Why does a rainbow appear? Scientific - research work in physics on the topic rainbow - arc.

As in the midst of transparent cloudy shrouds

Above the onion, the onion is inflorescence and circumferential

Exalted by the messenger of Juno,

And formed by the inner outer.

The rainbow is in plain sight - it is usually observed in the form of two colored arcs (two inflorescences, which Dante writes about), and in the upper arc the colors are arranged in this order from top to bottom: purple, blue, cyan, green, yellow, orange, red , and in the lower arc, on the contrary, from red to purple. To memorize their sequence, there are mnemonic phrases, the first letters of each word in which correspond to the first letters of the color name. For example, this is the phrase "Every Hunter Wants to Know Where the Pheasant Sits" or another, no less famous, "How Once Jean the Bell Ringer Hit a Lantern with His Head ". True, the tradition of distinguishing 7 colors in the rainbow is not universal. For example, Bulgarians have 6 colors in the rainbow.

rainbow gives unique opportunity watch in vivo decomposition of white light into a spectrum.

Rainbows usually appear after rain, when the Sun is fairly low. Somewhere between the Sun and the observer, it is still raining. Sunlight, passing through drops of water, is repeatedly reflected and refracted in them, as in small prisms, and the rays different color emerge from the droplets at different angles. This phenomenon is called dispersion (i.e. decomposition) of light. As a result, a bright colored arc is formed (but it is actually steep; you can see it in its entirety from an airplane).

Sometimes two are observed at once, less often - three multi-colored arcs. The first rainbow is created by rays reflected inside the drops once, the second - by rays reflected twice, etc. In 1948 in Leningrad (now St. Petersburg), four rainbows appeared at once among the clouds over the Neva.

The type of rainbow, the brightness of the colors, the width of the stripes depend on the size and number of water droplets in the air. bright rainbow happens in the summer after a thunderstorm, during which large drops fall. As a rule, such a rainbow portends good weather.

On a bright moonlit night, you can see a rainbow from the moon. A rainbow appears in the light of a full moon when it's raining. Since human vision is designed so that in low light the most sensitive receptors of the eye - "rods" - do not perceive colors, the lunar rainbow looks whitish; the brighter the light, the "colorier" the rainbow (color receptors - "cones" are included in its perception).

fiery rainbow

She was lucky to see a resident of Sweden, Marian Erikson. The rainbow stretched across the night sky and stood at full moon within a minute.

Signs and legends.

Once upon a time, a person began to wonder why rainbows appear in the sky. In those days, they didn’t even hear about optics. Therefore, people invented myths and legends, and there were also many signs. Here are some of them:

• In Scandinavian mythology, the rainbow is the Bifrost Bridge, connecting Midgard (the world of people) and Asgard (the world of the gods).
• In ancient Indian mythology - the bow of Indra, the god of thunder and lightning.
• AT ancient Greek mythology- the road of Irida, messenger between the worlds of gods and people.
• According to Slavic beliefs, a rainbow, like a snake, drinks water from lakes, rivers and seas, which then rains.
• An Irish leprechaun hides a pot of gold where the rainbow touched the ground.
• According to Chuvash beliefs, if you pass through a rainbow, you can change gender.
• In the Bible, the rainbow appeared after the Flood as a symbol of the forgiveness of mankind.
• Superstitious people believed that the rainbow is a bad omen. They believed that the souls of the dead pass into the other world along the rainbow, and if a rainbow appeared, this means someone's imminent death.

The history of the explanation of the rainbow.

Already Aristotle, ancient Greek philosopher, tried to explain the reason for the rainbow. And the Persian astronomer Qutb al-Din al-Shirazi (1236-1311), and perhaps his student Kamal al-din al-Farisi (1260-1320), was apparently the first to give a sufficiently accurate explanation of the phenomenon.

The general physical picture of the rainbow was already clearly described by Mark Antony de Dominis (1611).

M.A. de Dominis

Based on experimental observations, he came to the conclusion that a rainbow is obtained as a result of reflection from inner surface raindrops and double refraction - at the entrance to the drop and at the exit from it. René Descartes gave a fuller explanation of the rainbow in his Meteora in the chapter On the Rainbow (1635).

Rene Descartes

Descartes writes:

“Firstly, when I took into account that a rainbow can appear not only in the sky, but also in the air near us, every time there are drops of water in it, illuminated by the sun, as is sometimes seen in fountains, it is easy for me it was concluded that it depends on how the rays of light act on these drops, and from them reach our eyes; further, knowing that these drops are spherical, and seeing that both with large and small drops, the rainbow always appears in the same way , I set myself the goal of creating a very large drop in order to be able to see it better. To do this, I filled a large glass vessel, quite round and completely transparent with water, and came to the following conclusion ... "

This conclusion repeats and refines the result obtained by Dominis. In particular, Descartes discovered that the second (outer) rainbow results from two refractions and two reflections. He also qualitatively explained the appearance of rainbow colors by comparing the refraction of light in a drop with refraction in a glass prism. Figure 1, which explains the path of a ray in a drop, is taken from the work of Descartes mentioned above. But the main merit of Descartes was that he quantitatively explained this phenomenon, for the first time using the law of refraction of light:

"I did not yet know why colors appear only at certain angles, until I took a pen and calculated in detail the course of all the rays that fall on different points of the water drop, in order to find out at what angles they can enter our eye after two refractions. and one or two reflections, I then found that after one reflection and two refractions, there are many more rays that can be seen at an angle from 41° to 42° (with respect to the sunbeam) than those that can be seen under any smaller angle, and there is not one that would be visible at a larger one.Furthermore, I also found that after two reflections and two refractions, there are many more rays that fall into the eye at an angle from 51 ° to 52 ° than those that would fall at any greater angle, and there are none at all that would fall at a lesser one.

Thus, Descartes not only calculates the path of the rays, but also determines the angular distribution of the intensity of the light scattered by the drops.

With regard to colors, the theory was supplemented by Isaac Newton.

Isaac Newton

Although the multi-color spectrum of the rainbow is continuous, according to tradition, 7 colors are distinguished in it. It is believed that Isaac Newton was the first to choose the number 7, for which the number 7 had a special symbolic meaning(for Pythagorean, theological or morological reasons).

In the well-known Lectures on Optics, which were written in the 1570s but published after Newton's death in 1729, the following summary is given:
"Of the rays entering the ball, some leave it after one reflection, others after two reflections; there are rays emerging after three reflections and even more reflections. Since raindrops are very small relative to the distance to the observer's eye, it is not worth considering their size at all, but only the angles formed by the incident rays with the outgoing ones. Where these angles are largest or smallest, the outgoing rays are most concentrated. As various genera rays (rays different colors) make up different largest and smallest angles, then the rays that gather most densely at different places tend to manifest their own colors.

Newton's statement about the possibility of not taking into account the size of the drop, as well as the words of Descartes that the rainbow always appears in the same way with large and small drops, turned out to be inaccurate. A complete theory of the rainbow, taking into account the diffraction of light, which depends on the ratio of the wavelength of light and the size of the drop, was built only in the 19th century by J.B. Airy (1836) and J.M. Pernther (1897).

Refraction and reflection of a ray in a drop of water.

The drawing of Descartes, which we reproduced as a relic, has one "methodological" imperfection. To an unprepared reader it may seem that both rainbows, external and internal, are due to different ways reflections in the same drop. It would be better to depict two drops: one related to the lower rainbow, the other to the upper one, leaving each with one way of reflection, as shown in Fig. 2. For ease of perception, in both cases the direction of the sunbeam incident on the droplet is taken as the abscissa axis. The y coordinate characterizing the point of incidence of the beam on the droplet will be called the impact parameter.

From fig. 2a, it can be seen that an incident ray with one reflection can be perceived by an observer only if the point of incidence belongs to the upper part of the drop (y > 0). On the contrary, with two reflections this will be possible for those rays that fall on lower part drops (y< 0).

Let us first assume that the drop is in a vertical plane passing through the position of the Sun and the observer's eye. Then the incident, refracted and reflected rays lie in the same plane. If α 1 is the angle of incidence, and α 2 is the angle of refraction, then from fig. 2, a and b, the angle of the emerging beam with respect to the incident one in the first case will be equal to φ 1 = 4α 2 -2α 1 (1)
and in the second - φ 2 = π - 6α 2 + 2α 1 (2)
moreover, according to the law of refraction: sin α 2 = sin α 1 / n
where n in our case is the refractive index of water. In addition, assuming conditionally the radius of the drop as a unit of length, we have:

Accordingly, in the first and second cases. Therefore, from (1) and (2) we obtain
φ 1 =4 arcsin(y/n) - 2 arcsin y, y>0 (3)
φ 2 \u003d π + 6 arcsin (y / n) - 2 arcsin y, y<0 (4)

These two equations are the main ones for further consideration. It is easy to plot the angles φ 1 and φ 2 as functions of y. They are shown in fig. 3 for refractive index n=1.331 (red). We see that at the value of the impact parameter y≈0.85, the maximum of the angle φ 1 is reached, approximately equal to 42°, and the angle has a minimum of ~53° at y≈-0.95. Let us show that these extremal points correspond to the maximum intensity of the light reflected by the drop.

Let us consider some small range of change of the impact parameter (for definiteness in the first case) y, y + Δy. Using the graph, you can find the change in the angle φ in this interval Δφ. On fig. 3 shows that Δφ=Δy*tg β, where β is the angle that the tangent to the graph at a given point forms with the x-axis. The value of Δy is proportional to the intensity of light ΔI incident on the drop in this interval of the impact parameter. The same light intensity (more precisely, a value proportional to it) is scattered by the drop in the angular interval Δφ. We can write ΔI ~ Δy =Δy*ctg β. Therefore, the intensity of the light scattered by the drop per unit angle of scattering can be expressed as I(φ) = ΔI/Δφ ~ ctg β (5)

Since at the extreme points ctg β = ∞, the value (5) goes to infinity. Note that the positions of these extreme points for different colors are somewhat different, which makes it possible to observe the rainbow.

How to draw a rainbow

Now we can draw a diagram of the observation of the rainbow. Such a construction is shown in Fig. 4. First, draw the surface of the Earth and the observer standing on it. In front of the observer is a curtain of rain (shaded in grey). Then we depict the sun's rays, the direction of which depends on the height of the Sun above the horizon. We pass red and violet rays through the observer's eye at the above angles with respect to the sun's rays. One can be sure, on the basis of the results of the previous section, that these rays will arise as a result of scattering by the corresponding raindrops. At the same time, as follows from Fig. 2, the lower rainbow is due to scattering processes with one reflection, and the upper one - with two reflections. Pay attention to the alternation of colors: violet rays are external, and red rays are internal. It is obvious that rays of other colors in each rainbow are placed between red and violet in accordance with the values ​​of the refractive indices.

Recall that we have so far considered the image of a rainbow in a vertical plane passing through the eye of the observer and the position of the Sun. Let's draw a straight line passing through the eye of the observer parallel to the sun's beam. If the vertical plane is rotated around the indicated straight line, then its new position for observing the rainbow will be completely equivalent to the original one. Therefore, the rainbow has the shape of an arc of a circle, the center of which is located on the constructed axis. The radius of this circle (as seen in Fig. 4) is approximately equal to the observer's distance from the rain curtain.

Note that when observing a rainbow, the Sun should not be too high above the horizon - no more than 53.48 °. Otherwise, the pattern of rays in the figure will rotate clockwise, so that even the violet ray of the upper rainbow cannot reach the eye of an observer standing on the Earth. True, this will be possible if the observer rises to a certain height, for example, by plane. If the observer rises high enough, he will be able to see the rainbow in the form of a full circle.

Rainbow Formation Diagram

Rainbow Formation Diagram
1) spherical a drop 2) internal reflection 3) primary rainbow
4) refraction 5) secondary rainbow 6) incoming beam of light
7) the course of the rays during the formation of the primary rainbow

8) the course of rays during the formation of a secondary rainbow
9) observer 10) primary rainbow formation area
11) secondary rainbow formation area 12) droplet cloud

This description of the rainbow should be clarified taking into account the fact that the sun's rays are not strictly parallel. This is due to the fact that the rays falling on the drop from different points of the Sun have slightly different directions. The maximum angular divergence of the rays is determined by the angular diameter of the Sun, which is known to be approximately 0.5°. What does this lead to? Each drop emits into the eye of the observer not so monochromatic light as it would be in the case of strict parallelism of the incident rays. If the angular diameter of the Sun were noticeably greater than the angular distance between the violet and red rays, then the colors of the rainbow would be indistinguishable. Fortunately, this is not the case, although, undoubtedly, the overlapping of rays with different wavelengths affects the contrast of the colors of the rainbow. Interestingly, the finiteness of the angular diameter of the Sun was already taken into account in the work of Descartes.

Rainbow

Rainbow - this beautiful celestial phenomenon - has always attracted the attention of man. In the old days, when people still knew little about the world around them, the rainbow was considered a "heavenly sign." So, the ancient Greeks thought that the rainbow is the smile of the goddess Irida.

The rainbow is observed in the direction opposite to the Sun, against the background of rain clouds or rain. A multi-colored arc is usually located at a distance of 1-2 km from the observer, and sometimes it can be observed at a distance of 2-3 m against the background of water drops formed by fountains or water sprays.

The center of the rainbow is on the continuation of the straight line connecting the Sun and the eye of the observer - on the anti-solar line. The angle between the direction to the main rainbow and the anti-solar line is 41º - 42º

At the time of sunrise, the antisolar point is on the horizon line, and the rainbow looks like a semicircle. As the sun rises, the antisolar point falls below the horizon and the size of the rainbow decreases. It is only part of a circle.

Often there is a secondary rainbow, concentric with the first, with an angular radius of about 52º and the reverse arrangement of colors.

The main rainbow is formed by the reflection of light in water droplets. A secondary rainbow is formed as a result of a double reflection of light inside each drop. In this case, the rays of light exit the drop at different angles than those that produce the main rainbow, and the colors in the secondary rainbow are in reverse order.

The path of rays in a drop of water: a - with one reflection, b - with two reflections

At a Sun height of 41º, the main rainbow ceases to be visible and only a part of the secondary rainbow appears above the horizon, and at a Sun height of more than 52º, the secondary rainbow is not visible either. Therefore, in the middle equatorial latitudes, this natural phenomenon is never observed during the near noon hours.

The rainbow has seven primary colors that smoothly transition from one to another. The shape of the arc, the brightness of the colors, the width of the stripes depend on the size of the water droplets and their number. Large drops create a narrower rainbow, with sharply prominent colors, small drops create an arc that is blurry, faded and even white. That is why a bright narrow rainbow is visible in the summer after a thunderstorm, during which large drops fall.

The rainbow theory was first given in 1637 by René Descartes. He explained the rainbow as a phenomenon associated with the reflection and refraction of light in raindrops. The formation of colors and their sequence were explained later, after unraveling the complex nature of white light and its dispersion in a medium.

rainbow formation

We can consider the simplest case: let a beam of parallel solar rays fall on drops having the shape of a ball. A beam incident on the surface of a drop at point A is refracted inside it according to the law of refraction: n sin b \u003d n sin c, where n=1, n?1.33 are the refractive indices of air and water, respectively, b is the angle of incidence, and in- the angle of refraction of light.

Inside the drop, the ray AB goes in a straight line. At point B, the beam is partially refracted and partially reflected. It should be noted that the smaller the angle of incidence at point B, and hence at point A, the lower the intensity of the reflected beam and the greater the intensity of the refracted beam.

Beam AB after reflection at point B occurs at an angle `` = in gets to point C, where there is also a partial reflection and partial refraction of light. The refracted beam leaves the drop at an angle r, while the reflected one can go further, to point D, etc. Thus, the light beam in the drop undergoes multiple reflections and refractions. With each reflection, some of the rays of light come out and their intensity inside the drop decreases. The most intense of the rays emerging into the air is the ray that emerged from the drop at point B. But it is difficult to observe it, since it is lost against the background of bright direct sunlight. The rays refracted at point C, together, create a primary rainbow against the background of a dark cloud, and rays refracted at point D give a secondary rainbow, which is less intense than the primary one.

When considering the formation of a rainbow, one more phenomenon must be taken into account - the unequal refraction of light waves of different lengths, that is, light rays of different colors. This phenomenon is called dispersion. Due to dispersion, the angles of refraction r and the angle of deflection of rays in a drop are different for rays of different colors.

A rainbow is caused by the dispersion of sunlight in water droplets. In each droplet, the beam experiences multiple internal reflections, but with each reflection, part of the energy goes out. Therefore, the more internal reflections experienced by the rays in the drop, the weaker the rainbow. You can observe a rainbow if the Sun is behind the observer. Therefore, the brightest, primary rainbow is formed from rays that have experienced one internal reflection. They cross the incident rays at an angle of about 42°. The locus of points located at an angle of 42° to the incident beam is a cone, perceived by the eye at its top as a circle. When illuminated with white light, a colored band will be obtained, with the red arc always higher than the violet one.

Most often we see one rainbow. It is not uncommon for two rainbow stripes to appear simultaneously in the sky, located one after the other; an even greater number of celestial arcs are observed - three, four and even five at the same time. It turns out that a rainbow can arise not only from direct rays; often it appears in the reflected rays of the sun. This can be seen on the coast of sea bays, large rivers and lakes. Three or four rainbows - ordinary and reflected - sometimes create a beautiful picture. Since the rays of the Sun reflected from the water surface go from bottom to top, the rainbow formed in the rays can sometimes look completely unusual.

You should not think that a rainbow can be observed only during the day. It happens at night, however, always weak. You can see such a rainbow after a night rain, when the moon looks out from behind the clouds.

Some semblance of a rainbow can be obtained on such experience : It is necessary to illuminate a flask filled with water with sunlight or a lamp through a hole in a white board. Then a rainbow will become clearly visible on the board, and the angle of divergence of the rays compared to the initial direction will be about 41 ° - 42 °. Under natural conditions, there is no screen, the image appears on the retina of the eye, and the eye projects this image onto the clouds.

If a rainbow appears in the evening before sunset, then a red rainbow is observed. In the last five or ten minutes before sunset, all colors of the rainbow, except for red, disappear, it becomes very bright and visible even ten minutes after sunset.

A beautiful sight is a rainbow on the dew. It can be observed at sunrise on the grass covered with dew. This rainbow is shaped like a hyperbola.

The center of the circle described by the rainbow lies on a straight line passing through the observer and the Sun, at the antisolar point, while the Sun is always behind the observer, and it is impossible to see the Sun and the rainbow at the same time without the use of optical devices. The corner radius of the circle is 42 degrees. For an observer on the ground, a rainbow usually looks like an arc of a circle, the lower the Sun above the horizon, the closer the arc is to half the circle, and the height of the top of the rainbow above the earth is 42 degrees. The higher the observation point, the fuller the arc (you can also see a full circle from an airplane). When the Sun rises above 42 degrees above the horizon, the circle of possible occurrence of a rainbow is below ground level, and an observer located on its surface cannot see a rainbow. You can't get close to the rainbow, just like the horizon.

Physics of the rainbow

A rainbow occurs when sunlight is refracted and reflected by water droplets (rain or fog) floating in the atmosphere. These droplets deflect light of different colors in different ways (the refractive index of water for longer wavelength (red) light is less than for short wavelength (violet), so red light is deflected the weakest - by 137 ° 30 ', and violet is most strongly deflected by 139 ° 20'). As a result, white light is decomposed into a spectrum. The observer, who stands with his back to the light source, sees a multi-colored glow that comes from space along concentric circles (arcs).

For one reflection inside the drop, such an angle has one value, for two - another, and so on. This corresponds to the primary (first-order rainbow), secondary (second-order rainbow), etc. rainbow. Primary - the brightest, it takes away most of the light from the drop. In nature, a rainbow of a higher order is usually not visible, since it is very weak.

The appearance of a rainbow of the third order in natural conditions is extremely rare. It is believed that over the past 250 years there have been only five scientific reports on the observation of this phenomenon. At the same time, thanks to the use of special methods of photography and subsequent processing of the resulting photographs, it is possible to register rainbows of the fourth, fifth, and even, as expected, seventh orders.

Under laboratory conditions, it is possible to obtain rainbows of much higher orders. So, in an article published in 1998, it was stated that the authors, using laser radiation, managed to obtain a rainbow of the two hundredth order.

Fancy rainbows

Most often, a simple rainbow-arc is observed, but many other optical phenomena are known that occur for similar reasons or look similar. Among them, for example, hazy (white) rainbow, which occurs on very small fog droplets, and fiery rainbow(one of the types of halo) that occurs on cirrus clouds. It looks like a rainbow and a faint parhelion - a halo at 22 ° to the left and right of the sun. Can be seen at night moon rainbow .

When a rainbow appears over the surface of water (or over another reflective surface such as wet sand), a so-called reflected rainbow(eng. Reflection rainbow). It occurs when sunlight reflects off the surface of water before it hits raindrops where it is refracted. It is necessary that the water surface is large enough, calm and close to the rain wall. Due to the large number of conditions, a reflected rainbow is a rare occurrence.

The reflected rainbow crosses the main one at the horizon level, then passes over it. Since sunlight is pre-reflected from the water, the brightness of the reflected rainbow is lower than the main one.

Under certain circumstances, you can see a double, inverted or even ring rainbow. In fact, these are phenomena of another process - the refraction of light in ice crystals scattered in the atmosphere, and belong to the halo. For the appearance of an inverted rainbow in the sky (near-zenithal arc, zenithal arc - one of the halo types), specific weather conditions are required that are characteristic of the North and South Poles. An inverted rainbow is formed due to the refraction of light passing through the icicles of a thin curtain of clouds at a height of 7 - 8 thousand meters. The colors in such a rainbow are also reversed: purple is at the top, and red is at the bottom.

Research History

Although the multi-color spectrum of the rainbow is continuous, in many countries 7 or 6 (for example, in English-speaking countries) colors are distinguished in it. It is believed that I. Newton was the first to choose the number 7.

Mnemonic phrases

The colors in the rainbow are arranged in a sequence corresponding to the spectrum of visible light. In Russian, there are such mnemonic phrases for remembering this sequence:

• To ak about once F ak- h vonar G tin with broke f onar
• To every about hotnik well does h nat, G de with goes f azan

The phrases are the so-called acrostic.

In these phrases, the initial letter of each word corresponds to the initial letter of the name of a certain color.

• To every- red
• O hotnik- orange
• F does- yellow
• W nat- green
• G de- blue
• With goes- blue
• F azan- Violet

The colors in the phrase are listed according to the order of the colors in the rainbow, from red (longest wavelength visible light) to violet (shortest wavelength visible light).

Rainbow in history, mythology and culture

• In Scandinavian mythology, the rainbow is the Bivrest bridge, connecting Midgard (the world of people) and Asgard (the world of the gods); the red stripe of the rainbow is eternal fire, which is harmless to Ases, but will burn any mortal who tries to climb the bridge. Bifrost is guarded by As Heimdall.
• In ancient Indian mythology, the bow of Indra, the god of thunder and lightning.
• In ancient Greek mythology - the road of Irida, a messenger between the worlds of gods and people.
• In Armenian mythology, the rainbow is the belt of Tyr (originally the god of the sun, then the god of writing, arts and sciences).
• According to Slavic beliefs, the rainbow drinks water from lakes, rivers and seas, which then rains. Sometimes she swallows fish and frogs along with the water, so sometimes they fall from the sky. The appearance of a rainbow foreshadowed misfortune, and if a person manages to pass under the rainbow, then the man will become a woman, and the woman will become a man.
• According to the beliefs of many African peoples, in those places where the rainbow touches the ground, you can find a treasure (precious stones, cowrie shells or beads).
• In Australian Aboriginal mythology, the Rainbow Serpent is considered the patron of water, rain, and shamans.
• An Irish leprechaun hides a pot of gold where the rainbow touched the ground.
• In the Bible, the rainbow appeared after the global flood as a symbol of the forgiveness of mankind, the union of God and mankind (in the face / through Noah) and the fact that the flood will never happen again (Gen.).
  “I put My rainbow in the cloud, so that it may be a sign of the covenant between Me and between the earth. And it will be when I gather clouds over the earth, a rainbow will appear in the cloud. The interpreter of the Pentateuch of Rashi explains this phrase as follows: “When I gather clouds over the earth,” when My Attribute of Judgment prompts Me to bring darkness and death to the earth, then ... “a rainbow will appear in the cloud.” That is, a rainbow is shown in the sky when humanity deserves death for its sins. “And it shall come to pass, when I bring a cloud upon the earth, that a rainbow shall appear in the cloud; and I will remember my covenant, which is between me and between you, and between every living soul in all flesh; And there will be no more water as a flood to destroy all flesh.” According to the Talmud, during the life of the great righteous there is no need for this sign, since the Universe is protected from death by their presence.
• In Japanese mythology, the gods Izanagi and Izanami stood on the heavenly bridge, dipping a spear from it, the drops from which became islands.
• The image of the rainbow was the personal emblem of Catherine de' Medici.
• In the book by Frank Baum "The Wonderful Wizard of Oz" and in the film based on it, the girl Dorothy, passing under the rainbow, enters the Magic Land.

Rainbow and associated terms

Rainbow as a symbol

see also

Notes

1. , with. 38.
2. Minnart M. Light and color in nature. - M.: "Nauka", 1969. - S. 182. - 344 p.
3. Who is making the rainbow? (Fragment from the book by Ya. E. Geguzin "The Drop") // Science and Life. - 2016. - No. 10. - pp. 73-75.
4. It can be seen (this is also clearly seen in the figure) that a noticeable amount of light reflected-refracted in the drops also enters the inner region of the cone. And although there is no sharp maximum of intensity in this region, which makes the light in it practically devoid of color, however, the total amount of light entering here is quite large. When observing (and in photographs), you can often notice that the sky (like the landscape and everything in general) inside the rainbow arc is noticeably lighter.
5. From myth to reality: photos prove triple rainbows exist - Article on The Optical Society (OSA) website
6. Theusner M. Photographic observation of a natural fourth-order rainbow // Applied Optics. - 2011. - Vol. 50, no. 28. - P.F129-F133. - DOI:10.1364/AO.50.00F129.
7. Edens H.E. Photographic observation of a natural fifth-order rainbow // Applied Optics. - 2015. - Vol. 54, no. 4 . - P.B26-B34. - DOI:10.1364/AO.54.000B26.
8. Edens H.E., Konnen G.P. Probable photographic detection of the natural seventh-order rainbow // Applied Optics. - 2015. - Vol. 54, no. 4 . - P.B93-B96. - DOI:10.1364/AO.54.000B93.
9. Ng P. H., Tse M. Y., Lee W. K. Observation of high-order rainbows formed by a pendant drop (English) // Journal of Optical Society of America B. - 1998. - Vol. 15, no. eleven . - P. 2782-2787.
10. Rainbow - A polarized arch?
11. Reflection Rainbows
12. Reflection Bow Formation
13. How a rainbow appears (indefinite) .

Instruction

As Newton established, a white light beam is obtained as a result of the interaction of rays of different colors: red, orange, yellow, green, blue, indigo, violet. Each color is characterized by a specific wavelength and vibration frequency. At the boundary of transparent media, the speed and length of light waves change, the oscillation frequency remains the same. Each color has its own refractive index. The red beam deviates the least from the previous direction, orange a little more, then yellow, and so on. The violet ray has the highest refractive index. If a glass prism is installed in the path of a light beam, then it will not only deviate, but also break up into several rays of different colors.

And now . In nature, the role of a glass prism is played by raindrops that the sun's rays collide with when passing through the atmosphere. Since the density of water is greater, the light beam at the boundary of two media is refracted and decomposed into components. Further, the color rays move already inside the drop until they collide with its opposite wall, which is also the boundary of two media, and, moreover, has mirror properties. Most of the light flux after the secondary refraction will continue to move in the air behind the raindrops. Some part of it will be reflected from the back wall of the drop and will be released into the air after secondary refraction on its front surface.

This process occurs simultaneously in many drops. To see a rainbow, the observer must stand with his back to the Sun and face the wall of rain. Spectral rays emerge from raindrops at different angles. Only one ray enters the observer's eye from each drop. Rays emerging from neighboring drops merge, forming an arc. Thus, from the uppermost drops, rays of red color enter the eye of the observer, from those below - orange, and so on. Violet rays are the strongest. The purple stripe will be the bottom. A rainbow in shape can be seen when the Sun is at an angle of no more than 42° relative to the horizon. The higher the Sun rises, the smaller the size of the rainbow.

In fact, the described process is somewhat more complicated. The light beam inside the drop is reflected multiple times. In this case, not one color arc can be observed, but two - a rainbow of the first and second order. The outer arc of the first-order rainbow is colored red, the inner arc purple. In a second-order rainbow, the opposite is true. It usually looks much paler than the first, since the intensity of the light flux decreases with multiple reflections.

Much less often, three, four and even five colored arcs can be observed in the sky at the same time. This was observed, for example, by residents of Leningrad in September 1948. This is because rainbows can also occur in reflected sunlight. Such multiple color arcs can be observed over a vast body of water. In this case, the reflected rays go from bottom to top,

Whenever a rainbow appears, it is always formed by the play of light on water droplets. Usually these are raindrops, occasionally small drops of fog. On the smallest droplets, such as those that make up the clouds, the rainbow is not visible.

A rainbow occurs because the sun light is refracted by water droplets suspended in the air. These droplets deflect light of different colors differently, causing white light to decompose into a spectrum.

On a bright moonlit night you can see rainbow from the moon. Since human vision is designed so that in low light the eye does not perceive colors well, the lunar rainbow looks whitish; the brighter the light, the "more colorful" the rainbow.

According to an old English belief, a pot of gold can be found at the foot of every rainbow. Even now there are people who imagine that they can really get to the bottom of the rainbow and that a special flickering light is visible there.

It is quite obvious that the rainbow is not in any particular place, like the real thing; it is nothing but light coming from a certain direction.

Most often observed primary rainbow where light undergoes one internal reflection. The path of the rays is shown in the figure below. In the primary rainbow, the red color is outside the arc, its angular radius is 40-42 °.

Sometimes you can see another, less bright rainbow around the first one. This is secondary rainbow, in which the light is reflected twice in the drop. In the secondary rainbow, the "inverted" order of colors is purple on the outside and red on the inside. The angular radius of the secondary rainbow is 50-53°.

The order of the colors in the second rainbow is the reverse of the order in the first; they face each other with red stripes.

Rainbow Formation Diagram

1. spherical drop,
2. internal reflection,
3. primary rainbow,
4. refraction,
5. secondary rainbow,
6. incoming beam of light
7. the course of rays during the formation of the primary rainbow,
8. the path of rays during the formation of a secondary rainbow,
9. observer,
10. rainbow Formation Area,
11. region of rainbow formation.
12. region of rainbow formation.

The center of the circle described by the rainbow always lies on a straight line passing through the Sun (Moon) and the eye of the observer, that is, it is impossible to see the sun and the rainbow at the same time without using mirrors.

In fact, the rainbow is a complete circle. We can't follow it beyond the horizon just because we can't see the raindrops falling below us.

From an airplane or high ground, a full circle can be seen.

"Seven Colors of the Rainbow" exist only in the imagination. It's a rhetorical phrase that has lived on for so long because we rarely see things as they really are. In fact, the colors of the rainbow gradually turn into one another, and only the eye involuntarily combines them into groups.

The tradition of highlighting in the rainbow 7 colors went from Isaac Newton, for which the number 7 had a special symbolic meaning (for either Pythagorean or theological reasons). The tradition of distinguishing 7 colors in the rainbow is not universal, for example, Bulgarians have 6 colors in the rainbow.

To memorize the sequence of colors in the rainbow, there are mnemonic phrases, the first letters of each word in which correspond to the first letters in the names of the colors (Red, Orange, Yellow, Green, Cyan, Blue, Violet

"To every about hotnik well does h nat, G de with goes f azan". "How once Jacques the bell-ringer broke a lantern with his head".