$I\; (t)\; =\; \backslash \; frac\; (1)\; (T)\; \backslash \; int\; \backslash \; limits\_t\; ^\; (t\; +\; T)\; \backslash \; left\; |\; \backslash \; vec\; S\; (t)\; \backslash \; right\; |\; dt,$

where the Poynting vector $\backslash \; vec\; S\; (t)\; =\; \backslash \; frac\; (c)\; (4\; \backslash \; pi)\; \backslash \; left\; [\backslash \; vec\; E\; (t)\; \backslash \; times\; \backslash \; vec\; B\; (t)\; \backslash \; right],$(in the SGS system), $E$- tension electric field, a $B$- magnetic induction.

For a monochromatic linearly polarized wave with an amplitude of the electric field strength $E\_0$ the intensity is:

$I\; =\; \backslash \; frac\; (\backslash \; epsilon\_0cE\_0\; ^\; 2)\; (8\; \backslash \; pi).$

For a monochromatic circularly polarized wave, this value is twice as large:

$I\; =\; \backslash \; frac\; (\backslash \; epsilon\_0cE\_0\; ^\; 2)\; (4\; \backslash \; pi).$

Sound intensity

Sound is a wave of mechanical vibrations of the medium. Sound intensity can be expressed in terms of the amplitude values ​​of the sound pressure p and the vibrational velocity of the medium v:

$I\; =\; \backslash \; frac\; (pv)\; (2).$

Write a review on the article "Intensity (physics)"

Notes (edit)

Intensity excerpt (physics)

“If all Russians, though a little like you,” he said to Pierre, “c“ est un sacrilege que de faire la guerre a un peuple comme le votre. from the French, you don't even have anger against them.
And now Pierre deserved the passionate love of the Italian only by what he evoked in him the best sides his soul and admired them.
During the last time of Pierre's stay in Oryol, his old acquaintance, the Mason, Count of Villars, came to him, the same one who introduced him to the box in 1807. Villarsky was married to a wealthy Russian, who had large estates in the Oryol province, and occupied a temporary position in the city for food.
Learning that Bezukhov was in Oryol, Villarsky, although he never knew him briefly, came to him with those declarations of friendship and closeness that people usually express to each other when they meet in the desert. Villarsky was bored in Oryol and was happy to meet a man of the same circle with him and with the same, as he believed, interests.
But, to his surprise, Villarsky noticed soon that Pierre was very far behind real life and fell, as he defined Pierre with himself, into apathy and egoism.
- Vous vous encroutez, mon cher, [You start, my dear.] - he told him. Despite the fact that Villarsky was now more pleasant with Pierre than before, and he visited him every day. But Pierre, looking at Villarski and listening to him now, was strange and incredible to think that he himself had been the same very recently.
Villarsky was married, a family man, busy with the affairs of his wife's estate, and service, and family. He believed that all these activities are a hindrance in life and that they are all despicable, because they are aimed at the personal welfare of him and his family. Military, administrative, political, Masonic considerations constantly consumed his attention. And Pierre, not trying to change his look, not condemning him, with his now constantly quiet, joyful mockery, admired this strange phenomenon so familiar to him.
In his relations with Villarsky, with the princess, with the doctor, with all the people with whom he now met, Pierre had a new feature that deserved him the favor of all people: this recognition of the ability of each person to think, feel and look at things in their own way; recognition of the impossibility of words to dissuade a person. This legitimate feature of every person, which previously worried and annoyed Pierre, now formed the basis of the participation and interest that he took in people. The difference, sometimes a complete contradiction between the views of people with their own lives and among themselves, delighted Pierre and evoked in him a mocking and meek smile.

Let us now calculate the total energy emitted by the charge during acceleration. For the sake of generality, let us take the case of arbitrary acceleration, assuming, however, that the motion is nonrelativistic. When the acceleration is directed, say, vertically, electric field radiation is equal to the product of the charge and the projection of the retarded acceleration divided by the distance. Thus, we know the electric field at any point, and from here we know the energy passing through the unit area for.

The quantity is often found in formulas for the propagation of radio waves. Its reciprocal can be called vacuum impedance (or vacuum resistance); it is equal ... Hence the power (in watts per square meter) is the mean square of the field divided by 377.

Using formula (29.1) for the electric field, we obtain

, (32.2)

where is the power on, emitted at an angle. As already noted, it is inversely proportional to the distance. By integrating, we get from here the total power radiated in all directions. To do this, first we multiply by the area of ​​the strip of the sphere, then we get the energy flux in the interval of the angle (Fig. 32.1). The area of ​​the strip is calculated as follows: if the radius is equal, then the thickness of the strip is equal, and the length, since the radius of the ring strip is. Thus, the area of ​​the strip is

(32.3)

Figure 32.1. The area of ​​the ring on the sphere is.

Multiplying the flux [power by, according to formula (32.2)] by the area of ​​the strip, we find the energy emitted in the range of angles and; then you need to integrate over all angles from to:

(32.4)

When calculating, we use the equality and as a result we get. From here finally

There are a few things to note about this expression. First of all, since there is a vector, then in the formula (32.5) means, that is, the square of the length of the vector. Secondly, the formula (32.2) for the flow includes the acceleration taken with the retardation taken into account, that is, the acceleration at the time when the energy was radiated and now passing through the surface of the sphere. One might think that the energy was actually radiated at exactly the specified time. But this is not entirely correct. The moment of radiation cannot be determined precisely. It is only possible to calculate the result of such a motion, for example, oscillations, etc., where the acceleration eventually disappears. Consequently, we can only find the total energy flux over the entire period of oscillation, proportional to the average square of the acceleration over the period. Therefore, in (32.5) should mean the time average of the square of the acceleration. For such a motion, when the acceleration at the beginning and at the end vanishes, the total radiated energy is equal to the time integral of expression (32.5).

Let's see what formula (32.5) gives for an oscillating system for which the acceleration has the form. The average over the period from the square of the acceleration is (when squaring, remember that in fact, instead of the exponent, its real part, the cosine, should enter, and the average of gives):

Hence,

These formulas were obtained relatively recently - at the beginning of the 20th century. These are wonderful formulas, they were of great historical importance, and they would be worth reading about in old books on physics. True, a different system of units was used there, and not the SI system. However, in the end results related to electrons, these complications can be eliminated by using next rule correspondences: the value where is the electron charge (in coulombs), earlier it was written as. It is easy to verify that in the SI system the value is numerically equal, since we know that and ... In what follows, we will often use the convenient notation (32.7)

If this numerical value is substituted into the old formulas, then all other quantities in them can be considered as defined in the SI system. For example, formula (32.5) previously had the form ... And the potential energy of a proton and an electron at a distance is or, where SI.

Light waves.

The laws of geometric (beam) optics

Light waves. Light intensity. Light flow. The laws of geometric optics. Total internal reflection

Optics is a branch of physics that studies the nature of light radiation, its propagation and interaction with matter. The branch of optics that studies the wave nature of light is called wave optics. The wave nature of light underlies such phenomena as interference, diffraction, polarization. The branch of optics, which does not take into account the wave properties of light and which is based on the concept of a ray, is called geometric optics.

§ 1. LIGHT WAVES

According to modern concepts, light is a complex phenomenon: in some cases it behaves like an electromagnetic wave, in others - like a stream of special particles (photons). This property is called wave-particle dualism (corpuscle - particle, dualism - duality). In this part of the lecture course, we will consider the wave phenomena of light.

A light wave is an electromagnetic wave with a wavelength in a vacuum in the range:

	= (0.4¸ 0.76) × 10-6 m = 0.4¸ 0.76 μm = 400¸ 760 nm =
4 000¸
A -		angstrom is a unit of measure for length. 1A = 10-10 m.
Waves of this range are perceived by the human eye.
Radiation with a wavelength of less than 400 nm is called ultraviolet, and
with more than 760 nm, -					infrared.
Light wave frequency n for visible light:
			= (0.39¸ 0.75) × 1015 Hz,
s = 3 × 108 m / s is the speed of light in vacuum.
Speed					matches		speed	spreading
electromagnetic wave.

Refractive index

The speed of propagation of light in a medium, like any electromagnetic wave, is (see (7.3)):

The refractive index is introduced to characterize the optical properties of the medium. The ratio of the speed of light in a vacuum to the speed of light in a given environment is called absolute refractive index:

Taking into account (7.3)

since for most transparent substances μ = 1.

Formula (8.2) connects the optical properties of a substance with its electrical properties. For any medium except vacuum, n> 1. For vacuum n = 1, for gases under normal conditions n≈ 1.

Refractive index characterizes optical density Wednesday... A medium with a higher refractive index is called optically denser. Let's designate the absolute refractive indices for two media:

						n 2 =
Then the relative refractive index is:
n 21 =
where v 1 and v 2 -						the speed of light in the first and second medium, respectively.
				dielectric					medium permeability ε depends on frequency

electromagnetic wave, then n = n (ν) or n = n (λ) - the refractive index will depend on the wavelength of light (see lectures № 16, 17).

The dependence of the refractive index on wavelength (or frequency) is called dispersion.

In a light wave, as in any electromagnetic wave, vectors E and H oscillate. These vectors are perpendicular to each other and to the direction

vector v. Experience shows that physiological, photochemical, photoelectric and other types of influences are caused by oscillations of the electric vector. Therefore, the light vector is the vector of the electric field of the light (electromagnetic) wave.

For a monochromatic light wave, the change in time and space of the projection of the light vector on the direction along which it

Here k is the wavenumber; r is the distance measured along the direction of wave propagation; E m is the amplitude of the light wave. For a plane wave, E m = const, for a spherical wave, it decreases as 1 / r.

§ 2. INTENSITY OF LIGHT. LIGHT FLOW

The frequency of the light waves is very high, so the light receiver or the eye captures the time-averaged flux. The intensity of light is the modulus of the time average value of the energy density at a given point in space. For a light wave, as for any electromagnetic wave, the intensity (see (7.8)) is equal to:

For a light wave μ≈ 1, therefore from (7.5) it follows:

μ0 H = ε0 ε E,

whence, taking into account (8.2):

								E ~ nE.

Let us substitute formulas (8.4) and (8.5) into (7.8). After averaging, we get:

Therefore, the light intensity is proportional to the square of the amplitude of the light wave and the refractive index. Note that for

vacuum and air n = 1, therefore I ~ E 2 m (compare with (7.9)).

To characterize the intensity of light, taking into account its ability to induce a visual sensation, the value of Ф, called the luminous flux, is introduced. The effect of light on the eye is highly wavelength dependent. Most

the eye is sensitive to radiation with a wavelength of λ z = 555 nm (green color).

For other waves, the sensitivity of the eye is lower, and outside the interval (400–760 nm), the sensitivity of the eye is zero.

Luminous flux is the flux of light energy, estimated by visual sensation... Unit luminous flux is the lumen (lm). Accordingly, the intensity is measured either in energy units (W / m2) or in light units (lm / m2).

The light intensity characterizes the numerical value of the average energy transferred by the light wave per unit time through the unit area of ​​the site, placed perpendicular to the direction of wave propagation. The lines along which light energy propagates are called rays. The section of optics, which studies the laws of propagation of light

radiation based on the concept of light rays is called geometric, or ray optics.

§ 3. BASIC LAWS OF GEOMETRIC OPTICS

Geometric optics is an approximate consideration of the propagation of light, assuming that light propagates along certain lines - rays (ray optics). In this approximation, the finiteness of the wavelengths of light is neglected, assuming that λ → 0.

Geometric optics allows in many cases to calculate the optical system quite well. But in a number of cases, a real calculation of optical systems requires taking into account the wave nature of light.

The first three laws of geometric optics have been known since ancient times. 1. The law of rectilinear light propagation.

The law of rectilinear propagation of light states that in

in a homogeneous medium, light propagates in a straight line.

If the medium is inhomogeneous, that is, its refractive index changes from point to point, or n = n (r), then light will not propagate in a straight line. At

the presence of sharp inhomogeneities, such as holes in opaque screens, the boundaries of these screens, a deviation of light from rectilinear propagation is observed.

2. The law of independence of light rays states that rays when crossing do not disturb each other... At high intensities, this law is not observed; light is scattered by light.

3 and 4. The laws of reflection and refraction state that reflection and refraction of the light beam occurs at the interface between the two media. The reflected and refracted rays lie in the same plane with the incident

beam and perpendicular restored to the interface at the point of incidence

Angle of incidence equal to the angle reflections:

for which the indicator

Light intensity is measured when placing lighting indoors or preparing equipment for photography. The term "intensity" is used in many different ways, and this article will show you which devices and techniques are right for your purposes. Professional photographers and lighting technicians use digital light meters, but you can make a simple device with a similar action - a Jolie photometer - yourself.

Steps

How to Measure Indoor Light Intensity and Lamp Light Intensity

Become familiar with photometers that measure light intensity in lux and foot-candles. Such devices measure the intensity of light on a surface, that is illumination... Typically, such devices are used to prepare for photography and when checking the room lighting.

Learn how to interpret the data. Here are some examples of typical readings to help you figure out if you should change your room lighting:

• Working in an office is comfortable under 250-500 lux (23-46 fc) illumination.
• In supermarkets and workplaces requiring fine work, an illumination of 750-1000 lux (70-93 ft-candela) is used. The upper value is comparable to the illumination in an open space outdoors on a bright sunny day.

1. Find out what lumens are. When the word "lumen" appears in the description of a light bulb, it describes how much energy the light bulb emits as visible light. You need to know the following:

   Measure the angle of inclination and the field of the beams. These characteristics apply to light sources that direct the luminous flux in a narrow beam in a certain direction (for example, flashlights). These values ​​can be measured with an exposure meter and with a ruler and protractor.

   • Hold the meter directly in front of the brightest beam. Move it until you find the area with the maximum light intensity (illumination).
   • Keeping the same distance to the light source, move the exposure meter to one side until the light intensity decreases to 50% of the maximum level. Using a ruler or string, draw a line from the light source to this point.
   • Do the same on the other side. Draw a line.
   • Use a protractor to measure the angle between the two lines. This will be the angle of the beam - that is, the angle at which the light diverges.
   • To measure the field, do the same, just mark the points where the light intensity will equal 10% of the maximum value.

   How to measure relative illumination with a homemade device

   1. DIY the device. It's easy to collect if you have necessary materials... This invention is called the Jolie photometer and can be used to measure the relative intensity of two light sources. Possessing necessary knowledge physicists, which will be discussed below, you can find out which of the two bulbs gives more light and which one is more efficient.

      • Since the value will be relative, it will not be expressed in exact units. You will know the relationship between the two lights, but you cannot figure out the exact numbers without doing another experiment.

   2. Cut a piece of paraffin wax in half. Buy wax from a hardware store, cut a 500 g piece, then use a sharp knife to cut the piece in half.

      Place the foil between the two pieces of wax. Tear off a piece of aluminum foil from the sheet and place it on one of the pieces, making sure to cover the entire top surface. Place the second piece of wax on top.

      Rotate the resulting structure vertically. For the device to work, it must be rotated so that the foil is in an upright position. If the wax won't hold by itself, you can leave it horizontal for now, but remember that the box you will be collecting will need to hold the wax upright.

      Cut through three windows in the cardboard box. Take the box that will hold the wax. Wax packaging may work for you. Measure out the windows and cut them out with scissors.

      • Cut two windows of the same size from opposite sides. The holes should be opposite different sides paraffin wax when they are in the box.
      • Cut through a third window of any size in the front of the box. The hole should be centered so you can see both parts of the wax pieces.

   3. Place the wax inside. The foil between the two pieces must be in an upright position. You may need to use duct tape, tape, small pieces of cardboard, or both, to keep the wax from rolling over and the foil to slide out.

      • If the box does not have a lid, cover it with cardboard or any other opaque object.

   4. Choose a starting point. Decide which light source you will use as starting point... If you compare more than two light sources, you will be able to use that lamp in every comparison.

      Place two lights in a straight line. Place two small bulbs, LEDs, or other light sources on flat surface on a straight line. The distance between them should be greater than the width of the box you just made.

      Place the meter between two light sources. It should be at the same height as the bulbs so that the bulbs can fully illuminate the wax inside the box through the windows. Remember that the light sources must be on great distance apart.

      Turn off the lights in the room. Close the window, close the curtains, lower the blinds to keep outside light out of the box.

      Adjust the bulbs so that the wax is lit equally on both sides. Bring the photometer to the side with less light. When moving the box, look through the window on the front of the box. Stop when both pieces of wax are lit the same way.

   5. Measure the distance from the exposure meter to each light source. Use a tape measure to measure the distance from the foil to the lamp you have chosen as a reference point. Label this point as d1... Record the distance, then measure the distance from the foil to the light source on the opposite side, d2.

      • Distance can be measured in any size, the main thing is not to confuse them. For example, if you are measuring in centimeters, write only centimeters (no meters).
   6. For example, suppose the distance d 1 to the reference light source is 60 centimeters, and the distance d 2 to the second light source is 1.5 meters.
   7. I 2 = 5 2/2 2 = 25/4 = 6.25
   8. The light intensity of the second source in 6.25 times larger than the first.

2. Calculate the efficiency. If the bulbs are marked with watts (for example, 60 watts), these numbers indicate how much electricity the bulb consumes. Divide the relative light intensity by this number and you get the light bulb's efficiency relative to other light sources. For example:

   • A 60 watt light bulb with a relative intensity of 6 has a relative efficiency of 6/60 = 0.1.
   • A 40 watt light bulb with a relative intensity of 1 has a relative efficiency of 1/40 = 0.025.
   • Since 0.1 / 0.025 = 4, a 60 watt light bulb is four times more efficient at converting electricity into the light. Remember that this will consume more power than a 40 watt light bulb, and that will cost you more. Efficiency is the percentage of benefit per unit of money spent.

• After calculating the comparative light intensity, you can measure the light intensity using an analog or digital exposure meter. Newer digital exposure meters measure intensity in lux, while old analog ones measure intensity in foot-candles. 1 foot candela = 10.76 lux.

Light plays a huge role not only in the interior, but also in our life in general. Indeed, the efficiency of work depends on the correct illumination of the room, as well as our psychological condition... Light gives a person the opportunity not only to see, but also to evaluate the colors and shapes of surrounding objects.

Of course, natural light is most comfortable for human eyes. In this light, everything is seen very well and without color distortion. But not always daylight present, in the dark, for example, you have to make do with artificial light sources.

So that the eyes do not strain, and vision does not deteriorate, it is necessary to create optimal conditions light and shadow, creating the most comfortable lighting.

The most pleasant lighting for the eyes is natural

Lighting, like many other factors, is assessed in terms of quantitative and qualitative parameters. Quantitative characteristics are determined by the intensity of light, and qualitative - by its spectral composition and distribution in space.

How and in what way is light intensity measured?

Light has many characteristics and each has its own unit of measurement:

• Luminous intensity characterizes the amount of light energy that is transferred over a certain time in any direction. It is measured in candelas (cd), 1 cd is approximately equal to the intensity of the light that a single burning candle emits;
• Brightness is also measured in candelas; in addition, there are such units of measurement as stilbe, apostilbe and lambert;
• Illuminance is the ratio of the luminous flux that falls on specific site, to its surface. It is measured in suites.

It is the illumination that is an important indicator for correct work vision. In order to determine this value, a special measuring device is used. It is called a luxometer.

A luxometer is a device for measuring illumination.

Consists this device from the light receiver and the measuring part, it can be of the arrow type or electronic. A light receiver is a photocell that converts a light wave into electrical signal and directs to the measuring part. This device is a photometer and has a specified spectral sensitivity. It can be used to measure not only visible light, but also infrared radiation, etc.

This device is used both in industrial premises and in educational institutions, as well as at home. Each type of activity and occupation has its own standards for what should be the intensity of light.

Comfortable light intensity

Visual comfort depends on many factors. By far the most pleasing to the human eye is sunlight. But the modern rhythm of life dictates its own rules, and very often you have to work or just be under artificial lighting.

Manufacturers lighting fixtures and lamps are trying to create such light sources that would meet the peculiarities of visual perception of people and would create the most comfortable light intensity.

Light from an incandescent lamp most accurately reproduces natural hues

In ordinary incandescent lamps, a hot spring is used as the light source, and therefore, this light is most similar to natural light.

Lamps are divided into the following categories by the type of light they give:

• warm light having a reddish hue, it is well suited for a home environment;
• neutral light, white, used to illuminate workplaces;
• cold light, bluish, intended for work places high precision or for hot climates.

It is important not only what type the lamps belong to, but also the design of the lamp or chandelier itself: how many bulbs are screwed in where the light is directed, whether the shades are closed or open - all these features must be taken into account when choosing a lighting device.

Illumination standards are fixed in several documents, the most important are: SNiP ( building codes and rules) and SanPiN ( sanitary regulations and norms). There are also MGSN (Moscow city building codes), as well as its own set of rules for each region.

It is on the basis of all these documents that a decision is made about what the lighting intensity should be.

Of course, when thinking about which chandelier to hang in the living room, bedroom or kitchen, no one measures the light intensity with a luxometer. However, know in general outline what kind of light will be more comfortable for the eyes is very useful.

Table 1 shows the illumination standards for residential premises:

Table 1

Table 2 shows the illumination standards for offices

At home, without special equipment, it is difficult to measure indoor lighting, and therefore, in order to understand which lamp to choose, you should pay attention to the color (cold, neutral or warm) and the number of watts. In recreation rooms, it is better to use not too bright ones, and in offices - with more intense light.

Since natural light is the most pleasant for the eyes, preference in a home environment should be given to lamps that give warm light. When we get home, our eyes definitely need a rest after a busy day at work. Correctly selected in terms of brightness lamps for chandeliers and lamps will help to create a suitable lighting intensity.