To quantify radiation, a fairly wide range of quantities is used, which can be conditionally divided into two systems of units: energy and light. In this case, the energy quantities characterize the radiation related to the entire optical region of the spectrum, and the lighting quantities characterize the visible radiation. The energy quantities are proportional to the corresponding lighting quantities.
The main quantity in the energy system, which makes it possible to judge the amount of radiation, is radiation flux Ph, or radiation power, i.e. amount of energy W, radiated, carried or absorbed per unit time:
The Fe value is expressed in watts (W). - energy unit
In most cases, they do not take into account the quantum nature of the appearance of radiation and consider it continuous.
A qualitative characteristic of radiation is the distribution of the radiation flux over the spectrum.
For radiations having a continuous spectrum, the concept is introduced spectral density of the radiation flux ( ) - the ratio of the radiation power attributable to a certain narrow section of the spectrum to the width of this section (Fig. 2.2). For a narrow spectral range d the radiation flux is dФ . The ordinate shows the spectral densities of the radiation flux = dФ /d , therefore, the flow is represented by the area of an elementary section of the graph, i.e.
Figure 2.2 - Dependence of the spectral flux density radiation from wavelength
E 
If the emission spectrum lies within the limits of
1
before
2
, then the magnitude of the radiation flux
Under luminous flux F, in general case, understand the power of radiation, estimated by its effect on the human eye. The unit of luminous flux is lumen (lm). – lighting unit
The action of the light flux on the eye causes its certain reaction. Depending on the level of action of the light flux, one or another type of light-sensitive eye receivers, called rods or cones, works. In low light conditions (for example, in the light of the moon), the eye sees the surrounding objects due to rods. At high levels illumination, the daytime vision apparatus begins to work, for which the cones are responsible.
In addition, cones are divided into three groups according to their light-sensitive substance with different sensitivity in different regions of the spectrum. Therefore, unlike rods, they react not only to the light flux, but also to its spectral composition.
In this regard, it can be said that light action two-dimensional.
The quantitative characteristic of the reaction of the eye associated with the level of illumination is called lightness. The quality characteristic associated with different levels reactions of three groups of cones, called chromaticity.
The power of light (I). In lighting technology, this value is taken as basic. This choice does not have a fundamental basis, but is made for reasons of convenience, since The intensity of light does not depend on distance.
The concept of luminous intensity refers only to point sources, i.e. to sources whose dimensions are small compared to the distance from them to the illuminated surface.
The luminous intensity of a point source in a certain direction is per unit solid angle light flow F emitted by this source in a given direction:
I=F / Ω
Energy luminous intensity is expressed in watts per steradian ( Tue/Wed).
Behind lighting unit of luminous intensity is accepted candela(cd) is the luminous intensity of a point source that emits a luminous flux of 1 lm, distributed evenly within a solid angle of 1 steradian (sr).
A solid angle is a part of space bounded by a conical surface and a closed curvilinear contour, not passing through the vertex of the corner (Fig. 2.3). When compressed conical surface the dimensions of the spherical area o become infinitesimal. The solid angle in this case also becomes infinitesimal:
Figure 2.3 - To the definition of the concept of "solid angle"
Illumination (E). Under energetic illumination E uh understand the flow of radiation on area unit illuminated surface Q:
Energy illumination is expressed in W/m 2 .
Light illumination E expressed by the light flux density F on the surface it illuminates (Fig. 2.4):
For the unit of light illumination is taken luxury, i.e. the illumination of a surface receiving a luminous flux of 1 lm uniformly distributed over it over an area of 1 m 2.
Among other quantities used in lighting engineering, important are energy radiation Wuh or light energy W, as well as energy Ne or light H exposure.
The values We and W are determined by the expressions
where 
are, respectively, the functions of changing the radiation flux and the luminous flux in time. We is measured in joules or Ws, a W
–
in lm s.
Under energy H uh or light exposure understand the surface energy density of radiation W uh or light energy W respectively on the illuminated surface.
I.e lightsand Iexposure H is the product of illumination E, created by the radiation source, for a time t action of this radiation.
Question 2. Photometric quantities and their units.
Photometry is a branch of optics that deals with the measurement of the energy characteristics of optical radiation in the processes of propagation and interaction with matter. Photometry uses energy quantities that characterize the energy parameters of optical radiation, regardless of its effect on radiation detectors, and also uses light quantities, which characterize the physiological effects of light and are evaluated by the effect on the human eye or other receivers.
Energy quantities.
Energy flowF e is the value, numerically equal to energy W radiation passing through a section perpendicular to the direction of energy transfer, per unit time
F e = W/ t, watt (Tue).
The flow of energy is equivalent to the power of energy.
The energy radiated by a real source into the surrounding space is distributed over its surface.
Energy luminosity(radiance) R e is the radiation power per unit surface area in all directions:
R e = F e / S, (Tue/m 2),
those. is the surface radiation flux density.
Energy power of light (radiation force) I e is defined using the concept of a point source of light - a source whose dimensions compared to the distance to the observation point can be neglected. Energy power of light I e value, equal to the ratio radiation flux F e source to solid angle ω , within which this radiation propagates:
I e= F e / ω , (Tue/Wed) - watt per steradian.
A solid angle is a part of space bounded by some conical surface. Particular cases of solid angles are trihedral and polyhedral angles. Solid angle ω measured by area ratio S that part of the sphere centered at the vertex of the conical surface, which is cut by this solid angle, to the square of the radius of the sphere, i.e. ω = S/r 2 . full sphere forms a solid angle equal to 4π steradians, i.e. ω = 4π r 2 /r 2 = 4π Wed.
The light intensity of the source often depends on the direction of radiation. If it does not depend on the direction of radiation, then such a source is called isotropic. For an isotropic source, the luminous intensity is
I e= F e /4π.
In the case of an extended source, we can talk about the luminous intensity of an element of its surface dS.
Energy Brightness (radiance) AT e is a value equal to the ratio of the energy intensity of light Δ I e element of the radiating surface to the area ∆S projections of this element onto a plane perpendicular to the direction of observation:
AT e = Δ I e / ∆ S. [(Tue/(sr.m 2)].
Energy illumination (irradiance) E e characterizes the degree of illumination of the surface and is equal to the magnitude of the radiation flux from all directions incident on the unit of the illuminated surface ( Tue/m 2).
In photometry, the inverse square law (Kepler's law) is used: the illumination of a plane from a perpendicular direction from a point source with a force I e in the distance r from it is equal to:
E e = I e/ r 2 .
Deviation of the beam of optical radiation from the perpendicular to the surface by an angle α leads to a decrease in illumination (Lambert's law):
E e = I e cos α /r 2 .
Important role when measuring the energy characteristics of radiation, the temporal and spectral distribution of its power play. If the duration of optical radiation is less than the observation time, then the radiation is considered pulsed, and if it is longer, it is considered continuous. Sources can emit radiation various lengths waves. Therefore, in practice, the concept of radiation spectrum is used - the distribution of radiation power on a wavelength scale λ (or frequencies). Almost all sources radiate differently in different parts of the spectrum.
For an infinitely small interval of wavelengths dλ the value of any photometric quantity can be specified using its spectral density. For example, the spectral density energy luminosity
R eλ = dW/dλ,
where dW is the energy radiated from a unit surface area per unit time in the wavelength range from λ before λ + dλ.
Light quantities. In optical measurements, various radiation receivers are used, the spectral characteristics of the sensitivity of which to light of different wavelengths are different. The spectral sensitivity of the photodetector of optical radiation is the ratio of the value characterizing the level of the response of the receiver to the flux or energy of monochromatic radiation that causes this reaction. Distinguish between the absolute spectral sensitivity, expressed in named units (for example, BUT/Tue if the receiver response is measured in BUT), and the dimensionless relative spectral sensitivity is the ratio of the spectral sensitivity at a given radiation wavelength to maximum value spectral sensitivity or to spectral sensitivity at a certain wavelength.
The spectral sensitivity of a photodetector depends only on its properties; it is different for different receivers. Relative spectral sensitivity human eye V(λ ) is shown in Fig. 5.3.
The eye is most sensitive to radiation with a wavelength λ =555 nm. Function V(λ ) for this wavelength is taken equal to unity.
With the same energy flux, the visually estimated light intensity for other wavelengths is less. The relative spectral sensitivity of the human eye for these wavelengths turns out to be less than one. For example, the value of the function means that the light of a given wavelength must have an energy flux density 2 times greater than the light for which , so that the visual sensations are the same.
The system of light quantities is introduced taking into account the relative spectral sensitivity of the human eye. Therefore, light measurements, being subjective, differ from objective, energy ones, and for them light units used only for visible light. The basic unit of light in the SI system is luminous intensity - candela (cd), which is equal to the intensity of light in given direction source emitting monochromatic radiation with a frequency of 5.4 10 14 Hz, energy force whose light in this direction is 1/683 W/sr. All other light quantities are expressed in terms of the candela.
The definition of light units is similar to energy units. To measure light quantities, special techniques and devices are used - photometers.
Light flow . The unit of luminous flux is lumen (lm). It is equal to the luminous flux emitted by an isotropic light source with a power of 1 cd within a solid angle of one steradian (with uniform radiation field inside the solid angle):
1 lm = 1 cd·one Wed.
It has been experimentally established that the luminous flux of 1 lm, formed by radiation with a wavelength λ = 555nm corresponds to an energy flux of 0.00146 Tue. Luminous flux in 1 lm, formed by radiation with a different wavelength λ , corresponds to the energy flow
F e = 0.00146/ V(λ ), Tue,
those. one lm = 0,00146 Tue.
illumination E- value wound by the ratio of the luminous flux F incident on the surface, to the area S this surface:
E = F/S, luxury (OK).
1 OK– surface illumination, per 1 m 2 which the luminous flux falls in 1 lm (1OK = 1 lm/m 2). For measurements of illumination, devices are used that measure the flux of optical radiation from all directions - luxmeters.
Brightness R C (luminosity) of a luminous surface in some direction φ is a quantity equal to the ratio of the luminous intensity I in this direction to the square S projection of a luminous surface onto a plane perpendicular to this direction:
R C= I/(S cos φ ), (cd/m 2).
In general, the brightness of light sources is different for different directions. Sources whose brightness is the same in all directions are called Lambertian or cosine, since the luminous flux emitted by an element of the surface of such a source is proportional to cosφ. Strictly satisfies this condition only absolutely black body.
Any photometer with a limited viewing angle is essentially a luminance meter. Spectral and spatial distribution brightness and illumination allows you to calculate all the other photometric quantities by integrating.
1. What is physical meaning absolute indicator
refraction of the medium?
2. What is relative indicator refraction?
3. Under what condition is observed total reflection?
4. What is the principle of operation of light guides?
5. What is Fermat's principle?
6. What is the difference between energy and light quantities in photometry?
The definitions of the photometric quantities of the light series and the mathematical relationships between them are similar to the corresponding quantities and relationships of the energy series. So light flow, propagating within the solid angle equals . Luminous flux unit ( lumen). For monochromatic light relationship between energy and light quantities given by the formulas:
where is a constant called the mechanical equivalent of light.
The luminous flux falling on the interval of wavelengths from l before ,
, (30.8)
where j is the distribution function of energy over wavelengths (see Fig. 30.1). Then the total luminous flux carried by all spectrum waves,
illumination
The luminous flux can also come from bodies that do not themselves glow, but reflect or scatter the light falling on them. In such cases, it is important to know what light flux falls on a particular area of the body surface. For this it serves physical quantity, called illumination
. (30.10)
illumination numerically equals the ratio of the total luminous flux incident on the surface element to the area of \u200b\u200bthis element (see Fig. 30.4). For an even light output
Illumination unit 
(lux). Suite equals the illumination of a surface with an area of 1 m 2 when a luminous flux of 1 lm falls on it. Energy illumination is defined similarly
Unit of energy illumination.
Brightness
For many lighting calculations, some sources can be considered as point sources. However, in most cases, the light sources are placed close enough to distinguish their shape, in other words, the angular dimensions of the source lie within the ability of the eye or optical instrument to distinguish an extended object from a point. For such sources, a physical quantity called brightness is introduced. The concept of brightness is not applicable to sources whose angular dimensions are less than the resolution of the eye or an optical instrument (for example, to stars). Brightness characterizes the radiation of a luminous surface in a certain direction. The source can glow with its own or reflected light.
Let's single out a luminous flux propagating in a certain direction in a solid angle from a section of a luminous surface. The axis of the beam forms an angle with the normal to the surface (see Fig. 30.5).
Projection of a section of a luminous surface onto a site perpendicular to the selected direction,
(30.14)
called visible surface source site element (see Figure 30.6).
The value of the luminous flux depends on the area of the visible surface, on the angle and on the solid angle:
The proportionality factor is called brightness, It depends on optical properties emitting surface and may be different for various directions. From (30.5) brightness
Thus, brightness is determined by the luminous flux emitted in a certain direction by a unit of visible surface per unit solid angle. Or in other words: the brightness in a certain direction is numerically equal to the intensity of light created by a unit area of the visible surface of the source.
In general, the brightness depends on the direction, but there are light sources for which the brightness does not depend on the direction. Such sources are called Lambertian or cosine, because Lambert's law is valid for them: the light intensity in a certain direction is proportional to the cosine of the angle between the normal to the source surface and this direction:
where is the light intensity in the direction of the normal to the surface, is the angle between the normal to the surface and the preferred direction. To ensure the same brightness in all directions, technical lamps are equipped with milk glass shells. Lambertian sources that emit diffused light include a surface coated with magnesium oxide, unglazed porcelain, drawing paper, and freshly fallen snow.
Unit of brightness 
(nit). Here are the brightness values of some light sources:
Moon - 2.5 knt,
fluorescent lamp - 7 knt,
light bulb filament - 5 Mnt,
the surface of the Sun is 1.5 Gnt.
The lowest brightness perceived by the human eye is about 1 micronth, and the brightness exceeding 100 knt causes pain in the eye and can damage vision. The brightness of a sheet of white paper when reading and writing should be at least 10 nits.
Energy brightness is defined similarly
. (30.18)
Unit of measurement of radiance 
.
Luminosity
Let us consider a light source of finite dimensions (shining with its own or reflected light). luminosity source is called surface density luminous flux emitted by a surface in all directions within a solid angle. If a surface element emits a luminous flux, then
For uniform luminosity, we can write:
Luminosity unit.
Energy luminosity is defined similarly
Unit of energy luminosity.
Laws of illumination
Photometric measurements are based on two laws of illumination.
1. The illumination of a surface by a point light source varies in inverse proportion to the square of the distance of the source from the illuminated surface. Consider a point source (see Figure 30.7) that emits light in all directions. Let us describe around the source concentric spheres with the source with radii and . Obviously, the luminous flux through the surface areas and is the same, since it propagates in one solid angle. Then the illumination of the areas and will be, respectively, and . Expressing the elements spherical surfaces through the solid angle , we get:
. (30.22)
2. The illumination created on an elementary section of the surface by a light flux incident on it at a certain angle is proportional to the cosine of the angle between the direction of the rays and the normal to the surface. Let's consider a parallel beam of rays (see Fig. 29.8) falling on areas of surfaces and . Rays are incident on the surface along the normal, and on the surface at an angle to the normal. The same light flux passes through both sections. The illumination of the first and second sections will be, respectively, and 
. But, therefore,
Combining these two laws, we can formulate basic law of illumination: the illumination of a surface by a point source is directly proportional to the luminous intensity of the source, the cosine of the angle of incidence of the rays, and inversely proportional to the square of the distance from the source to the surface
. (30.24)
Calculations using this formula give a fairly accurate result if the linear dimensions of the source do not exceed 1/10 of the distance to the illuminated surface. If the source is a disk with a diameter of 50 cm, then at a point on the normal to the center of the disk relative error in calculations for a distance of 50 cm it reaches 25%, for a distance of 2 m it does not exceed 1.5%, and for a distance of 5 m it decreases to 0.25%.
If there are several sources, then the resulting illumination is equal to the sum of the illuminations created by each individual source. If the source cannot be considered as a point source, its surface is divided into elementary sections and, having determined the illumination created by each of them, according to the law 
, then integrate over the entire surface of the source.
There are lighting standards for workplaces and premises. On the tables classrooms illumination should be at least 150 lux, for reading books you need illumination, and for drawing - 200 lux. For corridors, illumination is considered sufficient, for streets -.
The most important source of light for all life on Earth - the Sun creates on upper bound atmosphere energy illumination, called the solar constant - and illumination of 137 klx. The energy illumination created on the Earth's surface by direct rays in summer is two times less. The illumination created by direct sunlight at noon at the middle latitude of the area is 100 klx. The change of seasons on Earth is explained by a change in the angle of incidence sun rays onto its surface. In the northern hemisphere, the largest angle of incidence of rays on the Earth's surface is in winter, and the smallest - in summer. Illumination on open space with a cloudy sky is 1000 lux. Illumination in a bright room near the window - 100 lux. For comparison, we present the illumination from full moon- 0.2 lux and from the night sky on a moonless night - 0.3 mlk. The distance from the Sun to the Earth is 150 million kilometers, but due to the fact that the force sunlight equals, the illumination created by the Sun on the surface of the Earth is so great.
For sources whose light intensity depends on direction, sometimes use average spherical luminous intensity, where is the total luminous flux of the lamp. Lumen ratio electric lamp to its electrical power is called light output lamps: . For example, a 100 W incandescent lamp has an average spherical luminous intensity of about 100 cd. The total luminous flux of such a lamp is 4 × 3.14 × 100 cd = 1260 lm, and the luminous efficiency is 12.6 lm / W. The luminous efficiency of fluorescent lamps is several times greater than that of incandescent lamps, and reaches 80 lm / W. In addition, the service life of fluorescent lamps exceeds 10 thousand hours, while for incandescent lamps it is less than 1000 hours.
Over millions of years of evolution, the human eye has adapted to sunlight, and therefore it is desirable that the spectral composition of the light of the lamp be as close as possible to the spectral composition of sunlight. This requirement in most respond to fluorescent lamps. That is why they are also called fluorescent lamps. The brightness of the filament of a light bulb causes pain in the eye. To prevent this, milky glass shades and lampshades are used.
With all their advantages, fluorescent lamps also have a number of disadvantages: the complexity of the switching circuit, the pulsation of the light flux (with a frequency of 100 Hz), the impossibility of starting in the cold (due to mercury condensation), the buzz of the throttle (due to magnetostriction), environmental hazard (mercury from a broken lamp poisons environment).
In order for the spectral composition of the radiation of an incandescent lamp to be the same as that of the Sun, it would be necessary to heat its filament to the temperature of the surface of the Sun, i.e., up to 6200 K. But tungsten, the most refractory of metals, melts already at 3660 K.
A temperature close to that of the solar surface is reached in an arc discharge in mercury vapor or in xenon at a pressure of about 15 atm. The light intensity of an arc lamp can be brought up to 10 Mcd. Such lamps are used in film projectors and spotlights. Lamps filled with sodium vapor are distinguished by the fact that in them a significant part of the radiation (about a third) is concentrated in the visible region of the spectrum (two intense yellow lines at 589.0 nm and 589.6 nm). Although the emission of sodium lamps is very different from the usual sunlight for the human eye, they are used to illuminate motorways, as their advantage is a high luminous efficiency, up to 140 lm / W.
Photometers
Instruments designed to measure luminous intensity or luminous fluxes different sources, are called photometers. According to the principle of registration, photometers are of two types: subjective (visual) and objective.
The principle of operation of a subjective photometer is based on the ability of the eye to fix the same illumination (more precisely, brightness) of two adjacent fields with a sufficiently high accuracy, provided that they are illuminated with light of the same color.
Photometers for comparing two sources are designed so that the role of the eye is reduced to establishing the same illumination of two adjacent fields illuminated by the compared sources (see Fig. 30.9). The observer's eye examines a white trihedral prism installed in the middle of a blackened tube inside. The prism is illuminated by and sources. By changing the distances and from the sources to the prism, it is possible to equalize the illumination of the surfaces and . Then , where and are the light intensities, respectively, of the sources and . If the luminous intensity of one of the sources is known (reference source), then the luminous intensity of the other source in the selected direction can be determined. By measuring the light intensity of the source in different directions, find the total luminous flux, illumination, etc. The reference source is an incandescent lamp, the luminous intensity of which is known.
The impossibility of changing the ratio of distances within a very wide range forces the use of other methods of attenuating the flow, such as light absorption by a filter of variable thickness - a wedge (see Fig. 30.10).
One of the varieties visual method photometry is a method of quenching based on the use of the constancy of the threshold sensitivity of the eye for each individual observer. The threshold sensitivity of the eye is the lowest brightness (about 1 micron) to which the human eye reacts. Having previously determined the sensitivity threshold of the eye, in some way (for example, with a calibrated absorbing wedge), the brightness of the source under study is reduced to the sensitivity threshold. Knowing how many times the brightness is weakened, it is possible to determine the absolute brightness of the source without a reference source. This method is extremely sensitive.
Direct measurement of the total luminous flux of the source is carried out in integral photometers, for example, in a spherical photometer (see Fig. 30.11). The source under study is suspended in the inner cavity of a sphere whitewashed inside with a matte surface. As a result of multiple reflections of light inside the sphere, illumination is created, determined by the average luminous intensity of the source. The illumination of the hole, protected from direct rays by the screen, is proportional to the luminous flux: , where is the constant of the device, depending on its size and color. The hole is covered with milky glass. The brightness of milk glass is also proportional to the light output. It is measured by the photometer described above or by another method. In technology, automated spherical photometers with photocells are used, for example, to control incandescent lamps on the conveyor of an electric lamp plant.
Objective Methods Photometry is divided into photographic and electrical. Photographic methods are based on the fact that the blackening of the photosensitive layer in a wide range is proportional to the density of light energy that fell on the layer during its illumination, i.e. exposure (see Table 30.1). This method determines the relative intensity of two closely spaced spectral lines in one spectrum or compare the intensities of the same line in two adjacent (taken on the same photographic plate) spectra by blackening certain sections of the photographic plate.
Visual and photographic methods are gradually being replaced by electrical ones. The advantage of the latter is that they simply perform automatic registration and processing of results, up to the use of a computer. Electric photometers make it possible to measure the intensity of radiation beyond the visible spectrum.
CHAPTER 31
31.1. Characteristics thermal radiation
Bodies heated to sufficiently high temperatures glow. The glow of bodies due to heating is called thermal (temperature) radiation. Thermal radiation, being the most common in nature, occurs due to energy thermal motion atoms and molecules of a substance (i.e., due to its internal energy) and is characteristic of all bodies at temperatures above 0 K. Thermal radiation is characterized by a continuous spectrum, the position of the maximum of which depends on temperature. At high temperatures, short (visible and ultraviolet) electromagnetic waves, at low - predominantly long (infrared).
Quantitative characteristic thermal radiation serves spectral density of energy luminosity (radiance) of a body- radiation power per unit area of the body surface in the frequency range of unit width:
Rv,T =, (31.1)
where is energy electromagnetic radiation emitted per unit time (radiation power) per unit surface area of the body in the frequency range v before v+dv.
Unit of spectral density of energy luminosity Rv,T- joule per square meter (J / m 2).
The written formula can be represented as a function of the wavelength:
=Rv,Tdv= R λ ,T dλ. (31.2)
As c = λvυ, then dλ/ dv = - c/v 2 = - λ 2 /with,
where the minus sign indicates that as one of the values increases ( λ or v) the other value decreases. Therefore, in what follows, the minus sign will be omitted.
Thus,
R υ,T =Rλ,T . (31.3)
Using formula (31.3), one can go from Rv,T to Rλ,T and vice versa.
Knowing the spectral density of energy luminosity, we can calculate integral energy luminosity(integral emissivity), summing over all frequencies:
R T = . (31.4)
The ability of bodies to absorb radiation incident on them is characterized by absorbance
And v,T =(31.5)
showing what fraction of the energy brought per unit time per unit area of the body surface by electromagnetic waves incident on it with frequencies from v before v+dv is absorbed by the body.
Spectral absorbance is a dimensionless quantity. Quantities Rv,T and A v,T depend on the nature of the body, its thermodynamic temperature, and at the same time differ for radiations with different frequencies. Therefore, these values are classified as T and v(or rather, to a fairly narrow frequency range from v before v+dv).
A body capable of absorbing completely at any temperature all radiation of any frequency incident on it is called black. Therefore, the spectral absorbance of a black body for all frequencies and temperatures is identically equal to unity ( A h v, T = one). There are no absolutely black bodies in nature, however, such bodies as soot, platinum black, black velvet and some others are close to them in a certain frequency range in their properties.
ideal model the black body is a closed cavity with a small opening, inner surface which is blackened (Fig.31.1). A beam of light that got inside Fig.31.1.
of such a cavity experiences multiple reflections from the walls, as a result of which the intensity of the emitted radiation turns out to be practically zero. Experience shows that when the hole size is less than 0.1 of the cavity diameter, the incident radiation of all frequencies is completely absorbed. Thereby open windows houses from the side of the street appear black, although inside the rooms it is quite light due to the reflection of light from the walls.
Along with the concept of a black body, the concept is used gray body- a body whose absorption capacity is less than unity, but is the same for all frequencies and depends only on temperature, material and the state of the surface of the body. Thus, for the gray body A with v,T< 1.
Kirchhoff's law
Kirchhoff's law: the ratio of the spectral density of energy luminosity to the spectral absorbance does not depend on the nature of the body; it is a universal function of frequency (wavelength) and temperature for all bodies:
= rv,T(31.6)
For black body A h v, T=1, so it follows from Kirchhoff's law that Rv,T for a black body is rv,T. Thus, the universal Kirchhoff function rv,T is nothing but the spectral density of the energy luminosity of a black body. Therefore, according to Kirchhoff's law, for all bodies the ratio of the spectral density of the energy luminosity to the spectral absorptivity is equal to the spectral density of the energy luminosity of a black body at the same temperature and frequency.
It follows from Kirchhoff's law that the spectral density of the energy luminosity of any body in any region of the spectrum is always less than the spectral density of the energy luminosity of a black body (for the same values T and v), as A v,T < 1, и поэтому Rv,T < r v υ,T. In addition, from (31.6) it follows that if the body at a given temperature T does not absorb electromagnetic waves in the frequency range from v, before v+dv, then it is them in this frequency range at a temperature T and does not radiate, since A v,T=0, Rv,T=0
Using the Kirchhoff law, the expression for the integral energy luminosity of a black body (31.4) can be written as
R T = .(31.7)
For the gray body R with T = A T = A T R e, (31.8)
where R e= -energy luminosity of the black body.
Kirchhoff's law describes only thermal radiation, being so characteristic of it that it can serve as a reliable criterion for determining the nature of radiation. Radiation that does not obey Kirchhoff's law is not thermal.
For practical purposes, it follows from Kirchhoff's law that bodies with a dark and rough surface have an absorption coefficient close to 1. For this reason, dark clothes are preferred in winter, and light in summer. But bodies with an absorption coefficient close to unity also have a correspondingly higher energy luminosity. If you take two identical vessels, one with a dark, rough surface, and the walls of the other are light and shiny, and pour the same amount of boiling water into them, then the first vessel will cool faster.
31.3. Stefan-Boltzmann laws and Wien displacements
It follows from Kirchhoff's law that the spectral density of the energy luminosity of a black body is a universal function, so finding its explicit dependence on frequency and temperature is important task theories of thermal radiation.
Stefan, analyzing experimental data, and Boltzmann, applying thermodynamic method, solved this problem only partially by establishing the dependence of the energy luminosity R e from temperature. According to Stefan-Boltzmann law,
R e \u003d σ T 4, (31.9)
i.e., the energy luminosity of a black body is proportional to the quarters of the power of its thermodynamic temperature; σ
- Stefan-Boltzmann constant: its experimental value is 5.67×10 -8 W/(m 2 ×K 4).
Stefan - Boltzmann's law, defining dependence R e on temperature, does not give an answer regarding spectral composition blackbody radiation. From the experimental curves of the dependence of the function rλ,T from the wavelength λ (r λ,T =´ ´ r ν,T) at various temperatures(Fig.30.2) Fig.31.2.
it follows that the distribution of energy in the spectrum of a black body is uneven. All curves have a pronounced maximum, which shifts towards shorter wavelengths as the temperature rises. Area bounded by the dependency curve rλ,T from λ and the abscissa axis, is proportional to the energy luminosity R e black body and, therefore, according to the Stefan-Boltzmann law, the quarters of the degree of temperature.
V. Vin, relying on the laws of thermo- and electrodynamics, established the dependence of the wavelength λ max corresponding to the maximum of the function rλ,T, on temperature T. According to Wien's displacement law,
λ max \u003d b / T, (31.10)
i.e. wavelength λ
max corresponding to the maximum value of the spectral
energy luminosity density rλ,T blackbody is inversely proportional to its thermodynamic temperature. b - constant fault its experimental value is 2.9×10 -3 m×K.
Expression (31.10) is called Wien's displacement law, it shows the displacement of the maximum position of the function rλ,T as the temperature increases to the region of short wavelengths. Wien's law explains why, as the temperature of heated bodies decreases, their spectrum is increasingly dominated by long-wave radiation (for example, the transition white heat turns red when the metal cools).
Rayleigh-Jeans and Planck formulas
From the consideration of the Stefan-Boltzmann and Wien laws, it follows that the thermodynamic approach to solving the problem of finding universal function Kirchhoff did not give the desired results.
A rigorous attempt at theoretical dependency inference rλ,T belongs to Rayleigh and Jeans, who applied the methods of statistical physics to thermal radiation, using classical law uniform distribution energy in degrees of freedom.
The Rayleigh-Jeans formula for the spectral density of the energy luminosity of a black body has the form:
r ν , T = <E> = kT, (31.11)
where <Е>= kT– average energy oscillator with natural frequency ν .
As experience has shown, expression (31.11) is consistent with experimental data only in the region of sufficiently low frequencies and high temperatures. In the region of high frequencies, this formula disagrees with the experiment, as well as with the Wien displacement law. And getting the Stefan-Boltzmann law from this formula leads to absurdity. This result is called " ultraviolet catastrophe". Those. within classical physics failed to explain the laws of energy distribution in the spectrum of a black body.
In the region of high frequencies, good agreement with experiment is given by Wien's formula (Wien's radiation law):
r ν, T \u003d Сν 3 A e -Аν / T, (31.12)
where rv, T- spectral density of the energy luminosity of the black body, With and BUT – constants. In modern notation using
Planck's constant Wien's radiation law can be written as
r ν, T = . (31.13)
The correct expression consistent with experimental data for the spectral density of the energy luminosity of a black body was found by Planck. According to the quantum hypothesis, atomic oscillators radiate energy not continuously, but in certain portions - quanta, and the quantum energy is proportional to the oscillation frequency
E 0 =hν = hс/λ,
where h\u003d 6.625 × 10 -34 J × s - Planck's constant. Since the radiation is emitted in portions, the oscillator energy E can only take on certain discrete values , multiples of an integer number of elementary portions of energy E 0
E = nhv(n= 0,1,2…).
AT this case average energy<E> oscillator cannot be taken equal to kT.
In the approximation that the distribution of oscillators over possible discrete states obeys the Boltzmann distribution, the average energy of the oscillator is
<E> = , (31.14)
and the spectral density of energy luminosity is determined by the formula
r ν , T = . (31.15)
Planck derived the formula for the universal Kirchhoff function
rv, T = , (31.16)
which agrees with the experimental data on the distribution of energy in the radiation spectra of a blackbody over the entire range of frequencies and temperatures.
From Planck's formula, knowing the universal constants h,k and with, we can calculate the Stefan-Boltzmann constants σ and wine b. And vice versa. Planck's formula is in good agreement with experimental data, but it also contains particular laws of thermal radiation, i.e. is an complete solution problems of thermal radiation.
Optical pyrometry
The laws of thermal radiation are used to measure the temperature of incandescent and self-luminous bodies (for example, stars). Methods for measuring high temperatures that use the dependence of the spectral density of energy luminosity or the integral energy luminosity of bodies on temperature are called optical pyrometry. Devices for measuring the temperature of heated bodies by the intensity of their thermal radiation in the optical range of the spectrum are called pyrometers. Depending on which law of thermal radiation is used when measuring the temperature of bodies, radiation, color and brightness temperatures are distinguished.
1. Radiation temperature is the temperature of a black body at which its energy luminosity R e equal to energy luminosity R t body under study. In this case, the energy luminosity of the body under study is recorded and, according to the Stefan-Boltzmann law, its radiation temperature is calculated:
T p =.
Radiation temperature T p body is always less than its true temperature T.
2.Colorful temperature. For gray bodies (or bodies close to them in properties), the spectral density of energy luminosity
R λ,Τ = A Τ r λ,Τ,
where A t = const < 1. Consequently, the distribution of energy in the emission spectrum of a gray body is the same as in the spectrum of a black body having the same temperature, therefore Wien's displacement law applies to gray bodies. Knowing the wavelength λ m ah, corresponding to the maximum spectral density of energy luminosity Rλ,Τ of the body under study, its temperature can be determined
T c = b/ λ m ah,
which is called color temperature. For gray bodies, the color temperature coincides with the true one. For bodies that are very different from gray (for example, those with selective absorption), the concept of color temperature loses its meaning. In this way, the temperature on the surface of the Sun is determined ( T c=6500 K) and stars.
3.Brightness temperature T i, is the temperature of a black body at which, for a certain wavelength, its spectral density of energy luminosity is equal to the spectral density of the energy luminosity of the body under study, i.e.
rλ,Τ = Rλ,Τ,
where T –true temperature body, which is always higher than the brightness.
A disappearing filament pyrometer is usually used as a brightness pyrometer. In this case, the image of the pyrometer thread becomes indistinguishable against the background of the surface of the hot body, i.e., the thread seems to “disappear”. Using a blackbody calibrated milliammeter, the brightness temperature can be determined.
Heat sources Sveta
The glow of hot bodies is used to create light sources. Black bodies should be the best thermal light sources, since their spectral energy luminosity density for any wavelength is greater than the spectral energy luminosity density of non-black bodies taken at the same temperatures. However, it turns out that for some bodies (for example, tungsten), which have selectivity of thermal radiation, the fraction of energy attributable to radiation in the visible region of the spectrum is much larger than for a black body heated to the same temperature. Therefore, tungsten, having also a high melting point, is the best material for making lamp filaments.
The temperature of the tungsten filament in vacuum lamps should not exceed 2450K, since at higher temperatures its strong sputtering occurs. The maximum radiation at this temperature corresponds to a wavelength of 1.1 μm, i.e., it is very far from the maximum sensitivity of the human eye (0.55 μm). Filling lamp bulbs with inert gases (for example, a mixture of krypton and xenon with the addition of nitrogen) at a pressure of 50 kPa makes it possible to increase the filament temperature to 3000 K, which leads to an improvement in the spectral composition of the radiation. However, the light output does not increase in this case, since additional energy losses occur due to heat exchange between the filament and the gas due to thermal conductivity and convection. To reduce energy losses due to heat transfer and increase the light output of gas-filled lamps, the filament is made in the form of a spiral, the individual turns of which heat each other. At high temperature a fixed layer of gas is formed around this spiral and heat exchange due to convection is excluded. Energy efficiency incandescent lamps currently does not exceed 5%.
