As we already know, a wave is characterized by energy transfer. Therefore, electromagnetic waves also carry energy with them. Let's consider some surface with area S. Let's assume that electromagnetic waves transfer energy through it.

The following figure shows such a surface.

Electromagnetic radiation flux density

The lines indicate the directions of propagation of electromagnetic waves. Lines perpendicular to the surface, at all points of which vibrations occur in the same phases, are called rays. And these surfaces are called wave surfaces.

The flux density of electromagnetic radiation is the ratio of electromagnetic energy ∆W passing through a surface of area S perpendicular to the rays, during time ∆t, to the product of S by ∆t.

I = ∆W/(S*∆t)

The SI unit of magnetic flux density is watts per square meter (W/m^2). Let us express the flux density through the speed of its propagation and the density of electromagnetic energy.

Let us take a surface S perpendicular to the rays. Let's build a cylinder on it with base c*∆t.

Here c is the speed of propagation of the electromagnetic wave. The volume of the cylinder is calculated by the formula:

∆V = S*c*∆t.

Electric energy magnetic field concentrated inside the cylinder will be calculated by the following formula:

Here ω is the electromagnetic energy density. This energy will pass through the right base of the cylinder in time ∆t. We get the following formula:

I = (ω*c*S*∆t)/(S*∆t) = ω*c.

The energy will decrease as you move away from the source. The following pattern will be true, the dependence of the current density on the distance to the source. The flux density of radiation directed from a point source will decrease in inverse proportion to the square of the distance to the source.

I = ∆W/(S*∆t) = (∆W/(4*pi∆t))*(1/R^2).

Electromagnetic waves are emitted by the accelerated movement of charged particles. In this case, the electric field strength and the magnetic induction vector of the electromagnetic wave will be directly proportional to the acceleration of the particles.

If we consider harmonic vibrations, then the acceleration will be directly proportional to the square of the cyclic frequency. The total energy density of the electromagnetic field will be equal to the sum of the energy density of the electric field and the energy of the magnetic field.

According to the formula I = ω*c, the flux density is proportional to the total energy density of the electromagnetic field.

Considering all of the above, we have.

The description of the radiation field is based on the idea of ​​intensity as energy flowing perpendicular to a flat surface of a unit area per unit time in a given direction in a selected frequency range. Full Definition intensity requires a preliminary introduction of some concepts.

1.1Control site

Let's call a flat surface a control platform S small in size through which radiation passes. Let us denote by D S is its area, and n is a unit vector perpendicular to it. By the direction of the site, as usual, we mean the direction of the vector n. The control site may have a physical boundary, like a section of the planet's surface. But it can be imagined mentally, for example, inside the atmosphere of a star. The platform can be filled with a substance that absorbs radiation incident on it and re-radiates it in another direction. But it can also be imagined as completely transparent, even devoid of substance. The only important thing is that radiation passes through the site. The direction of radiation is characterized by two quantities: vector k and solid angle DW Around him.

1.2 Solid angle

Let us describe a sphere of radius R around the point ABOUT, in which the observer is located . On the surface of the sphere, select an area S area S. Attitude

called the solid angle at which the surface is visible S from point ABOUT. Range DW is a necessary element in determining intensity. The point is that the amount of energy flowing in any precisely fixed direction ( DW=0) is equal to zero.

However, there is one exception - point sources. In astronomy, the concept of a point source is very important: all stars except the Sun, as well as some other sources of radiation, belong to them. We consider point sources to be all objects whose angular dimensions are less than the resolution of the equipment used. Therefore, for small telescopes, an extended object may look like a point object. Let's return to the definition of intensity. Magnitude DW should be so small that the radiation does not change noticeably within the selected solid angle. If this condition is met, then the energy D E passing through the control area in a given direction is proportional to . Sometimes they simply talk about radiation in a certain direction, implicitly implying a certain solid angle.

1.3 Intensity

The definition of intensity contains several points, each of which is useful to be presented separately. First, let's rotate the platform along the vector k, then we will consider an arbitrary direction and, finally, we will discuss the agreement on the sign of the energy passing through the site.

Intensity in the direction of the reference area

The radiation in Fig. 3 passes in the direction of the vector n. Size DS let us set it so small that the radiation can be considered uniform along the area. We will conduct observation for such a short period of time that none of its characteristics have time to change. Under such conditions, the amount of energy flowing through the site is proportional to the product DS× DW× Dt. therefore the attitude

does not depend on the size of the control area, the duration of the measurement and the selected opening angle. In other words, it characterizes precisely the radiation field in the direction of the vector n.

Intensity in any direction

Let us denote by q angle between vectors k And n. Due to the arbitrariness of their relative position, it can take any value between zero and p. The reasoning in the previous section corresponds to the case q=0. We exclude the situation when vectors k And n perpendicular ( q=p/2), since the question of energy flow along the edge of the platform is meaningless. Thus we arrive at the range

The amount of energy flowing through the area at a fixed field is proportional to the area of ​​its projection onto the plane of the wave front:

In Fig. 4, the generatrix of the horizontal cylinder is directed along the vector k. Strictly speaking, we had to draw not a cylinder, but a truncated cone with a certain solid angle DW, but for the illustration of formula (3.2) this does not matter. Control platforms are sections of the cylinder with inclined planes. We see all the sites from the edge. The arrows indicate the direction of the vector n each site. The same energy flows inside the cylinder, regardless of the direction of the pads. Magnitude DE proportional to the vertical section of the cylinder. Therefore the ratio

no longer depends on the direction of the control area and can be taken as a characteristic of the radiation field in a given direction.

Intensity is the limit of relation (3.3), when Dt,DS And DW tend to zero:

Below, in the tenth section of this chapter, we will clarify the last definition by including the dependence of intensity on frequency or on the wavelength of radiation.

The intensity can depend on time, on the position of a point in space and on direction. If the radiation field does not change over time, then it is called stationary. In this case, the intensity does not depend on time. Similarly, the intensity does not depend on spatial coordinates in the case of a uniform radiation field and does not depend on the direction if the radiation field is isotropic.

Energy Sign Agreement

Intensity is always considered a positive value, that is D Ecos q  >  0. At the same time cos q can take both positive and negative values. This forces us to attribute a certain sign to the energy passing through the site:

.

If θ is an acute angle, then we speak of radiation “emanating” from the site (ΔE > 0). Otherwise, it is considered that the radiation “enters” it. We will stick to this terminology in what follows. However, you need to remember that it is conditional, since it is determined by the choice of the sign of the direction of the vector n. By changing the direction of n to the opposite, we turn the “incoming” radiation into “outgoing” and vice versa.

1.4 Flow

Flux is a measure of the total energy flowing through a test area. Let's divide the total solid angle 4π into N small sections:

taking into account agreement (3.5) on the sign of Δ Ei. In the limit (4.1) turns into the integral

in all directions, taking into account the sign dE. During summation over angles, we assumed the quantities DS And Dt so small that the energy DE is proportional to the product DS× Dt.

Flow F called the limit of the ratio

with the denominator tending to zero:

Comparing the definitions of intensity (3.4) and flow (4.2), we arrive at the important formula

expressing flow through intensity.

Note the difference between intensity and flow. Although we introduced the concept of intensity with the help of a control platform, nevertheless, intensity is a characteristic only of the radiation field and does not depend in any way on the measuring device. We are talking about the intensity of radiation in an arbitrarily chosen direction, without specifying exactly how the measuring device is located. On the contrary, it makes no sense to talk about “flux in a certain direction”, since when calculating it, summation is performed over all angles. True, the magnitude of the flow depends on the direction of the control platform. But we will always assume that the reference area S is directed along the line of sight towards the light source.

1.5 Radiation field of a source of small angular dimensions

In astronomical applications, it is often necessary to know the intensity and flux of radiation produced by a source whose angular size is small. For example, the radius of the Sun is 15΄ = 4.36∙10 -3 rad. The radiation characteristics of an isotropic and homogeneous source of small angular dimensions can be found in a relatively simple way. In Fig. 5 a light source whose linear radius is R, situated on long distance r>>R from the observer. For small angular sizes it is true

and the angular radius of the source is equal to

The last formula is valid if we neglect the difference in the lengths of the arc and the chord subtending it. The area occupied by the source on the sphere can be estimated in the same approximation as pR 2, from where the solid angle subtended by it W 0, according to definition (1.1), turns out to be equal

.

We denote the luminosity of the source L. Through the surface of a sphere of radius r, whose center coincides with the source of radiation, per unit time an amount of energy passes through L, and through unit surface, respectively, L/ 4π r 2. According to the above definition, this quantity is the radiation flux F:

.

In deriving this formula, we used the assumption that the radiation source is isotropic.

Let's move on to calculating the intensity. According to the assumption of homogeneity, the same energy emanates from any unit area located on the surface of the source per unit time, which we denote I 0 . There is no radiation source outside the disk. Due to its small angular dimensions, we can assume the value of cos θ equal to unity at θ< θ 0 . В этом случае (4.3) сводится к

.

From (5.1) – (5.3) we obtain an explicit expression for I 0:

.

We can now write the final formula for intensity as a function of direction:

,

Where I 0 is given by formula (5.4).

Intensity and flux describe in different ways how the radiation field changes as the source moves away. As follows from (5.2), the flow decreases in inverse proportion to the square of the distance r. Intensity amplitude I 0, according to (5.4), does not depend on the distance, but the range of angles θ 0 in which the intensity is different from zero decreases.

Point radiation source

To move on to the case of a point source, we need a radius R rush towards zero. As a result, the amplitude I 0 from (5.4) becomes infinitely large, and the region in which the intensity is different from zero, according to (5.5), contracts to a point. Thus, intensity is an inconvenient tool for describing a point source and should only be used for extended sources.

The concept of flow has no such shortcoming. Formula (5.2) includes only one characteristic of the source - luminosity L. The flux does not depend on the radius of the object, so it is equally applicable to both extended and point sources of radiation.

So, in the case of an extended source, we can measure the intensity and flux of radiation, and in the case of a point source, only the flux.

1.6 Average intensity and energy density

The average intensity J is defined as the integral of the intensity in all directions divided by 4π:

In the case of an isotropic radiation field, the intensity as a constant value can be taken out of the integral sign. Considering that the solid angle of a complete sphere is 4π, we obtain

The average intensity, unlike the flux, does not depend on the direction of the control area, since we are summing up the intensity, and not the energy passed through the area.

Important characteristic radiation is the energy density U. In its meaning it does not depend on the direction. But to calculate it, we introduce an intermediate value UΩ - energy density of quanta flying in the direction k inside a cone with solid angle ΔΩ. During Dt through the platform DS located perpendicular to the direction in question, an amount of energy passes through equal to the product of UΩ by the volume of the parallelepiped with area DS and height cDt, Where With- speed of light. Using (3.4), we obtain

Having integrated the last expression in all directions, we arrive at the final result:

Thus, the average intensity is related to the radiation energy density.

1.7 Integration over angular variables.

In Section 1.5 we found the relationship between intensity and flux without performing directional integrals. We were able to do this for a single reason: the radiation source was assumed to be so small that we could take sinθ ≈ θ and cos θ ≈ 1. But in the case of a source of arbitrary size, it is necessary to develop a mathematical apparatus that allows us to actually perform integration in (4.3) and others similar expressions.

Spherical coordinate system

Rice. 6 . Spherical coordinate system.

The calculation of an integral of type (4.3) requires the introduction of a coordinate system on the sphere. The angles are measured from a great circle PQ, called the “prime meridian”, and from a point P on it, called the “pole”. Figure 6 shows a sphere with a center at point O, pole P and prime meridian. The big circle E stands for the equator. The equatorial plane passes through the center of the sphere perpendicular to the radius OP. The equator intersects the prime meridian at point Q.

Let M be an arbitrary point on the sphere. Let's draw a meridian through P and M ( big circle) and denote as R its point of intersection with the equator, and θ - the angle between OP and OM. Using the same letter as for the angle between the vectors entered above k And n is traditional and does not lead to confusion. Moreover, in the calculations below we will choose a frame of reference in such a way that OP and OM actually make sense n and k. The equatorial plane coincides with the control area. The angle θ takes values ​​from the range

If point M is in the upper hemisphere (as in Fig. 6), then θ<π/2, а если в нижней, то θ>π/2. The position of M at the equator corresponds to θ=π/2, at the “north” (P) pole θ=0, and at the “south” θ=π.

The direction of the prime meridian PM is determined by the angle φ measured in the equatorial plane between OQ and OT:

So, the position of any point on the sphere can be specified using angles θ and φ, varying in the range (7.1).

Solid angle element

Let us express the solid angle element ΔΩ through the intervals of linear angles Δθ and Δφ. In Fig. 7, the spherical rectangle ABCD is formed by the intersection of two meridians of a sphere of radius R with two parallels - small circles parallel to the equator. We will consider its dimensions AB and BC to be so small that its shape is close to a flat rectangle, therefore its area Δ S approximately equal to the product of adjacent sides a=AB and b = B.C. Let us introduce the notation Δθ for the angle between the radii OA and OB. The length of arc AB is R∙Δθ. Let us denote by F the point of intersection of the small circle BC and the axis OP. Radius Rθ parallel BC is equal to

,

where Δφ is the angle between FB and FC. Thus,

Letting Δθ and Δφ tend to zero and following the definition of the solid angle, we finally obtain

.

In all the problems we solve, we will limit ourselves to isotropic sources. Their radiation field has enough high degree symmetry. By at least, it is always cylindrically symmetric if the pole P of the spherical coordinate system is directed to the center of the source. The direction of the prime meridian can be chosen arbitrarily, since with such a choice of coordinate system the intensity does not depend on the azimuthal angle j.Therefore, integration over j in this case it comes down to simply multiplying by 2 p. In what follows, we will assume that the reference system is chosen in exactly this way. Therefore, the intensity depends only on the azimuthal angle q, and when integrating over the solid angle, the equality is true

.

Below we will always use the simple formula (7.3), assuming that the conditions for its applicability are satisfied.

1.8. Flux is a measure of intensity anisotropy

Radiation, as mentioned above, is called isotropic if its intensity does not depend on the direction:

Where I 0 is some number.

The flux of isotropic radiation through any area is zero. This statement will become obvious if we choose the following method for summing the energy in (4.1). For each direction, we add up the amount of energy flowing in the positive and negative directions. By assumption, they are the same, therefore their sum is zero. Thus, we have divided the sum (4.1) into zero terms, which means that the total flux is zero.

The equality of the total radiation flux to zero can also be verified by direct calculation using formula (7.3). Bringing out the constant I 0 for the sign of the integral, we get

.

Equality to zero flux is a necessary but not sufficient condition for the isotropy of radiation. Consider, for example, the function

.

It describes anisotropic radiation. However the flow is zero:

.

This happened due to the following reason. We selected the direction of the control area in such a way that the intensity in both directions along the vector n is the same:

.

For any other choice n the flow will be non-zero. Consequently, a conclusion about the degree of radiation isotropy can be made only after measuring the flux in all possible directions of the control area.

1.9 Isotropic source boundary and astrophysical flow

Rice. 8 . Boundary of an isotropic source.

Let the source be a half-space limited by the plane G. We will assume that the radiation field inside the source is isotropic, and there is no radiation entering it from the right. Thus, to the right of the G boundary, the radiation is anisotropic. Let's direct the vector n perpendicular to the boundary G, as in Fig. 8, and write the intensity as a function of the angle θ:

.

This model underlies the theory of stellar atmospheres. We calculate the flow using formula (7.3):

.

Formula relating flux and intensity amplitude for the boundary of a plane-parallel atmosphere

,
often used in another form. We enter the value

It is usually called the “astrophysical flow”. Formula (9.2) now takes on a very simple form:

.

Let us emphasize that (9.2) and (9.4) are in no way a connection between intensity and flow. This follows at least from the fact that flow is a number, and intensity is a function of angle. Equality between a number and a function is possible only if the function is reduced to constant value. But the intensity is equal I 0 in all directions corresponds to zero flux. Relations (9.2) and (9.4) between the flow and the amplitude of the anisotropic intensity are valid specifically for the function I(θ) from (9.1). For brevity, they sometimes write that “the astrophysical flux at the boundary of the radiating body is equal to the intensity,” implying the above.

1.10 Spectral characteristics of radiation

Let's move on to studying intensity as a function of frequency. To do this, let us return to definition (3.3). In addition to all the characteristics indicated there, we will assume that the energy passing through the control area Δ E concentrated in a certain frequency range Δν, so narrow that the value Δ E is proportional to Δν. Proportionality factor Iν is called the intensity calculated for a unit frequency interval:

Similarly, you can enter Iλ - intensity in a unit wavelength interval:

In area

Maximum I n .

Over a sufficiently large spectral interval, the function Iλ and Iν depend on frequency (or wavelength) non-monotonically: they increase in the region of low frequencies, pass through a maximum and then decrease. The nonlinearity of the relationship between frequency and wavelength leads to the fact that the positions of the maxima Iλ and Iν are different. Let's show this in two ways, first choosing the more visual one. In Fig. 9 the frequency range is near the maximum Iν is divided into equal intervals Δν. In this region of the spectrum the value Iν almost does not change from interval to interval. But due to the nonlinear relationship (10.3), identical frequency intervals correspond to wavelength intervals Δλ that decrease with frequency. In fact, according to (10.4) we have:

So, a decrease in the wavelength interval in the region of maximum Iν is accompanied by an increase Iλ. Therefore, the maximum Iλ occurs at higher frequencies than the maximum I ν .

The same result can be obtained by differentiation (10.5):

The following inequalities follow from the relationship (10.3) between frequency and wavelength:

.

Therefore, at the maximum point Iν, where

derivative dI λ / dν turns out to be positive. Consequently, its maximum lies at higher frequencies.

From (10.7) it is clearly seen that the difference in the frequencies of the maxima Iν and Iλ is due precisely to the nonlinearity of the function ν(λ). With a linear relationship, the second term on the right would be equal to zero, which means that the maxima coincide.

Magnitude

Stellar magnitude is determined by the flux of radiation from the source Fλ and spectral sensitivity of the receiver W(λ):

.

Here A- some constant, the numerical value of which can be chosen by anyone. Let us recall that, by virtue of (10.5), the same result will be obtained if we choose frequency as the integration variable and replace Fλ on F n .

Let us note an important difference between stellar magnitude and flux. The radiation flux through a fixed area remains the same, no matter what instrument it is measured, while the magnitude depends on the spectral sensitivity of the receiver. By measuring the magnitude of the same source of radiation using different instruments, we will, generally speaking, obtain different results. The concept of magnitude is meaningless if the function is not specified W(λ) and constant A, or, as they say, the photometric system is not installed.

There are currently several photometric systems; and the most common of them is the UBV system, or Johnson system. It consists of several filters, the response curves of three of them are shown in Fig. 10. Stellar magnitudes in the Johnson system are defined as follows

Here the notation is introduced

Integrals Δ B and Δ V are calculated similarly, only in integrands instead of the transmission curve W U (λ) must be written, respectively, W B(λ) and W V(λ). The radiation source in the UBV system is characterized by color indicators U-B And B-V:

Numerical values ​​of constants A on the right side (10.9) of the Johnson system are chosen in such a way that the color indices U-B And B-V turned out to be equal to zero for stars of spectral class A0.

Radiation flux. 2. The concept of the spectrum of electromagnetic radiation.

3. The principle of measuring the distribution of radiation flux across the spectrum. 4. Spectral intensity of radiation flux. 5. Energy quantities.

Radiation power (or flux) take the energy transferred per unit time. Measured in watts (W). Often the properties of radiation are expressed not only by the total power, but also by its distribution over the spectrum (Fig. 1.2).

To characterize the spectral distribution of radiation flux with a continuous spectrum, a quantity called spectral intensity (or spectral density) of radiation is used.

Let us select on the curve of the spectral distribution of the radiation flux a certain finite interval of wavelengths, which accounts for the radiation power. Then

And

Knowing the distribution of the function over the spectrum, it is possible to determine the radiation flux of any part of the spectrum in the interval:

If

Then the formula will take the form expressing the total radiation power with a continuous spectrum:

The power of light(I). In lighting engineering, this quantity is taken as the basic one. 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 energy intensity of light in a given direction is understood as the flux of radiation per unit solid angle.

In energy units where is the solid angle expressed in steradians (sr). The energetic intensity of light is expressed in watts per steradian (W/sr).

Solid angle. A solid angle is a part of space bounded by a conical surface and a closed curved contour that does not pass through the vertex of the angle (Fig. 1.4).

Illumination(E). Energy illumination is understood as the radiation flux per unit area of ​​the illuminated surface Q:

The irradiance is expressed in .

Luminosity(R). Luminosity, for energy and light quantities, respectively, is understood as the total flux of radiation emitted from a unit area of ​​a luminous or reflective surface.

,

Brightness(IN). The energetic brightness () of a radiation source in a given direction is understood as the energetic intensity of light from a source in this direction, per unit area of ​​projection of its surface onto a plane perpendicular to this direction:

The unit of measurement is . By relating the value to the main quantity - the radiation flux Ф and taking into account that , we get

Brightness characterizes not only sources that directly emit light, but also secondary sources - bodies that reflect light from the primary source.

Radiation energy measured in joules or .

where Ф(t) is a function of changes in radiation flux over time.

Energy exposition- surface radiation energy density on the illuminated surface. The unit of measurement is .

In the case of fixed values ​​and taking into account the fact that:

Question No. 2.

6. The concept of a radiation receiver. 7. Receiver reactions. 8. Classification of radiation receivers. 10. Spectral sensitivity of the radiation receiver. 11. Feature of the eye as a receiver. 12. Luminous flux(F).13. Relationship between luminous flux and radiation flux. 14. Visibility curve.

6. As a result of the absorption of light in media and bodies, whole line phenomena:

A body that has absorbed radiation begins to radiate itself. In this case, the secondary radiation may have a different spectral range compared to the absorbed one. For example, when illuminated by ultraviolet light, the body emits visible light.

The energy of absorbed radiation is converted into electrical energy, as in the case of the photoelectric effect, or produces a change in the electrical properties of the material, which occurs in photoconductors. Such transformations are called photophysical.

Another type of photophysical transformation is the conversion of radiation energy into thermal energy. This phenomenon has found application in thermocouples used to measure radiation power.

Radiation energy is converted into chemical energy. A photochemical transformation of the substance that has absorbed light occurs. This transformation occurs in most photosensitive materials.

7. Bodies in which such transformations occur under the influence of optical radiation have received the general name in lighting engineering " radiation receivers".

8. Classification of radiation receivers.

Conventionally, radiation receivers can be divided into three groups.

1. The natural receiver of radiation is human eye.

2. A whole group of radiation receivers consists of photosensitive materials, using traditional or digital methods: projection photography, contact copying, element-by-element image recording using lasers or LED rulers.

3. Receivers are also photosensitive elements of measuring instruments (densitometers, colorimeters, spectrophotometers, etc.) and sensors of optical control devices used in printing equipment.

10. Spectral sensitivity of the radiation receiver.

Spectral sensitivity depends on wavelength.

S=cPλ eff. / Φλ and Pλ eff.=kΦλSλ (for monochromatic radiation)

The quantities Φλ and Pλ are called monochromatic radiation flux and monochromatic effective flux, respectively, and Sλ is called monochromatic spectral sensitivity.

Most of the receivers used in lighting engineering and printing have a limited range of spectral sensitivity. Thus, the human eye is sensitive to the “visible” zone of the spectrum (from 400 to 700 nm), photographic films are sensitive to the near ultraviolet and visible zones, and copy layers are sensitive to the ultraviolet and blue zones of the spectrum.

Question #3 Feature of the eye as a receiver. Luminous flux(F).

Its connection with the flow of radiation. Visibility curve. Relationship between K and Vλ and their definition. Light quantities The difference between light and energy fluxes in the range of 400-700 nm.

11. Feature of the eye as a receiver.

The effect of light on the eye causes a certain reaction. Depending on the level of action of the light flux, one or another type of light-sensitive receptors of the eye, called rods or cones, works. To the terms low level illumination of the eye sees surrounding objects due to rods. At high levels After illumination, the daytime vision apparatus, for which the cones are responsible, begins to work. In addition, according to their light-sensitive substance, cones are divided into three groups (red-sensitive, green-sensitive and blue-sensitive) with different sensitivities 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, we can say that the effect of light is two-dimensional. Quantitative characteristics The reaction of the eye associated with the level of illumination is called lightness. Qualitative characteristic associated with different levels reactions of three groups of cones is called chromaticity.

12. Luminous flux (F).

Luminous flux is understood as the radiation power assessed by its effect on the human eye. The unit of measurement for luminous flux is lumen (lm).

13. Relationship between luminous flux and radiation flux.

For monochromatic radiation:

For integral radiation:

F=680ʃύλΦλdλ (under the integral sign λ=380nm, and above the integral sign λ=780nm).

14. Visibility curve.

An important characteristic of practical interest is the distribution curve of the relative spectral sensitivity of the eye (relative spectral luminous efficiency) in daylight ύλ=ƒ(λ)

ύλ=Vλ / Vλmax,

where Vλ and Vλ max – absolute values sensitivity of the eye to radiation with wavelength λ and maximum sensitivity of the eye.

In daylight conditions, the human eye has maximum sensitivity to radiation with λ = 555 nm (ν555 = 1).

400 500 600 λ, nm

15. Relationship between K and Vλ and their definition

Vλ- the absolute value of the sensitivity of the eye to radiation with wavelength λ. It has been established that in daylight conditions the human eye has maximum sensitivity to radiation with λ = 555 nm( V555=1). In this case, for each unit of luminous flux from F 555 there is a radiation power of F 555 = 0.00146 W. The ratio of the luminous flux F 555 to Ф 555 is called spectral luminous efficiency: k= F 555/ Ф 555= 680[lm/W] For any wavelength of radiation in the visible range k=const.

Light quantities

There are 2 unit systems: energy and light. Light quantities include: 1) Luminous flux (F) - radiation power, estimated by its effect on the human eye. Unit of measurement is lumen (lm). 2) Illumination (E) – luminous flux incident per unit area of ​​the illuminated surface (Q). Unit of measurement - lux. The unit of illumination is the illumination created by a uniformly distributed luminous flux of 1 lm per 1 m (square) of the surface. E= ∂F/∂Q 3) Luminosity (R) - the total flux of radiation (luminous flux) emitted from a unit area of ​​a luminous or reflective surface. Unit of measurement – ​​lm/m (square) R=∂F/∂Q.4) Brightness (V)- V=

Unit of measurement - cd/m (square) 5) Light energy (W) W=∫F(t)∂t, lm*s 6) light exposure (N) - surface density of light energy on the illuminated surface H=E* t, lx*s

As is known, electromagnetic oscillations in the wavelength range from 1 nm to 1 mm are called optical radiation. This range is bordered on the short-wave side by x-rays, and on the long-wave side by radio waves.

In Fig. 82 shows the position of optical radiation in the general spectrum of electromagnetic vibrations, which is represented by gamma radiation, x-rays, ultraviolet, visible and infrared radiation and radio waves. The visible portion of optical radiation is characterized by wavelengths

It should be noted that the boundaries between individual areas are conditional. For example, ultraviolet radiation overlaps with X-ray and infrared with radio waves.

The radiation spectrum, or, as it is sometimes called, the spectral composition of radiation, is the distribution of radiation power over wavelengths or vibration frequencies. Radiation characterized by one wavelength is monochromatic. A radiation spectrum of this type is called line spectrum (Fig. 83, a). Radiation, which is a continuous set of monochromatic radiation, has a continuous spectrum (Fig. 83, b). The wavelength range for a continuous spectrum can be considered from zero to infinity. Source Continuous spectrum nicks are usually heated solids and liquids, linear - hot gases or vapors, also lasers.

Ideal monochromatic radiation does not exist in nature, therefore, in practice, monochromatic radiation means radiation that includes such a narrow range of wavelengths that can be characterized by a single wavelength.

For the visible range of optical radiation German physicist Fraunhofer (1787-1826), while studying the radiation of the Sun, measured the wavelengths corresponding to certain lines in the solar spectrum. These lines are reproduced by the spectra of certain chemical elements that fill the bulbs of lamps with an arc, glow or high-frequency discharge in the form of gases or vapors.

For the wavelengths of the Fraunhofer lines, the refractive indices of optical media are fixed. In table 4 shows the designations of spectral lines, their corresponding wavelengths and region

Rice. 82. Spectrum of electromagnetic vibrations

Rice. 83. Types of spectra: a - line; b - solid

spectrum (color), as well as that chemical element, whose line radiation has a given spectral line.

The energy of optical radiation, like any other, is measured in joules

The average power of optical radiation over a time significantly longer than the period of light oscillations is called radiation flux and is estimated in watts

If within a narrow spectral region the radiation flux is equal, then the ratio

is the spectral flux density of radiation.

Table 4 (see scan) Fraunhofer spectral laaaa

In Fig. 84 shows the wavelength dependence of the spectral radiation flux density in the continuous spectrum, which is called the spectral characteristic of the radiation flux. From this dependence it follows that the flow is represented by the area of ​​the elementary section

Electromagnetic waves transfer energy from one area of ​​space to another. Energy transfer occurs along rays - imaginary lines indicating the direction of wave propagation. The most important energy characteristic of electromagnetic waves is the radiation flux density. Let's imagine a platform of area S located perpendicular to the rays. Let us assume that during time t the wave transfers energy W through this area. In other words, the radiation flux density is the energy transferred through a unit area (perpendicular to the rays) per unit time; or, which is the same thing, is the radiation power transferred through a single area. The unit of measurement for radiation flux density is W/m2. The radiation flux density is related by a simple relationship with the energy density of the electromagnetic field. We fix the area S, perpendicular to the rays, and a short period of time t. Energy will pass through the area: W = ISt. This energy will be concentrated in a cylinder with base area S and height ct, where c is the speed of the electromagnetic wave. The volume of this cylinder is equal to: V = Sct. Therefore, if w is the energy density of the electromagnetic field, then for the energy W we also obtain: W = wV = wSct. Equating the right-hand sides of the formulas and and reducing by St, we obtain the relation: I = wc. The radiation flux density characterizes, in particular, the degree of influence of electromagnetic radiation on its receivers; When they talk about the intensity of electromagnetic waves, they mean the radiation flux density. An interesting question is how the intensity of radiation depends on its frequency. Let an electromagnetic wave be emitted by a charge performing harmonic oscillations along the X axis according to the law x = x0 sin iet. The cyclic frequency w of charge oscillations will at the same time be the cyclic frequency of the emitted electromagnetic wave. For the speed and acceleration of the charge we have: v = X = x0ш cos Шt and a = v = -x0Ш2 sin Шt. As we see, a ~ w2. The electric field strength and magnetic field induction in an electromagnetic wave are proportional to the acceleration of the charge: E ~ a and B ~ a. Therefore, E ~ w2 and B ~ w2. The electromagnetic field energy density is the sum of the electric field energy density and the magnetic field energy density: w = wel + wMarH. The energy density of the electric field, as we know, is proportional to the square of the field strength: w^ ~ E2. Similarly, it can be shown that wMarH ~ B2. Consequently, w^ ~ w4 and wMarH ~ w4, so w ~ w4. According to the formula, the radiation flux density is proportional to the energy density: I ~ w. Therefore I ~ wA. We have obtained an important result: the intensity of electromagnetic radiation is proportional to the fourth power of its frequency. Another important result is that the radiation intensity decreases with increasing distance from the source. This is understandable: after all, the source radiates in different directions, and as you move away from the source, the emitted energy is distributed over an increasingly larger and larger area. The quantitative dependence of the radiation flux density on the distance to the source is easy to obtain for the so-called point source of radiation. A point source of radiation is a source whose dimensions can be neglected in a given situation. In addition, a point source is assumed to radiate equally in all directions. Of course, a point source is an idealization, but for some problems this idealization works great. For example, when studying the radiation of stars, they can be considered point sources - after all, the distances to the stars are so enormous that their own sizes can be ignored. At a distance r from the source, the emitted energy is uniformly distributed over the surface of a sphere of radius r. The area of ​​the sphere, recall, is S = 4nr2. If the radiation power of our source is P, then during time t energy W = Pt passes through the surface of the sphere. Using the formula, we then obtain: = Pt = P 4 nr2t 4 nr2 Thus, the radiation intensity of a point source is inversely proportional to the distance to it. Types of electromagnetic radiation The spectrum of electromagnetic waves is unusually wide: the wavelength can be measured in thousands of kilometers, or less than a picometer. However, this entire spectrum can be divided into several characteristic wavelength ranges; Within each range, electromagnetic waves have more or less similar properties and methods of emission.