Total internal reflection
Internal reflection- the phenomenon of reflection of electromagnetic waves from the interface between two transparent media, provided that the wave falls from a medium with a higher refractive index.
Incomplete internal reflection- internal reflection, provided that the angle of incidence is less than the critical angle. In this case, the beam splits into refracted and reflected.
Total internal reflection- 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. In addition, the reflection coefficient for total internal reflection does not depend on the wavelength .
This optical phenomenon is observed for a wide spectrum of electromagnetic radiation including the X-ray range.
Within the framework of geometric optics, the explanation of the phenomenon is trivial: based on Snell's law and taking into account that the angle of refraction cannot exceed 90 °, we obtain that at an angle of incidence whose sine is greater than the ratio of the smaller refractive index to the larger coefficient, an electromagnetic wave should be completely reflected into the first medium .
In accordance with the wave theory of the phenomenon, the electromagnetic wave nevertheless penetrates into the second medium - the so-called "non-uniform wave" propagates there, which decays exponentially and does not carry away energy with it. The characteristic depth of penetration of an inhomogeneous wave into the second medium is of the order of the wavelength.
Total internal light reflection
Consider internal reflection using the example of two monochromatic rays incident on the interface between two media. Rays fall from a zone of denser medium (indicated in darker blue) with a refractive index to the boundary with a less dense medium (indicated in light blue) with a refractive index.
The red beam falls at an angle 
, that is, at the boundary of the media, it bifurcates - it is partially refracted and partially reflected. Part of the beam is refracted at an angle.
The green beam falls and is completely reflected src="/pictures/wiki/files/100/d833a2d69df321055f1e0bf120a53eff.png" border="0">.
Total internal reflection in nature and technology
Reflection of x-rays
The refraction of X-rays in grazing incidence was first formulated by M. A. Kumakhov, who developed the X-ray mirror, and theoretically substantiated by Arthur Compton in 1923.
Other wave phenomena
Demonstration of refraction, and hence the effect of total internal reflection, is possible, for example, for sound waves on the surface and in the bulk of a liquid during the transition between zones of different viscosity or density.
Phenomena similar to the effect of total internal reflection of electromagnetic radiation are observed for beams of slow neutrons.
If a vertically polarized wave falls on the interface at the Brewster angle, then the effect of complete refraction will be observed - there will be no reflected wave.
Notes
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TOTAL INTERNAL REFLECTION- reflection email. magn. radiation (in particular, light) when it falls on the interface between two transparent media from a medium with a high refractive index. P. in. about. is carried out when the angle of incidence i exceeds a certain limiting (critical) angle ... Physical Encyclopedia
Total internal reflection- Total internal reflection. When light passes from a medium with n1 > n2, total internal reflection occurs if the angle of incidence a2 > apr; at an angle of incidence a1 Illustrated Encyclopedic Dictionary
Total internal reflection- reflection of optical radiation (See Optical radiation) (light) or electromagnetic radiation of a different range (for example, radio waves) when it falls on the interface between two transparent media from a medium with a high refractive index ... ... Great Soviet Encyclopedia
TOTAL INTERNAL REFLECTION- electromagnetic waves, occurs when they pass from a medium with a high refractive index n1 to a medium with a lower refractive index n2 at an angle of incidence a exceeding the limiting angle apr, determined by the ratio sinapr=n2/n1. Complete… … Modern Encyclopedia
TOTAL INTERNAL REFLECTION- TOTAL INTERNAL REFLECTION, REFLECTION without light refraction at the boundary. When light passes from a denser medium (such as glass) to a less dense one (water or air), there is a zone of refraction angles in which light does not pass through the boundary ... Scientific and technical encyclopedic dictionary
total internal reflection- Reflection of light from an optically less dense medium with complete return to the medium from which it falls. [Collection of recommended terms. Issue 79. Physical optics. USSR Academy of Sciences. Committee of Scientific and Technical Terminology. 1970] Topics… … Technical Translator's Handbook
TOTAL INTERNAL REFLECTION- electromagnetic waves occur when they fall obliquely on the interface between 2 media, when radiation passes from a medium with a high refractive index n1 to a medium with a lower refractive index n2, and the angle of incidence i exceeds the limiting angle ... ... Big Encyclopedic Dictionary
total internal reflection- electromagnetic waves, occurs with oblique incidence on the interface between 2 media, when radiation passes from a medium with a high refractive index n1 to a medium with a lower refractive index n2, and the angle of incidence i exceeds the limiting angle ipr ... encyclopedic Dictionary
Geometric and wave optics. Conditions for applying these approaches (from the ratio of the wavelength and the size of the object). Wave coherence. The concept of spatial and temporal coherence. forced 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 beam of light does not propagate in any one direction, but has a finite angular distribution, i.e. diffraction takes place. However, in those cases where the characteristic transverse dimensions of light beams are sufficiently large compared to the wavelength, one 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. Phenomena of wave optics - interference, diffraction, polarization, etc.
Wave interference - mutual amplification or attenuation of the amplitude of two or more coherent waves simultaneously propagating in space.
Diffraction of waves is a phenomenon that manifests itself as a deviation from the laws of geometric optics during the propagation of waves.
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 the difference between their phases is constant in time and when the oscillations are added, an oscillation of the same frequency is obtained.
If the phase difference of two oscillations changes very slowly, then the oscillations are said to remain coherent for some time. This time is called the coherence time.
Spatial coherence - the coherence of oscillations that occur at the same time at different points in a plane perpendicular to the direction of wave propagation.
Stimulated emission - 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 a constant power, or pulsed, reaching extremely high peak powers. In some schemes, the working element of the laser is used as an optical amplifier for radiation from another source.
The physical basis for the operation of a laser is the phenomenon of stimulated (induced) radiation. The essence of the phenomenon is that an excited atom is able to emit 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 to the photon that caused the radiation (it is its “exact copy”). This is how the light is amplified. This phenomenon differs from spontaneous emission, in which the emitted photons have random directions of propagation, 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 the amplifier mode).
Each of them provides for the operation of the laser to perform 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 during the passage of light in optical systems without taking into account its wave properties.
Total internal reflection is internal reflection provided that the angle of incidence exceeds some 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 reflection coefficient for total internal reflection does not depend on the wavelength.
Limiting angle of total internal reflection
The angle of incidence at which the refracted beam begins to slide along the interface between two media without transition to an optically denser medium
Ray path in mirrors, prisms and lenses
Light rays from a point source propagate in all directions. In optical systems, bending back and reflecting from the interface between the media, some of the rays can again intersect at some point. A point is called a point image. When a ray is bounced off mirrors, the law is fulfilled: "the reflected ray always lies in the same plane as the incident ray and the normal to the bouncing surface, which passes through the point of incidence, and the angle of incidence subtracted from this normal is equal to the bouncing angle."
Fiber optics - this term means
branch of optics that studies the physical phenomena that occur and occur in optical fibers, or
products of precision engineering industries, which include 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.
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 long 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.
Decision:
One can give such an example. If the highway is very hot, then the air temperature is maximum near the asphalt surface and decreases with increasing distance from the road. This means that the refractive index of air is minimal at the surface and increases with increasing distance. As a result of this, rays having a small angle with respect to the highway surface suffer total reflection. If you focus your attention, while driving in a car, on a suitable section of the surface of the highway, you can see a car going upside down quite far ahead.
Example 2
Exercise: What is the Brewster angle for a beam of light that falls on the surface of a crystal if the limiting angle of total reflection for this beam at the air-crystal interface is 400?
Decision:
\[(tg(\alpha )_b)=\frac(n)(n_v)=n\left(2.2\right).\]
From expression (2.1) we have:
We substitute the right side of expression (2.3) into formula (2.2), we express the desired angle:
\[(\alpha )_b=arctg\left(\frac(1)((sin \left((\alpha )_(pred)\right)\ ))\right).\]
Let's do the calculations:
\[(\alpha )_b=arctg\left(\frac(1)((sin \left(40()^\circ \right)\ ))\right)\approx 57()^\circ .\]
Answer:$(\alpha )_b=57()^\circ .$
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 course 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 of this, 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.
Decision
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?
Decision
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 actual 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.
First, let's fantasize a little. Imagine a hot summer day BC, a primitive man hunts fish with a spear. He notices her position, aims and strikes for some reason not at all where the fish was visible. Missed? No, the fisherman has the 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 dipped 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 theme of which is: “Refraction of light. The law of refraction of light. Total internal reflection.
In previous lessons, we talked about the fate of a ray in two cases: what happens if a ray of light propagates in a transparently homogeneous medium? The correct answer is that it will spread in a straight line. And what will happen 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 consider that part of the light beam that is absorbed by the medium.
What will be the fate of the beam that has 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, while the other part passes inward to the second medium and, as a rule, changes its direction.
The change in the direction of propagation of light in the case of its passage 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 beam that will set the direction of the refracted beam of light will be called the refracted beam. The angle between the perpendicular to the interface between the media, restored from the point of incidence, and the refracted beam is called the angle of refraction, in the figure this is the angle γ. To complete the picture, we 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 from which medium the beam passed into which, what will be the angle of refraction? It turns out you can!
We obtain a law that quantitatively describes the relationship between the angle of incidence and the angle of refraction. Let us use the Huygens principle, which regulates the propagation of a wave 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, after the Dutch scientist who first formulated it. The reason for refraction is the difference in the speeds 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 ratios of the sines of these angles, we will be convinced that the law of refraction is indeed valid.
Evidence of the law of refraction using the 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 for the change in the direction of light when passing from one medium to another is the different speed of light in two media. The term "optical density of a medium" is often used to characterize the optical properties of a medium (Fig. 3).
Rice. 3. Optical density of the medium (α > γ)
If the beam 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 reverse 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 denser to a less optically dense medium (from glass to water).
The optical density of two media can differ quite significantly, so the situation shown in the photograph (Fig. 5) becomes possible:
Rice. 5. The difference between the optical density of media
Pay attention to how the head is displaced relative to the body, which is in the liquid, in a medium with a higher optical density.
However, the relative refractive index is not always a convenient characteristic for work, because it depends on the speeds 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 one absolute environment was introduced, in comparison with which the speed of light in other environments is compared. Vacuum was chosen as the absolute and the speeds of light are compared with the speed of light in vacuum.
Absolute refractive index of the medium n- this is a value that characterizes the optical density of the medium and is equal to the ratio of the speed of light With in vacuum to the speed of light in a given medium.
The absolute refractive index is more convenient for work, because we always know the speed of light in 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, so 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 the refractive index of air is close to unity, so we will take it as a unit when solving problems.
Rice. 6. Table of absolute refractive indices for different media
It is easy to get the relationship between the absolute and relative refractive index of media.
The relative refractive index, that is, for a beam 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 the two media are almost the same, this means that the relative refractive index when passing from one medium to another will be equal to one, that is, the light beam will not actually be refracted. For example, when passing from anise oil to a gem, beryl will practically not deviate light, that is, it will behave as it does when passing through anise oil, since their refractive index is 1.56 and 1.57, respectively, so the gem can be how to hide in a liquid, it simply will not be visible.
If you pour water into a transparent glass and look through the wall of the glass into the light, then we will see a silvery sheen of 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 goes from water to air. Let us assume that there is a point source of light S in the depth of the reservoir, emitting rays in all directions. For example, a diver shines a flashlight.
Beam SO 1 falls on the surface of the water at the smallest angle, this beam is partially refracted - beam O 1 A 1 and partially reflected back into the water - beam O 1 B 1. Thus, part of the energy of the incident beam is transferred to the refracted beam, and the remaining part of the energy is transferred to the reflected beam.
Rice. 7. Total internal reflection
Beam SO 2, whose angle of incidence is larger, is also divided into two beams: refracted and reflected, but the energy of the original beam is distributed between them in a different way: the refracted beam O 2 A 2 will be dimmer than the beam O 1 A 1, that is, it will receive a smaller fraction of energy, and the reflected beam O 2 V 2, respectively, will be brighter than the beam O 1 V 1, that is, it will receive a larger share of energy. As the angle of incidence increases, the same regularity is traced - an increasing share of the energy of the incident beam goes to the reflected beam and an ever smaller share to the refracted beam. The refracted beam becomes dimmer and at some point disappears completely, this disappearance occurs when the angle of incidence is reached, which corresponds to a refraction angle of 90 0 . In this situation, the refracted beam OA would have to go parallel to the water surface, but there is nothing 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 is easy to find 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 way of signaling that is used by modern telecommunications companies on the Internet.
We got the law of refraction of light, introduced a new concept - relative and absolute refractive indices, and also figured out the phenomenon of total internal reflection and its applications, such as fiber optics. You can consolidate knowledge by examining the relevant tests and simulators in the lesson section.
Let's get the proof of the law of refraction of light using the Huygens principle. It is important to understand that the cause of refraction is the difference in the speeds of light in two different media. Let us denote the speed of light in the first medium V 1 , and in the second medium - 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 AC is perpendicular to the rays and , the interface between the media MN first reaches the beam , and the beam reaches the same surface after a time interval ∆t, which will be equal to the path SW divided by the speed of light in the first medium .
Therefore, at the moment when the secondary wave at point B only 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 by ∆t: AD = ∆t, that is, the 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 on the interface between the media, in this case it 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. Therefore, SW 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 the angle ABD in the triangle ABD, therefore:
AD = ∆t = AB 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 refraction of light, the sine of the angle of incidence to the sine of the angle of refraction is a constant value for the given two media and equal to the ratio of the speeds of light in the two given media.
A cubic vessel with opaque walls is located in such a way that the observer's eye does not see its bottom, but completely sees the wall of the vessel CD. How much water must be poured into the vessel so that the observer can see the object F, located at a distance b = 10 cm from the corner D? Vessel edge α = 40 cm (Fig. 9).
What is very important in 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, then 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. The task of the exam
The beam falls to point F, which 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 NFC, the tangent of the angle β, the tangent of the angle of refraction, is the ratio of the opposite leg 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 optic systems.
Rice. 10. Fiber optics
If a beam of light is directed to the end of a solid glass tube, then after multiple total internal reflection the beam will emerge 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 whether the tube is straight or curved (Figure 10). The first light guides, this is the second name of wave guides, 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 right place). The main application is medicine, defectoscopy of motors, however, such waveguides are most widely used in information transmission systems. The carrier frequency of a light wave is a million times 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 huge amount of information in a simple and inexpensive way. As a rule, information is transmitted over 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 at the heart of all this lies such a simple and common phenomenon as the refraction of light.
Bibliography
- Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemozina, 2012.
- Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
- Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.
- edu.glavsprav.ru ().
- Nvtc.ee ().
- Raal100.narod.ru ().
- Optika.ucoz.ru ().
Homework
- Define refraction of light.
- Name the reason for the refraction of light.
- Name the most popular applications of total internal reflection.
