Let's conduct an experiment. Let's place a glass plate in the center of the optical disk and direct a beam of light onto it. We will see that at the border of air and glass, light will not only be reflected, but will also penetrate into the glass, changing the direction of its propagation (Fig. 84).

The change in the direction of propagation of light as it passes through the interface between two media is called refraction of light.

In Figure 84 the following are indicated: AO - incident beam; OB - reflected beam; OE - refracted ray.

Note that if we directed the beam in the direction EO, then, due to the reversibility of light rays, it would exit the glass in the direction OA.

The refraction of light is explained by the change in the speed of propagation of light as it passes from one medium to another. For the first time such an explanation for this phenomenon was given in the middle of the 17th century. Father Maignan. According to Maignan, when light passes from one medium to another, the ray of light changes its direction in the same way as the direction of movement of the “soldier’s front” changes when the meadow along which the soldiers are walking is blocked by arable land, the border of which runs at an angle to the front. Each of the soldiers who have reached the arable land slows down, while those of the soldiers who have not yet reached it continue to walk at the same speed. As a result of this, the soldiers who entered the arable land begin to lag behind those walking through the meadow, and the column of troops turns around (Fig. 85).

To determine in which direction a beam of light will deviate when it passes through the interface between two media, you need to know in which of these media the speed of light is less and in which it is greater.

Light is electromagnetic waves. Therefore, everything that was said about the speed of propagation of electromagnetic waves (see § 28) equally applies to the speed of light. For example, the speed of light in vacuum is maximum and equal to:

c = 299792 km/s ≈ 300000 km/s.

The speed of light in matter v is always less than in vacuum:

The speed of light values ​​in various media are given in Table 6.

Of the two media, the one in which the speed of light is less is called optically more dense, and the one in which the speed of light is greater - optically less dense. For example, water is an optically denser medium than air, and glass is an optically denser medium than water.

Experience shows that, when entering a medium that is optically denser, a ray of light deviates from its original direction towards the perpendicular to the interface between two media (Fig. 86, a), and when entering a medium that is optically less dense, the ray of light deviates towards reverse side (Fig. 86, b).

The angle between the refracted ray and the perpendicular to the interface between two media at the point of incidence of the ray is called refraction angle. In Figure 86

α is the angle of incidence, β is the angle of refraction.

From Figure 86 it can be seen that the angle of refraction can be either greater or less than the angle of incidence. Can these angles coincide? They can, but only when a beam of light falls on the interface between the media at right angles to it; in this case α = β = 0.

The ability to refract rays varies among different media. The more significantly the speed of light in two media differs, the more strongly the rays are refracted at the boundary between them.

One of the main parts of many optical instruments is a glass triangular prism (Fig. 87, a). Figure 87, b shows the path of the ray in such a prism: as a result of double refraction, the triangular prism deflects the ray incident on it towards its base.

The refraction of light is the reason why the depth of a body of water (river, pond, bathtub with water) seems to us less than it actually is. After all, in order to see any point S at the bottom of a reservoir, it is necessary that the rays of light emerging from it enter the eye of the observer (Fig. 88). But after refraction at the boundary of water with air, the beam of light will be perceived by the eye as light coming from a virtual image S 1 located higher than the corresponding point S at the bottom of the reservoir. It can be proven that the apparent depth of a reservoir h is approximately ¾ of its true depth H.

This phenomenon was first described by Euclid. One of his books talks about an experience with a ring. The observer looks at the cup with the ring lying on its bottom so that the edges of the cup do not allow him to be seen; then, without changing the position of the eyes, they begin to pour water into the cup, and after a while the ring becomes visible.

Many other phenomena are also explained by the refraction of light, for example, the apparent bending of a spoon dropped into a glass of water; a higher than actual position of the stars and the Sun above the horizon, etc.

1. What is called the refraction of light? 2. What angle is called the angle of refraction? How is it designated? 3. What is the speed of light in vacuum? 4. Which medium is optically denser: ice or quartz? Why? 5. In what case is the angle of refraction of light less than the angle of incidence and in what case is it greater? 6. What is the angle of incidence of the beam if the refracted beam is perpendicular to the interface? 7. Why does the depth of the reservoir seem shallower to an observer looking at the water from above than it actually is? What will the depth of the river appear to be if in reality it is 2 m? 8. There are pieces of glass, quartz and diamond in the air. On whose surface are light rays refracted the most?

Experimental task. Repeat Euclid's experiment. Place a ring (or coin) on the bottom of the tea cup, then place it in front of you so that the edges of the cup cover its bottom. If, without changing the relative position of the cup and the eyes, you pour water into it, then the ring (or coin) becomes visible. Why?

Laws of light refraction.

Physical meaning of the refractive index. Light is refracted due to changes in the speed of its propagation when passing from one medium to another. The refractive index of the second medium relative to the first is numerically equal to the ratio of the speed of light in the first medium to the speed of light in the second medium:

Thus, the refractive index shows how many times the speed of light in the medium from which the beam exits is greater (smaller) than the speed of light in the medium into which it enters.

Since the speed of propagation of electromagnetic waves in a vacuum is constant, it is advisable to determine the refractive indices of various media relative to vacuum. Speed ​​ratio With propagation of light in a vacuum to the speed of its propagation in a given medium is called absolute refractive index of a given substance () and is the main characteristic of its optical properties,

,

those. the refractive index of the second medium relative to the first is equal to the ratio of the absolute indices of these media.

Typically, the optical properties of a substance are characterized by its refractive index n relative to air, which differs little from the absolute refractive index. In this case, a medium with a larger absolute index is called optically denser.

Limit angle of refraction. If light passes from a medium with a lower refractive index to a medium with a higher refractive index ( n 1< n 2 ), then the angle of refraction is less than the angle of incidence

r< i (Fig. 3).

Rice. 3. Refraction of light during transition

from an optically less dense medium to a medium

optically denser.

When the angle of incidence increases to i m = 90° (beam 3, Fig. 2) light in the second medium will propagate only within the angle r pr , called limiting angle of refraction. In the region of the second medium within an angle additional to the limiting angle of refraction (90° - i pr ), light does not penetrate (in Fig. 3 this area is shaded).

Limit angle of refraction r pr

But sin i m = 1, therefore .

The phenomenon of total internal reflection. When light travels from a medium with a high refractive index n 1 > n 2 (Fig. 4), then the angle of refraction is greater than the angle of incidence. Light is refracted (passes into a second medium) only within the angle of incidence i pr , which corresponds to the angle of refraction r m = 90°.

Rice. 4. Refraction of light when passing from an optically denser medium to a medium

optically less dense.

Light incident at a large angle is completely reflected from the boundary of the media (Fig. 4, ray 3). This phenomenon is called total internal reflection, and the angle of incidence i pr – limiting angle of total internal reflection.

Limiting angle of total internal reflection i pr determined according to the condition:

, then sin r m =1, therefore, .

If light comes from any medium into a vacuum or air, then

Due to the reversibility of the ray path for two given media, the limiting angle of refraction during the transition from the first medium to the second is equal to the limiting angle of total internal reflection when the ray passes from the second medium to the first.

The limiting angle of total internal reflection for glass is less than 42°. Therefore, rays traveling through glass and falling on its surface at an angle of 45° are completely reflected. This property of glass is used in rotating (Fig. 5a) and reversible (Fig. 4b) prisms, often used in optical instruments.

Rice. 5: a – rotary prism; b – reversible prism.

Fiber optics. Total internal reflection is used in the construction of flexible light guides. Light, entering a transparent fiber surrounded by a substance with a lower refractive index, is reflected many times and propagates along this fiber (Fig. 6).

Fig.6. Passage of light inside a transparent fiber surrounded by a substance

with a lower refractive index.

To transmit large light fluxes and maintain the flexibility of the light-conducting system, individual fibers are collected into bundles - light guides. The branch of optics that deals with the transmission of light and images through optical fibers is called fiber optics. The same term is used to refer to the fiber optic parts and devices themselves. In medicine, light guides are used to illuminate internal cavities with cold light and transmit images.

Practical part

Devices for determining the refractive index of substances are called refractometers(Fig. 7).

Fig.7. Optical diagram of the refractometer.

1 – mirror, 2 – measuring head, 3 – prism system to eliminate dispersion, 4 – lens, 5 – rotating prism (beam rotation by 90 0), 6 – scale (in some refractometers

there are two scales: the refractive index scale and the solution concentration scale),

7 – eyepiece.

The main part of the refractometer is the measuring head, consisting of two prisms: the lighting one, which is located in the folding part of the head, and the measuring one.

At the exit of the lighting prism, its matte surface creates a diffuse beam of light, which passes through the liquid under study (2-3 drops) between the prisms. The rays fall onto the surface of the measuring prism at different angles, including at an angle of 90 0 . In the measuring prism, the rays are collected in the region of the limiting angle of refraction, which explains the formation of the light-shadow boundary on the device screen.

Fig.8. Beam path in the measuring head:

1 – lighting prism, 2 – test liquid,

3 – measuring prism, 4 – screen.

DETERMINING THE PERCENTAGE OF SUGAR IN A SOLUTION

Natural and polarized light. Visible light- This electromagnetic waves with an oscillation frequency in the range from 4∙10 14 to 7.5∙10 14 Hz. Electromagnetic waves are transverse: vectors E and H of the electric and magnetic field strengths are mutually perpendicular and lie in a plane perpendicular to the wave velocity vector.

Due to the fact that both the chemical and biological effects of light are associated mainly with the electrical component of the electromagnetic wave, the vector E the strength of this field is called light vector, and the plane of oscillation of this vector is plane of light wave oscillations.

In any light source, waves are emitted by many atoms and molecules, the light vectors of these waves are located in various planes, and vibrations occur in different phases. Consequently, the plane of oscillation of the light vector of the resulting wave continuously changes its position in space (Fig. 1). This kind of light is called natural, or unpolarized.

Rice. 1. Schematic representation of beam and natural light.

If you select two mutually perpendicular planes passing through a beam of natural light and project the vectors E onto the planes, then on average these projections will be the same. Thus, it is convenient to depict a ray of natural light as a straight line on which the same number of both projections are located in the form of dashes and dots:

When light passes through crystals, it is possible to obtain light whose plane of wave oscillation occupies a constant position in space. This kind of light is called flat- or linearly polarized. Due to the ordered arrangement of atoms and molecules in the spatial lattice, the crystal transmits only vibrations of the light vector occurring in a certain plane characteristic of a given lattice.

It is convenient to represent a plane-polarized light wave as follows:

Polarization of light can also be partial. In this case, the amplitude of oscillations of the light vector in any one plane significantly exceeds the amplitudes of oscillations in other planes.

Partially polarized light can be conventionally depicted as follows: , etc. The ratio of the number of lines and dots determines the degree of polarization of light.

In all methods of converting natural light into polarized light, components with a very specific orientation of the polarization plane are completely or partially selected from natural light.

Methods for producing polarized light: a) reflection and refraction of light at the boundary of two dielectrics; b) transmitting light through optically anisotropic uniaxial crystals; c) transmission of light through media whose optical anisotropy is artificially created by the action of an electric or magnetic field, as well as due to deformation. These methods are based on the phenomenon anisotropy.

Anisotropy is the dependence of a number of properties (mechanical, thermal, electrical, optical) on direction. Bodies whose properties are the same in all directions are called isotropic.

Polarization is also observed during light scattering. The smaller the size of the particles on which scattering occurs, the higher the degree of polarization.

Devices designed to produce polarized light are called polarizers.

Polarization of light during reflection and refraction at the interface between two dielectrics. When natural light is reflected and refracted at the interface between two isotropic dielectrics, it undergoes linear polarization. At an arbitrary angle of incidence, the polarization of the reflected light is partial. The reflected beam is dominated by vibrations perpendicular to the plane of incidence, and the refracted beam is dominated by vibrations parallel to it (Fig. 2).

Rice. 2. Partial polarization of natural light during reflection and refraction

If the angle of incidence satisfies the condition tan i B = n 21, then the reflected light is completely polarized (Brewster’s law), and the refracted beam is not completely polarized, but maximally (Fig. 3). In this case, the reflected and refracted rays are mutually perpendicular.

– relative refractive index of two media, i B – Brewster angle.

Rice. 3. Full polarization of the reflected beam during reflection and refraction

at the interface between two isotropic dielectrics.

Birefringence. There are a number of crystals (calcite, quartz, etc.) in which a ray of light, when refracted, splits into two rays with different properties. Calcite (Iceland spar) is a crystal with a hexagonal lattice. The axis of symmetry of the hexagonal prism that forms its cell is called the optical axis. The optical axis is not a line, but a direction in the crystal. Any straight line parallel to this direction is also an optical axis.

If you cut a plate from a calcite crystal so that its edges are perpendicular to the optical axis, and direct a beam of light along the optical axis, then no changes will occur in it. If you direct the beam at an angle to the optical axis, it will split into two beams (Fig. 4), of which one is called ordinary, the second is called extraordinary.

Rice. 4. Birefringence when light passes through a calcite plate.

MN – optical axis.

An ordinary ray lies in the plane of incidence and has a refractive index normal for a given substance. The extraordinary beam lies in a plane passing through the incident beam and the optical axis of the crystal drawn at the point of incidence of the beam. This plane is called main plane of the crystal. The refractive indices for ordinary and extraordinary rays are different.

Both ordinary and extraordinary rays are polarized. The plane of oscillation of ordinary rays is perpendicular to the main plane. Oscillations of extraordinary rays occur in the main plane of the crystal.

The phenomenon of double refraction is due to the anisotropy of crystals. Along the optical axis, the speed of the light wave for ordinary and extraordinary rays is the same. In other directions, the speed of the extraordinary wave in calcite is greater than that of the ordinary one. The greatest difference between the speeds of both waves occurs in the direction perpendicular to the optical axis.

According to Huygens' principle, with birefringence, at each point on the surface of a wave reaching the crystal boundary, two elementary waves arise simultaneously (not one, as in ordinary media!), which propagate in the crystal.

The speed of propagation of one wave in all directions is the same, i.e. the wave has a spherical shape and is called ordinary. The speed of propagation of another wave in the direction of the optical axis of the crystal is the same as the speed of an ordinary wave, and in the direction perpendicular to the optical axis, it differs from it. The wave has an ellipsoidal shape and is called extraordinary(Fig. 5).

Rice. 5. Propagation of ordinary (o) and extraordinary (e) waves in a crystal

with double refraction.

Prism Nicolas. To obtain polarized light, a Nicolas polarizing prism is used. A prism of a certain shape and size is cut out of calcite, then it is sawed along a diagonal plane and glued together with Canada balsam. When a light beam falls on the upper face along the axis of the prism (Fig. 6), the extraordinary beam falls on the gluing plane at a smaller angle and passes through almost without changing direction. An ordinary beam falls at an angle greater than the angle of total reflection for Canada balsam, is reflected from the gluing plane and is absorbed by the blackened edge of the prism. A Nicolas prism produces fully polarized light, the plane of vibration of which lies in the main plane of the prism.

Rice. 6. Nicolas prism. Ordinary passage scheme

and extraordinary rays.

Dichroism. There are crystals that absorb ordinary and extraordinary rays differently. Thus, if a beam of natural light is directed at a tourmaline crystal perpendicular to the direction of the optical axis, then with a plate thickness of only a few millimeters, the ordinary beam will be completely absorbed, and only an extraordinary beam will emerge from the crystal (Fig. 7).

Rice. 7. Passage of light through a tourmaline crystal.

The different nature of absorption of ordinary and extraordinary rays is called absorption anisotropy, or dichroism. Thus, tourmaline crystals can also be used as polarizers.

Polaroids. Currently, polarizers are widely used Polaroids. To make a Polaroid, a transparent film containing crystals of a light-polarizing dichroic substance (for example, iodoquinone sulfate) is glued between two glass or plexiglass plates. During the film manufacturing process, the crystals are oriented so that their optical axes are parallel. This entire system is fixed in the frame.

The low cost of polaroids and the ability to produce plates with a large area ensured their widespread use in practice.

Analysis of polarized light. To study the nature and degree of polarization of light, devices called analyzers. Analyzers use the same devices that are used to obtain linearly polarized light - polarizers, but adapted for rotation around the longitudinal axis. The analyzer passes only vibrations that coincide with its main plane. Otherwise, only the vibration component that coincides with this plane passes through the analyzer.

If the light wave entering the analyzer is linearly polarized, then the intensity of the wave leaving the analyzer is Malus's law:

,

where I 0 is the intensity of the incoming light, φ is the angle between the planes of the incoming light and the light transmitted by the analyzer.

The passage of light through the polarizer-analyzer system is shown schematically in Fig. 8.

Rice. 8. Diagram of the passage of light through the polarizer-analyzer system (P – polarizer,

A – analyzer, E – screen):

a) the main planes of the polarizer and analyzer coincide;

b) the main planes of the polarizer and analyzer are located at a certain angle;

c) the main planes of the polarizer and analyzer are mutually perpendicular.

If the main planes of the polarizer and analyzer coincide, then the light passes completely through the analyzer and illuminates the screen (Fig. 7a). If they are located at a certain angle, the light passes through the analyzer, but is weakened (Fig. 7b) the more, the closer this angle is to 90 0. If these planes are mutually perpendicular, then the light is completely extinguished by the analyzer (Fig. 7c)

Rotation of the plane of vibration of polarized light. Polarimetry. Some crystals, as well as solutions of organic substances, have the property of rotating the plane of oscillation of polarized light passing through them. These substances are called optically A active. These include sugars, acids, alkaloids, etc.

For the majority of optically active substances, the existence of two modifications has been discovered, rotating the plane of polarization respectively clockwise and counterclockwise (for an observer looking towards the beam). The first modification is called dextrorotatory or positive, second – left-handed, or negative.

The natural optical activity of a substance in a non-crystalline state is due to the asymmetry of the molecules. In crystalline substances, optical activity can also be determined by the peculiarities of the arrangement of molecules in the lattice.

In solids, the angle φ of rotation of the plane of polarization is directly proportional to the length d of the path of the light beam in the body:

where α – rotational capacity (specific rotation), depending on the type of substance, temperature and wavelength. For left- and right-handed modifications, the rotational abilities are the same in magnitude.

For solutions, the angle of rotation of the plane of polarization

,

where α is the specific rotation, c is the concentration of the optically active substance in the solution. The value of α depends on the nature of the optically active substance and solvent, temperature and wavelength of light. Specific rotation– this is the angle of rotation increased by 100 times for a solution 1 dm thick at a substance concentration of 1 gram per 100 cm 3 of solution at a temperature of 20 0 C and at a light wavelength λ = 589 nm. A very sensitive method for determining concentration c based on this relationship is called polarimetry (saccharimetry).

The dependence of the rotation of the plane of polarization on the wavelength of light is called rotational dispersion. To a first approximation, we have Biot's law:

where A is a coefficient depending on the nature of the substance and temperature.

In a clinical setting, the method polarimetry used to determine the concentration of sugar in urine. The device used for this is called saccharimeter(Fig.9).

Rice. 9. Optical design of the saccharimeter:

I is a source of natural light;

C – light filter (monochromator), ensuring coordination of the device operation

with Biot Law;

L – a collecting lens that produces a parallel beam of light at the output;

P – polarizer;

K – tube with the test solution;

A – analyzer mounted on a rotating disk D with divisions.

When conducting a study, the analyzer is first set to maximum darkening of the field of view without the test solution. Then a tube with a solution is placed in the device and, by rotating the analyzer, the field of view is again darkened. The smaller of the two angles through which the analyzer must be rotated is the angle of rotation for the substance under study. The concentration of sugar in the solution is calculated from the angle.

To simplify calculations, the tube with the solution is made so long that the angle of rotation of the analyzer (in degrees) is numerically equal to the concentration With solution (in grams per 100 cm3). The length of the glucose tube is 19 cm.

Polarization microscopy. The method is based on anisotropy some components of cells and tissues, appearing when observing them in polarized light. Structures consisting of molecules arranged in parallel or disks arranged in a stack, when introduced into a medium with a refractive index different from the refractive index of the particles of the structure, exhibit the ability to double refraction. This means that the structure will transmit polarized light only when the plane of polarization is parallel to the long axes of the particles. This remains true even when the particles do not exhibit intrinsic birefringence. Optical anisotropy observed in muscle, connective tissue (collagen) and nerve fibers.

The very name of skeletal muscles " striated" is associated with differences in the optical properties of individual sections of muscle fiber. It consists of alternating darker and lighter areas of tissue matter. This gives the fiber cross-striations. Examination of muscle fibers under polarized light reveals that darker areas are anisotropic and have properties birefringence, while the darker areas are isotropic. Collagen the fibers are anisotropic, their optical axis is located along the fiber axis. Micelles in pulp shell neurofibrils are also anisotropic, but their optical axes are located in radial directions. A polarizing microscope is used for histological examination of these structures.

The most important component of a polarizing microscope is the polarizer, which is located between the light source and the capacitor. In addition, the microscope has a rotating stage or sample holder, an analyzer located between the objective and the eyepiece, which can be installed so that its axis is perpendicular to the axis of the polarizer, and a compensator.

When the polarizer and analyzer are crossed and the object is missing or isotropic, the field appears uniformly dark. If there is an object with birefringence, and it is located so that its axis is at an angle to the plane of polarization other than 0 0 or 90 0, it will separate the polarized light into two components - parallel and perpendicular to the plane of the analyzer. Consequently, some of the light will pass through the analyzer, resulting in a bright image of the object against a dark background. As the object rotates, the brightness of its image will change, reaching a maximum at an angle of 45 0 relative to the polarizer or analyzer.

Polarization microscopy is used to study the orientation of molecules in biological structures (for example, muscle cells), as well as to observe structures that are invisible using other methods (for example, the mitotic spindle during cell division), identifying helical structure.

Polarized light is used under simulated conditions to assess mechanical stresses occurring in bone tissue. This method is based on the phenomenon of photoelasticity, which consists in the appearance of optical anisotropy in initially isotropic solids under the action of mechanical loads.

DETERMINING THE WAVELENGTH OF LIGHT USING A DIFFRACTION GRATING

Interference of light. Light interference is a phenomenon that occurs when light waves are superimposed and are accompanied by their strengthening or weakening. A stable interference pattern arises when coherent waves are superimposed. Coherent waves are waves with equal frequencies and identical phases or having a constant phase shift. The amplification of light waves during interference (maximum condition) occurs in the case where Δ contains an even number of half-wavelengths:

Where k – maximum order, k=0,±1,±2,±,…±n;

λ – light wavelength.

Attenuation of light waves during interference (minimum condition) is observed if the optical path difference Δ contains an odd number of half-wavelengths:

Where k – minimum order.

The optical difference in the path of two beams is the difference in distances from the sources to the observation point of the interference pattern.

Interference in thin films. Interference in thin films can be observed in soap bubbles, in a spot of kerosene on the surface of water when illuminated by sunlight.

Let beam 1 fall on the surface of a thin film (see Fig. 2). The beam, refracted at the air-film boundary, passes through the film, is reflected from its inner surface, approaches the outer surface of the film, is refracted at the film-air boundary and the beam comes out. We direct beam 2 to the exit point of the beam, which runs parallel to beam 1. Beam 2 is reflected from the surface of the film, superimposed on the beam, and both beams interfere.

When the film is illuminated with polychromatic light, we get a rainbow picture. This is explained by the fact that the film is not uniform in thickness. Consequently, path differences of different magnitudes arise, which correspond to different wavelengths (colored soap films, iridescent colors of the wings of some insects and birds, films of oil or oils on the surface of water, etc.).

Light interference is used in devices called interferometers. Interferometers are optical devices that can be used to spatially separate two beams and create a certain path difference between them. Interferometers are used to determine wavelengths with a high degree of accuracy over short distances, refractive indices of substances and determine the quality of optical surfaces.

For sanitary and hygienic purposes, the interferometer is used to determine the content of harmful gases.

The combination of an interferometer and a microscope (interference microscope) is used in biology to measure the refractive index, dry matter concentration, and thickness of transparent microobjects.

Huygens–Fresnel principle. According to Huygens, every point in the medium that the primary wave reaches at a given moment is a source of secondary waves. Fresnel clarified this position of Huygens, adding that secondary waves are coherent, i.e. when superimposed they will produce a stable interference pattern.

Diffraction of light. Diffraction of light is the phenomenon of deviation of light from rectilinear propagation.

Diffraction in parallel rays from a single slit. Let the target width V a parallel beam of monochromatic light falls (see Fig. 3):

A lens is installed in the path of the rays L , in the focal plane of which the screen is located E . Most rays do not diffract, i.e. do not change their direction, and they are focused by the lens L in the center of the screen, forming a central maximum or a zero-order maximum. Rays diffracting at equal diffraction angles φ , will form maximums 1,2,3,…, on the screen n - orders of magnitude.

Thus, the diffraction pattern obtained from one slit in parallel beams when illuminated with monochromatic light is a light stripe with maximum illumination in the center of the screen, then there is a dark stripe (minimum of the 1st order), then there is a light stripe (maximum of the 1st order order), dark band (2nd order minimum), 2nd order maximum, etc. The diffraction pattern is symmetrical relative to the central maximum. When the slit is illuminated with white light, a system of color stripes is formed on the screen; only the central maximum will retain the color of the incident light.

Conditions max And min diffraction. If in the optical path difference Δ an odd number of segments equal to , then an increase in light intensity is observed ( max diffraction):

Where k – order of maximum; k =±1,±2,±…,± n;

λ – wavelength.

If in the optical path difference Δ an even number of segments equal to , then a weakening of the light intensity is observed ( min diffraction):

Where k – minimum order.

Diffraction grating. A diffraction grating consists of alternating stripes that are opaque to the passage of light with stripes (slits) of equal width that are transparent to light.

The main characteristic of a diffraction grating is its period d . The period of the diffraction grating is the total width of the transparent and opaque stripes:

A diffraction grating is used in optical instruments to enhance the resolution of the device. The resolution of a diffraction grating depends on the order of the spectrum k and on the number of strokes N :

Where R - resolution.

Derivation of the diffraction grating formula. Let us direct two parallel beams to the diffraction grating: 1 and 2 so that the distance between them is equal to the grating period d .

At points A And IN rays 1 and 2 diffract, deviating from the rectilinear direction at an angle φ – diffraction angle.

Rays And focused by lens L onto the screen located in the focal plane of the lens (Fig. 5). Each grating slit can be considered as a source of secondary waves (Huygens–Fresnel principle). On the screen at point D we observe the maximum of the interference pattern.

From point A on the beam path drop the perpendicular and get point C. consider the triangle ABC : right triangle, ÐVAS=Ðφ like angles with mutually perpendicular sides. From Δ ABC:

Where AB=d (by construction),

CB = Δ – optical path difference.

Since at point D we observe maximum interference, then

Where k – order of maximum,

λ – light wavelength.

Substituting values AB=d, into the formula for sinφ :

From here we get:

In general, the diffraction grating formula is:

The ± signs indicate that the interference pattern on the screen is symmetrical with respect to the central maximum.

Physical foundations of holography. Holography is a method of recording and reconstructing a wave field, which is based on the phenomena of diffraction and wave interference. If in a regular photograph only the intensity of the waves reflected from an object is recorded, then the phases of the waves are additionally recorded on the hologram, which provides additional information about the object and allows one to obtain a three-dimensional image of the object.

1308. Is it possible for a ray to pass through the interface between two different media without being refracted? If yes, under what conditions?
Yes. Under the condition of vertical fall onto the interface between two different media.

1309. What is the speed of light:
a) in water,
b) in glass,
c) in diamond?

1310. Calculate the refractive index of glass relative to water when a ray of light passes from water to glass.

1311. Figure 161 shows a ray that goes obliquely to the edge of a glass plate and then goes out into the air. Draw the path of the beam in the air.

1312. Figure 162 shows a ray that falls from the air onto the face of a glass plate, passes through it and exits into the air. Draw the path of the ray.

1313. A ray from the air goes into medium A (Fig. 163). Find the refractive index of medium A.

1314. The optical density of air increases as it approaches the Earth's surface. How will this affect the path of the beam entering the atmosphere:
a) vertically,
b) obliquely?
A) for a beam entering the atmosphere vertically the speed will decrease
B) for a beam entering the atmosphere obliquely, the speed will decrease and the trajectory will be bent.

1315. When you look through thick glass, objects appear displaced. Why?
Because passing through the glass, light rays are refracted. Thus changing its direction.

1316. Why do the planets in the sky glow with an even light and the stars twinkle?

1317. The Moon is spherical, but to us from Earth its surface appears flat, not convex. Why?

1318. When we look down through the water to the bottom of the reservoir, it seems closer than it actually is. Why?
Because light is refracted as it passes through the water-air interface. And the bottom seems closer than it actually is.

1319*. Read the previous problem. Determine how many times the actual depth is greater than the apparent depth.

1320*. The stone lies at the bottom of the river at a depth of 2 m (Fig. 164). If we look at it from above, at what depth will it appear to us?

1321. A straight rod is lowered into water (Fig. 165). The observer looks from above. How does he see the end of the rod?

1322. There is a hollow glass prism filled with air in water. Draw the path of a ray incident on one of the refractive faces of such a prism. Can we say that such a prism deflects a ray of light passing through it twice towards the base?
When a beam passes from water to air, the beam is deflected upward horizontally, because The angle of refraction in air is greater than the angle of incidence in water. After passing through the prism, the beam falls on the air-water interface. Then it refracts, deviating a little more upward.

1323. The refractive index of water is 1.33, turpentine is 1.51. Find the refractive index of turpentine relative to water.

1325. Determine the speed of light in a diamond whose refractive index is 2.4.

1326. Draw the path of the ray as it passes from glass to air, if the angle of incidence is 45° and the refractive index of glass is 1.72.

1327. Find the limiting angle of total internal reflection for rock salt (n=1.54).

1328. Determine the displacement of the beam when passing through a plane-parallel glass plate of thickness d=3 cm, if the beam falls at an angle of 60°. Refractive index of glass n=1.51.

1329. Find the position of the image of an object located at a distance of 4 cm from the front surface of a plane-parallel plate 1 cm thick, silvered on the back side, assuming that the refractive index of the plate substance is 1.51.

1330. A thick glass plate is completely immersed flat in water. Draw the path of the ray coming from the air through the water and the plate. (Glass is a medium optically denser than water).

1331. Sometimes the objects we observe through the window seem to be curved. Why?
Because the glass is not perfectly even and smooth. This is due to the non-uniform distribution of the optical plane of the glass.

1332. Figure 166 shows a point light source S located in front of a triangular prism. If we look at S through a prism, where will this point appear to us? Draw the path of the rays.

1333. The light beam goes perpendicular to one of the faces of a glass rectangular trihedral prism (Fig. 167). Draw the path of the ray through the prism.

Processes that are associated with light are an important component of physics and surround us everywhere in our everyday lives. The most important in this situation are the laws of reflection and refraction of light, on which modern optics is based. The refraction of light is an important part of modern science.

Distortion effect

This article will tell you what the phenomenon of light refraction is, as well as what the law of refraction looks like and what follows from it.

Basics of a physical phenomenon

When a beam falls on a surface that is separated by two transparent substances that have different optical densities (for example, different glasses or in water), some of the rays will be reflected, and some will penetrate into the second structure (for example, they will propagate in water or glass). When moving from one medium to another, a ray typically changes its direction. This is the phenomenon of light refraction.
The reflection and refraction of light is especially visible in water.

Distortion effect in water

Looking at things in water, they appear distorted. This is especially noticeable at the boundary between air and water. Visually, underwater objects appear to be slightly deflected. The described physical phenomenon is precisely the reason why all objects appear distorted in water. When the rays hit the glass, this effect is less noticeable.
Refraction of light is a physical phenomenon that is characterized by a change in the direction of movement of a solar ray at the moment it moves from one medium (structure) to another.
To improve our understanding of this process, consider an example of a beam hitting water from air (similarly for glass). By drawing a perpendicular line along the interface, the angle of refraction and return of the light beam can be measured. This index (angle of refraction) will change as the flow penetrates the water (inside the glass).
Note! This parameter is understood as the angle formed by a perpendicular drawn to the separation of two substances when a beam penetrates from the first structure to the second.

Beam Passage

The same indicator is typical for other environments. It has been established that this indicator depends on the density of the substance. If the beam falls from a less dense to a denser structure, then the angle of distortion created will be greater. And if it’s the other way around, then it’s less.
At the same time, a change in the slope of the decline will also affect this indicator. But the relationship between them does not remain constant. At the same time, the ratio of their sines will remain a constant value, which is reflected by the following formula: sinα / sinγ = n, where:

• n is a constant value that is described for each specific substance (air, glass, water, etc.). Therefore, what this value will be can be determined using special tables;
• α – angle of incidence;
• γ – angle of refraction.

To determine this physical phenomenon, the law of refraction was created.

Physical law

The law of refraction of light fluxes allows us to determine the characteristics of transparent substances. The law itself consists of two provisions:

• First part. The beam (incident, modified) and the perpendicular, which was restored at the point of incidence on the boundary, for example, of air and water (glass, etc.), will be located in the same plane;
• The second part. The ratio of the sine of the angle of incidence to the sine of the same angle formed when crossing the boundary will be a constant value.

Description of the law

In this case, at the moment the beam exits the second structure into the first (for example, when the light flux passes from the air, through the glass and back into the air), a distortion effect will also occur.

An important parameter for different objects

The main indicator in this situation is the ratio of the sine of the angle of incidence to a similar parameter, but for distortion. As follows from the law described above, this indicator is a constant value.
Moreover, when the value of the decline slope changes, the same situation will be typical for a similar indicator. This parameter is of great importance because it is an integral characteristic of transparent substances.

Indicators for different objects

Thanks to this parameter, you can quite effectively distinguish between types of glass, as well as various precious stones. It is also important for determining the speed of light in various environments.

Note! The highest speed of light flow is in a vacuum.

When moving from one substance to another, its speed will decrease. For example, in diamond, which has the highest refractive index, the speed of photon propagation will be 2.42 times higher than that of air. In water, they will spread 1.33 times slower. For different types of glass, this parameter ranges from 1.4 to 2.2.

Note! Some glasses have a refractive index of 2.2, which is very close to diamond (2.4). Therefore, it is not always possible to distinguish a piece of glass from a real diamond.

Optical density of substances

Light can penetrate through different substances, which are characterized by different optical densities. As we said earlier, using this law you can determine the density characteristic of the medium (structure). The denser it is, the slower the speed at which light will propagate through it. For example, glass or water will be more optically dense than air.
In addition to the fact that this parameter is a constant value, it also reflects the ratio of the speed of light in two substances. The physical meaning can be displayed as the following formula:

This indicator tells how the speed of propagation of photons changes when moving from one substance to another.

Another important indicator

When a light flux moves through transparent objects, its polarization is possible. It is observed during the passage of a light flux from dielectric isotropic media. Polarization occurs when photons pass through glass.

Polarization effect

Partial polarization is observed when the angle of incidence of the light flux at the boundary of two dielectrics differs from zero. The degree of polarization depends on what the angles of incidence were (Brewster's law).

Full internal reflection

Concluding our short excursion, it is still necessary to consider such an effect as full internal reflection.

The phenomenon of full display

For this effect to appear, it is necessary to increase the angle of incidence of the light flux at the moment of its transition from a more dense to a less dense medium at the interface between substances. In a situation where this parameter exceeds a certain limiting value, then photons incident on the boundary of this section will be completely reflected. Actually, this will be our desired phenomenon. Without it, it was impossible to make fiber optics.

Conclusion

The practical application of the behavior of light flux has given a lot, creating a variety of technical devices to improve our lives. At the same time, light has not yet revealed all its possibilities to humanity, and its practical potential has not yet been fully realized.

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