3 and the law of refraction of light, it will be pressed against the perpendicular, that is, the angle of refraction is less than the angle of incidence. In this case, the beam is said to have passed from a less dense optical medium to a more optically dense medium. Example: from air to water; from water to glass.

The opposite situation is also possible: the speed of light in the first medium is less than the speed of light in the second medium (Fig. 4).

Rice. 4. Optical density of the medium (α< γ)

Then the angle of refraction will be greater than the angle of incidence, and such a transition will be said to be made from an optically more dense to a less optically dense medium (from glass to water).

The optical density of two media can differ quite significantly, thus the situation shown in the photograph becomes possible (Fig. 5):

Rice. 5. Differences in optical density of media

Notice how the head is displaced relative to the body in the liquid, in an environment with higher optical density.

However, the relative refractive index is not always a convenient characteristic to work with, because it depends on the speed of light in the first and second media, but there can be a lot of such combinations and combinations of two media (water - air, glass - diamond, glycerin - alcohol , glass - water and so on). The tables would be very cumbersome, it would be inconvenient to work, and then they introduced one absolute medium, in comparison with which the speed of light in other media is compared. Vacuum was chosen as an absolute and the speed of light was compared with the speed of light in vacuum.

Absolute refractive index of the medium n- this is a quantity that characterizes the optical density of the medium and is equal to the ratio of the speed of light WITH in a vacuum to the speed of light in a given environment.

The absolute refractive index is more convenient for work, because we always know the speed of light in a vacuum; it is equal to 3·10 8 m/s and is a universal physical constant.

The absolute refractive index depends on external parameters: temperature, density, and also on the wavelength of light, therefore tables usually indicate the average refractive index for a given wavelength range. If we compare the refractive indices of air, water and glass (Fig. 6), we see that air has a refractive index close to unity, so we will take it as unity when solving problems.

Rice. 6. Table of absolute refractive indices for different media

It is not difficult to obtain a relationship between the absolute and relative refractive index of media.

The relative refractive index, that is, for a ray passing from medium one to medium two, is equal to the ratio of the absolute refractive index in the second medium to the absolute refractive index in the first medium.

For example: = ≈ 1.16

If the absolute refractive indices of two media are almost the same, this means that the relative refractive index when passing from one medium to another will be equal to unity, that is, the light ray will actually not be refracted. For example, when passing from anise oil to a beryl gemstone, the light will practically not bend, that is, it will behave the same as when passing through anise oil, since their refractive index is 1.56 and 1.57 respectively, so the gemstone can be as if hidden in a liquid, it simply won’t be visible.

If we pour water into a transparent glass and look through the wall of the glass into the light, we will see a silvery sheen on the surface due to the phenomenon of total internal reflection, which will be discussed now. When a light beam passes from a denser optical medium to a less dense optical medium, an interesting effect can be observed. For definiteness, we will assume that light comes from water into air. Let us assume that in the depths of the reservoir there is a point source of light S, emitting rays in all directions. For example, a diver shines a flashlight.

The SO 1 beam falls on the surface of the water at the smallest angle, this beam is partially refracted - the O 1 A 1 beam and is partially reflected back into the water - the O 1 B 1 beam. Thus, part of the energy of the incident beam is transferred to the refracted beam, and the remaining energy is transferred to the reflected beam.

Rice. 7. Total internal reflection

The SO 2 beam, whose angle of incidence is greater, is also divided into two beams: refracted and reflected, but the energy of the original beam is distributed between them differently: the refracted beam O 2 A 2 will be dimmer than the O 1 A 1 beam, that is, it will receive a smaller share of energy, and the reflected beam O 2 B 2, accordingly, will be brighter than the beam O 1 B 1, that is, it will receive a larger share of energy. As the angle of incidence increases, the same pattern is observed - an increasingly larger share of the energy of the incident beam goes to the reflected beam and a smaller and smaller share to the refracted beam. The refracted beam becomes dimmer and dimmer and at some point disappears completely; this disappearance occurs when it reaches the angle of incidence, which corresponds to the angle of refraction of 90 0. In this situation, the refracted beam OA should have gone parallel to the surface of the water, but there was nothing left to go - all the energy of the incident beam SO went entirely to the reflected beam OB. Naturally, with a further increase in the angle of incidence, the refracted beam will be absent. The described phenomenon is total internal reflection, that is, a denser optical medium at the considered angles does not emit rays from itself, they are all reflected inside it. The angle at which this phenomenon occurs is called limiting angle of total internal reflection.

The value of the limiting angle can be easily found from the law of refraction:

= => = arcsin, for water ≈ 49 0

The most interesting and popular application of the phenomenon of total internal reflection is the so-called waveguides, or fiber optics. This is exactly the method of sending signals that is used by modern telecommunications companies on the Internet.

We obtained the law of refraction of light, introduced a new concept - relative and absolute refractive indices, and also understood the phenomenon of total internal reflection and its applications, such as fiber optics. You can consolidate your knowledge by analyzing the relevant tests and simulators in the lesson section.

Let us obtain a proof of the law of light refraction using Huygens' principle. It is important to understand that the cause of refraction is the difference in the speed of light in two different media. Let us denote the speed of light in the first medium as V 1, and in the second medium as V 2 (Fig. 8).

Rice. 8. Proof of the law of refraction of light

Let a plane light wave fall on a flat interface between two media, for example from air into water. The wave surface AS is perpendicular to the rays and, the interface between the media MN is first reached by the ray, and the ray reaches the same surface after a time interval ∆t, which will be equal to the path of SW divided by the speed of light in the first medium.

Therefore, at the moment of time when the secondary wave at point B just begins to be excited, the wave from point A already has the form of a hemisphere with radius AD, which is equal to the speed of light in the second medium at ∆t: AD = ·∆t, that is, Huygens’ principle in visual action . The wave surface of a refracted wave can be obtained by drawing a surface tangent to all secondary waves in the second medium, the centers of which lie at the interface between the media, in this case this is the plane BD, it is the envelope of the secondary waves. The angle of incidence α of the beam is equal to the angle CAB in the triangle ABC, the sides of one of these angles are perpendicular to the sides of the other. Consequently, SV will be equal to the speed of light in the first medium by ∆t

CB = ∆t = AB sin α

In turn, the angle of refraction will be equal to angle ABD in triangle ABD, therefore:

АD = ∆t = АВ sin γ

Dividing the expressions term by term, we get:

n is a constant value that does not depend on the angle of incidence.

We have obtained the law of light refraction, the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media and is equal to the ratio of the speeds of light in the two given media.

A cubic vessel with opaque walls is positioned so that the eye of the observer does not see its bottom, but completely sees the wall of the vessel CD. What amount of water must be poured into the vessel so that the observer can see an object F located at a distance b = 10 cm from angle D? Vessel edge α = 40 cm (Fig. 9).

What is very important when solving this problem? Guess that since the eye does not see the bottom of the vessel, but sees the extreme point of the side wall, and the vessel is a cube, the angle of incidence of the beam on the surface of the water when we pour it will be equal to 45 0.

Rice. 9. Unified State Examination task

The beam falls at point F, this means that we clearly see the object, and the black dotted line shows the course of the beam if there were no water, that is, to point D. From the triangle NFK, the tangent of the angle β, the tangent of the angle of refraction, is the ratio of the opposite side to the adjacent or, based on the figure, h minus b divided by h.

tg β = = , h is the height of the liquid that we poured;

The most intense phenomenon of total internal reflection is used in fiber optical systems.

Rice. 10. Fiber optics

If a beam of light is directed at the end of a solid glass tube, then after multiple total internal reflection the beam will come out from the opposite side of the tube. It turns out that the glass tube is a conductor of a light wave or a waveguide. This will happen regardless of whether the tube is straight or curved (Figure 10). The first light guides, this is the second name for waveguides, were used to illuminate hard-to-reach places (during medical research, when light is supplied to one end of the light guide, and the other end illuminates the desired place). The main application is medicine, flaw detection of motors, but such waveguides are most widely used in information transmission systems. The carrier frequency when transmitting a signal by a light wave is a million times higher than the frequency of a radio signal, which means that the amount of information that we can transmit using a light wave is millions of times greater than the amount of information transmitted by radio waves. This is a great opportunity to convey a wealth of information in a simple and inexpensive way. Typically, information is transmitted through a fiber cable using laser radiation. Fiber optics is indispensable for fast and high-quality transmission of a computer signal containing a large amount of transmitted information. And the basis of all this is such a simple and ordinary phenomenon as the refraction of light.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemosyne, 2012.
2. Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

1. Edu.glavsprav.ru ().
2. Nvtc.ee ().
3. Raal100.narod.ru ().
4. Optika.ucoz.ru ().

Homework

1. Define the refraction of light.
2. Name the reason for the refraction of light.
3. Name the most popular applications of total internal reflection.