Gray reflectance. Optics
When passing through interfaces between media, acoustic waves experience not only reflection and refraction, but also the transformation of waves of one type into another. Let us consider the simplest case of normal incidence of a wave on the boundary of two extended media (Fig. 3.1). There is no wave transformation in this case.
Let us consider the energy relationships between the incident, reflected and transmitted waves. They are characterized by reflection and refraction coefficients.
Amplitude reflection coefficient The ratio of the amplitudes of the reflected and incident waves is called:
Amplitude transmission coefficient The ratio of the amplitude of the transmitted and incident waves is called:
These coefficients can be determined by knowing the acoustic characteristics of the media. When a wave falls from medium 1 to medium 2, the reflection coefficient is determined as
, (3.3)
where , are the acoustic impedances of media 1 and 2, respectively.
When a wave falls from medium 1 to medium 2, the transmission coefficient is denoted and defined as
. (3.4)
When a wave falls from medium 2 to medium 1, the transmission coefficient is denoted and defined as
. (3.5)
From formula (3.3) for the reflection coefficient it is clear that the more the acoustic impedances of the media differ, the greater the energy sound wave will be reflected from the interface between two media. This determines both the possibility and effectiveness of detecting violations of the continuity of the material (inclusions of a medium with an acoustic resistance that differs from the resistance of the controlled material).
It is precisely because of the differences in the reflection coefficients that slag inclusions are detected much worse than defects of the same size, but with air filling. The reflection from a discontinuity filled with gas approaches 100%, and for a discontinuity filled with slag, this coefficient is much lower.
When a wave is normally incident on the boundary of two extended media, the relationship between the amplitudes of the incident, reflected and transmitted waves is
. (3.6)
The energy of the incident wave in the case of normal incidence on the boundary of two extended media is distributed between the reflected and transmitted waves according to the conservation law.
In addition to the amplitude reflection and transmission coefficients, the intensity reflection and transmission coefficients are also used.
Intensity reflectance is the ratio of the intensities of the reflected and incident waves. At normal wave incidence
, (3.7)
where is the reflection coefficient when falling from medium 1 to medium 2;
– reflection coefficient when falling from medium 2 to medium 1.
Passage coefficient by intensity– the ratio of the intensities of the transmitted and incident waves. When a wave is incident normally
, (3.8)
where is the transmission coefficient when falling from environment 1 to environment 2;
– transmission coefficient when falling from environment 2 to environment 1.
The direction of wave incidence does not affect the values of reflection and transmission coefficients in intensity. The law of conservation of energy in terms of reflection and transmission coefficients is written as follows
With an oblique incidence of a wave on the interface between media, transformation of a wave of one type into another is possible. The processes of reflection and transmission in this case are characterized by several reflection and transmission coefficients depending on the type of incident, reflected and transmitted waves. The reflection coefficient in this form has the designation ( – index indicating the type of incident wave, – index indicating the type of reflected wave). There may be cases. The transmission coefficient is designated ( – index indicating the type of incident wave, – index indicating the type of transmitted wave). There may be cases of , and .
Low-emissivity coating: A coating, when applied to glass, the thermal characteristics of the glass are significantly improved (the heat transfer resistance of glazing using glass with a low-emissivity coating increases, and the heat transfer coefficient decreases).
Sun protection coating
Solar control coating: A coating that, when applied to glass, improves the protection of a room from the penetration of excess solar radiation.
Emission factor
Emissivity (corrected emissivity): The ratio of the emissive power of a glass surface to the emissive power of a black body.
Normal emission factor
Normal emissivity (normal emissivity): The ability of glass to reflect normally incident radiation; is calculated as the difference between unity and the reflectance in the direction normal to the glass surface.
Solar factor
Solar factor (total solar energy transmittance coefficient): The ratio of the total solar energy entering the room through a translucent structure to the energy of incident solar radiation. The total solar energy entering the room through a translucent structure is the sum of the energy directly passing through the translucent structure and that part of the energy absorbed by the translucent structure that is transferred into the room.
Directional light transmittance
The coefficient of directional light transmission (equivalent terms: light transmittance, light transmission coefficient), is denoted as τv (LT) - the ratio of the value of the light flux normally passing through the sample to the value of the light flux normally incident on the sample (in the wavelength range of visible light) .
Light reflectance
Light reflection coefficient (equivalent term: coefficient of normal light reflection, light reflectance coefficient) is denoted as ρv (LR) - the ratio of the value of the luminous flux normally reflected from the sample to the value of the luminous flux normally incident on the sample (in the wavelength range of visible light).
Light absorption coefficient
The light absorption coefficient (equivalent term: light absorption coefficient) is denoted as av (LA) - the ratio of the value of the light flux absorbed by the sample to the value of the light flux normally incident on the sample (in the wavelength range of the visible spectrum).
Solar transmittance
The solar energy transmittance coefficient (equivalent term: direct solar energy transmittance coefficient) is denoted as τе (DET) - the ratio of the value of the solar radiation flux normally passing through the sample to the value of the solar radiation flux normally incident on the sample.
Solar reflectance
The solar energy reflectance coefficient is denoted as ρе (ER) - the ratio of the solar radiation flux normally reflected from the sample to the solar radiation flux normally incident on the sample.
Solar absorption coefficient
The solar energy absorption coefficient (equivalent term: energy absorption coefficient) is denoted as ae (EA) - the ratio of the value of the solar radiation flux absorbed by the sample to the value of the solar radiation flux normally incident on the sample.
Shading coefficient
The shading coefficient is designated as SC or G - the shading coefficient is defined as the ratio of the flux of solar radiation passing through a given glass in the wave range from 300 to 2500 nm (2.5 microns) to the flux of solar energy passing through glass 3 mm thick. The shading coefficient shows the proportion of the passage of not only the direct flow of solar energy (near infrared radiation), but also the radiation due to energy absorbed in the glass (far infrared radiation).
Heat transfer coefficient
Heat transfer coefficient - denoted as U, characterizes the amount of heat in watts (W) that passes through 1 m2 of structure with a temperature difference on both sides of one degree on the Kelvin scale (K), unit of measurement W/(m2 K).
Heat transfer resistance
Heat transfer resistance is designated as R - the reciprocal of the heat transfer coefficient.
Voltage and current reflection coefficients. Traveling, standing and mixed waves
To estimate the relationship between the incident and reflected waves of voltages and currents, we introduce the concepts voltage reflection coefficients N_u =U_() /Ts_p And current =/() //„, where the indices “p” and “o” denote the incident and reflected waves. Omitting the details, let's rewrite these coefficients in terms of resistance...(ELECTRIC CIRCUIT THEORY)
Line reflection coefficient. Determination of integration constants.
The distribution of currents and voltages in a long line is determined not only by the wave parameters, which characterize the line’s own properties and do not depend on the properties of the circuit sections external to the line, but also by the line reflection coefficient, which depends on the degree of matching of the line with the load....(ELECTRIC CIRCUIT THEORY)
Values of the coefficient of utilization of the luminous flux of lamps with incandescent lamps at different values of reflection coefficients p of room surfaces
Reflection coefficient Lamp type U, UPM, PU Ge, GPM Gs, GsU 1 * V4A-200 without reflector Rpt 0.3; 0.5; 0.7 0.3; 0.5; 0.7 0.3; 0.5; 0.7 0.3; 0.5; 0.7 0.3; 0.5; 0.7 Рst 0.1; 0.3; 0.5; 0.1,; 0.3; 0.5 0.1; 0.3; 0.5 0.1; 0.3; 0.5 0.1; 0.3; 0.5 Рп 0.1; 0.1; 0.3 0.1; 0.1; 0.3 0.1; 0.1; 0.3 o o o i" o o...(LIFE SAFETY: DESIGN AND CALCULATION OF SAFETY ENSURING MEANS)
Light when colliding with reflective surface.
It lies in the fact that falling, And reflected beam placed in a single plane with a perpendicular to the surface, and this perpendicular divides the angle between the indicated rays into equal components.
More often it is simplistically formulated as follows: corner falls and angle light reflections the same:
α = β.
The law of reflection is based on features wave optics. It was experimentally substantiated by Euclid in the 3rd century BC. It can be considered a consequence of using Fermat's principle for mirror surface. Also, these laws can be formulated as a consequence of Huygens’ principle, according to which every point in the medium to which a disturbance has reached acts as a source secondary waves.
Any environment specifically reflects and absorbs light radiation. The parameter describing the reflectivity of the surface of a substance is denoted as reflection coefficient(ρ orR) . Quantitatively, the reflection coefficient is equal to the ratio radiation flux, reflected by the body, to the flow hitting the body:
The light is completely reflected from a thin film of silver or liquid mercury deposited on a sheet of glass.
Highlight diffuse And mirror image.
Transmittance
reflection coefficient
And absorption coefficient
The coefficients t, r and a depend on the properties of the body itself and the wavelength of the incident radiation. Spectral dependence, i.e. the dependence of the coefficients on the wavelength determines the color of both transparent and opaque (t = 0) bodies.
According to the law of conservation of energy
F neg + F absorb + F pr = . (8)
Dividing both sides of the equality by , we get:
r + a +t = 1. (9)
A body for which r=0, t=0, a=1 is called absolutely black .
A completely black body at any temperature completely absorbs all the energy of radiation of any wavelength incident on it. All real bodies are not completely black. However, some of them in certain wavelength intervals are close in their properties to an absolutely black body. For example, in the wavelength region of visible light, the absorption coefficients of soot, platinum black and black velvet differ little from unity. The most perfect model of an absolutely black body can be a small hole in a closed cavity. Obviously, this model is closer in characteristics to a black body, the greater the ratio of the surface area of the cavity to the area of the hole (Fig. 1).
The spectral characteristic of absorption of electromagnetic waves by a body is spectral absorption coefficient a l is a quantity determined by the ratio of the radiation flux absorbed by the body in a small spectral range (from l to l + d l) to the flux of radiation incident on it in the same spectral range:
.
(10)
The emissive and absorptive abilities of an opaque body are interrelated. The ratio of the spectral density of the energy luminosity of the equilibrium radiation of a body to its spectral absorption coefficient does not depend on the nature of the body; for all bodies it is a universal function of wavelength and temperature ( Kirchhoff's law ):
. (11)
For an absolutely black body a l = 1. Therefore, from Kirchhoff’s law it follows that M e, l = , i.e. The universal Kirchhoff function represents the spectral density of the energy luminosity of an absolutely black body.
Thus, according to Kirchhoff’s law, for all bodies the ratio of the spectral density of energy luminosity to the spectral absorption coefficient is equal to the spectral density of energy luminosity of an absolutely black body at the same values T and l.
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 an absolutely black body (at the same values of wavelength and temperature). In addition, it follows from this law that if a body at a certain temperature does not absorb electromagnetic waves in the range from l to l + d l, then it does not emit them in this length range at a given temperature.
Analytical form of the function for an absolutely black body
was established by Planck on the basis of quantum concepts about the nature of radiation:
(12)
The emission spectrum of a completely black body has a characteristic maximum (Fig. 2), which shifts to the shorter wavelength region with increasing temperature (Fig. 3). The position of the maximum spectral density of energy luminosity can be determined from expression (12) in the usual way, by equating the first derivative to zero:
. (13)
Denoting , we get:
X – 5 ( – 1) = 0. (14)
Rice. 2 Fig. 3
Solving this transcendental equation numerically gives
X = 4, 965.
Hence,
, (15)
= = b 1 = 2.898 m K, (16)
Thus, the function reaches a maximum at a wavelength inversely proportional to the thermodynamic temperature of a black body ( Wien's first law ).
From Wien's law it follows that at low temperatures predominantly long (infrared) electromagnetic waves are emitted. As the temperature increases, the proportion of radiation in the visible region of the spectrum increases, and the body begins to glow. With a further increase in temperature, the brightness of its glow increases and the color changes. Therefore, the color of the radiation can serve as a characteristic of the temperature of the radiation. The approximate dependence of the color of a body’s glow on its temperature is given in Table. 1.
Table 1
Wien's first law is also called displacement law , thereby emphasizing that with increasing temperature the maximum spectral density of energetic luminosity shifts towards shorter wavelengths.
Substituting formula (17) into expression (12), it is easy to show that the maximum value of the function is proportional to the fifth power of the thermodynamic body temperature ( Wien's second law ):
The energetic luminosity of an absolutely black body can be found from expression (12) by simple integration over the wavelength
(18)
where is the reduced Planck constant,
The energetic luminosity of an absolutely black body is proportional to the fourth power of its thermodynamic temperature. This provision is called Stefan–Boltzmann law , and proportionality coefficient s = 5.67×10 -8 – Stefan–Boltzmann constant.
A completely black body is an idealization of real bodies. Real bodies emit radiation whose spectrum is not described by Planck's formula. Their energetic luminosity, in addition to temperature, depends on the nature of the body and the state of its surface. These factors can be taken into account if a coefficient is introduced into formula (19), showing how many times the energy luminosity of an absolutely black body at a given temperature is greater than the energy luminosity of a real body at the same temperature
from where , or (21)
For all real bodies<1 и зависит как от природы тела и состояния его поверхности, так и от температуры. В частности, для вольфрамовых нитей электроламп накаливания зависимость от T has the form shown in Fig. 4.
The measurement of radiation energy and temperature of an electric furnace is based on Seebeck effect, which consists in the occurrence of an electromotive force in an electrical circuit consisting of several dissimilar conductors, the contacts of which have different temperatures.
Two dissimilar conductors form thermocouple , and series-connected thermocouples are a thermocouple. If the contacts (usually junctions) of the conductors are at different temperatures, then in a closed circuit including thermocouples, a thermoEMF arises, the magnitude of which is uniquely determined by the temperature difference between the hot and cold contacts, the number of thermocouples connected in series and the nature of the conductor materials.
The magnitude of thermoEMF arising in the circuit due to the energy of radiation incident on the junctions of the thermal column is measured by a millivoltmeter located on the front panel of the measuring device. The scale of this device is graduated in millivolts.
The temperature of a blackbody (furnace) is measured using a thermoelectric thermometer consisting of a single thermocouple. Its EMF is measured by a millivoltmeter, also located on the front panel of the measuring device and calibrated in °C.
Note. The millivoltmeter records the temperature difference between the hot and cold junctions of the thermocouple, so to obtain the furnace temperature, you need to add the room temperature to the reading of the device.
In this work, the thermoEMF of a thermocouple is measured, the value of which is proportional to the energy spent on heating one of the contacts of each thermocouple of the column, and, consequently, the energy luminosity (at equal time intervals between measurements and a constant emitter area):
Where b– proportionality coefficient.
Equating the right-hand sides of equalities (19) and (22), we obtain:
s× T 4 =b×e,
Where With– constant value.
Simultaneously with measuring the thermoEMF of the thermocolumn, the temperature difference Δ is measured t hot and cold junctions of a thermocouple placed in an electric furnace and determine the temperature of the furnace.
Using experimentally obtained values of the temperature of a completely black body (furnace) and the corresponding thermoEMF values of the thermocolumn, determine the value of the coefficient proportional to
sti With, which should be the same in all experiments. Then plot the dependence c= f(T), which should look like a straight line parallel to the temperature axis.
Thus, in laboratory work the nature of the dependence of the energetic luminosity of an absolutely black body on its temperature is established, i.e. The Stefan–Boltzmann law is verified.
