Math Is Fun Forum

City Quotes - VIII

1. Throughout my 20s and early 30s, I had jobs that I loved. I worked in city government. I ran a youth organization. I served as an associate dean at a university. And I couldn't imagine how a baby would fit into all of that. - Michelle Obama

2. I think Star City should have Unesco World Heritage status. It will need to be adapted a little bit and made more glamorous than it looks now, but it should definitely be protected for the future. - Valentina Tereshkova

3. I've shot many films in Hindi and some in Bangla in Kolkata. It's always a pleasure to be part of the city. - Waheeda Rehman

4. London is the most commercially important city in Europe, and it's the most populous city. It should be for the whole of the European continent what New York is to America. That's what it should be. - Boris Johnson

5. The country's top chefs, designers, media personalities and businesses are part of this dynamic city. We know that Chicagoans are used to the highest standards. - Ivanka Trump

6. I'd like to design something like a city or a museum. I want to do something hands on rather than just play golf which is the sport of the religious right. - Brad Pitt

7. You can't have a relationship when you're shooting a 14-hour day and your husband is shooting a 14-hour day in the same city. It's a time thing and it's a together thing. - Eva Longoria.

Rainbow

Gist

When sunlight hits a rain droplet, some of the light is reflected. The electromagnetic spectrum is made of light with many different wavelengths, and each is reflected at a different angle. Thus, spectrum is separated, producing a rainbow.

VIBGYOR (Violet–Indigo–Blue–Green–Yellow–Orange–Red) is a popular mnemonic device used for memorizing the traditional optical spectrum.

A rainbow has seven colors because water droplets in the atmosphere break sunlight into seven colors. A prism similarly divides light into seven colors. When light leaves one medium and enters another, the light changes its propagation direction and bends. This is called refraction.

When sunlight hits a rain droplet, some of the light is reflected. The electromagnetic spectrum is made of light with many different wavelengths, and each is reflected at a different angle. Thus, spectrum is separated, producing a rainbow.

Summary

A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.

Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground,[3] and centered on a line from the Sun to the observer's eye.

In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.

In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, with red on the inner side of the arc. This is caused by the light being reflected twice on the inside of the droplet before leaving it.

Visibility

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle. Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening. The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the Sun. The result is a luminous rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible. It appears about 10° outside of the primary rainbow, with inverse order of colours.

The rainbow effect is also commonly seen near waterfalls or fountains. In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white.

It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an angle of view of 84°. For a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be required. Now that software for stitching several images into a panorama is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames.

From above the Earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle. This phenomenon can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°.

The sky inside a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light over an entire circular disc in the sky. The radius of the disc depends on the wavelength of light, with red light being scattered over a larger angle than blue light. Over most of the disc, scattered light at all wavelengths overlaps, resulting in white light which brightens the sky. At the edge, the wavelength dependence of the scattering gives rise to the rainbow.

The light of a primary rainbow arc is 96% polarised tangential to the arc. The light of the second arc is 90% polarised.

Details

A rainbow is a multicolored arc made by light striking water droplets.

The most familiar type rainbow is produced when sunlight strikes raindrops in front of a viewer at a precise angle (42 degrees). Rainbows can also be viewed around fog, sea spray, or waterfalls.

A rainbow is an optical illusion—it does not actually exist in a specific spot in the sky. The appearance of a rainbow depends on where you're standing and where the sun (or other source of light) is shining.

The sun or other source of light is usually behind the person seeing the rainbow. In fact, the center of a primary rainbow is the antisolar point, the imaginary point exactly opposite the sun.

Rainbows are the result of the refraction and reflection of light. Both refraction and reflection are phenomena that involve a change in a wave's direction. A refracted wave may appear "bent," while a reflected wave might seem to "bounce back" from a surface or other wavefront.

Light entering a water droplet is refracted. It is then reflected by the back of the droplet. As this reflected light leaves the droplet, it is refracted again, at multiple angles.

The radius of a rainbow is determined by the water droplets' refractive index. A refractive index is the measure of how much a ray of light refracts (bends) as it passes from one medium to another—from air to water, for example. A droplet with a high refractive index will help produce a rainbow with a smaller radius. Saltwater has a higher refractive index than freshwater, for instance, so rainbows formed by sea spray will be smaller than rainbows formed by rain.

Rainbows are actually full circles. The antisolar point is the center of the circle. Viewers in aircraft can sometimes see these circular rainbows.

Viewers on the ground can only see the light reflected by raindrops above the horizon. Because each person's horizon is a little different, no one actually sees a full rainbow from the ground. In fact, no one sees the same rainbow—each person has a different antisolar point, each person has a different horizon. Someone who appears below or near the "end" of a rainbow to one viewer will see another rainbow, extending from his or her own horizon.

Colors

A rainbow shows up as a spectrum of light: a band of familiar colors that include red, orange, yellow, green, blue, and violet. The name "Roy G. Biv" is an easy way to remember the colors of the rainbow, and the order in which they appear: red, orange, yellow, green, blue, indigo, and violet. (Many scientists, however, think "indigo" is too close to blue to be truly distinguishable.)

White light is how our eyes perceive all the colors of the rainbow mixed together. Sunlight appears white.

When sunlight hits a rain droplet, some of the light is reflected. The electromagnetic spectrum is made of light with many different wavelengths, and each is reflected at a different angle. Thus, spectrum is separated, producing a rainbow.

Red has the longest wavelength of visible light, about 650 nanometers. It usually appears on the outer part of a rainbow's arch. Violet has the shortest wavelength (about 400 nanometers) and it usually appears on the inner arch of the rainbow.

At their edges, the colors of a rainbow actually overlap. This produces a sheen of "white" light, making the inside of a rainbow much brighter than the outside.

Visible light is only part of a rainbow. Infrared radiation exists just beyond visible red light, while ultraviolet is just beyond violet. There are also radio waves (beyond infrared), x-rays (beyond ultraviolet), and gamma radiation (beyond x-rays). Scientists use an instrument called a spectrometer to study these invisible parts of the rainbow.

Rainbow Variations:

Glow

The atmosphere opposite a rainbow, facing the sun, is often glowing. This glow appears when rain or drizzle is falling between the viewer and the sun.

The glow is formed by light passing through raindrops, not reflected by them. Some scientists call this glow a zero-order glow.

Double Rainbow

Sometimes, a viewer may see a "double rainbow." In this phenomenon, a faint, secondary rainbow appears above the primary one.

Double rainbows are caused by light being reflected twice inside the raindrop. As a result of this second reflection, the spectrum of the secondary rainbow is reversed: red is on the inner section of the arch, while violet is on the outside.

Higher-Order Rainbows

Light can be reflected from many angles inside the raindrop. A rainbow's "order" is its reflective number. (Primary rainbows are first-order rainbows, while secondary rainbows are second-order rainbows.) Higher-order rainbows appear to viewers facing both toward and away from the sun.

A tertiary rainbow, for example, appears to a viewer facing the sun. Tertiary rainbows are third-order rainbows—the third reflection of light. Their spectrum is the same as the primary rainbow.

Tertiary rainbows are difficult to see for three main reasons. First, the viewer is looking toward the sun—the center of a tertiary rainbow is not the antisolar point, it's the sun itself. Second, tertiary rainbows are much, much fainter than primary or secondary rainbows. Finally, tertiary rainbows are much, much broader than primary and secondary rainbows.

Quaternary rainbows are fourth-order rainbows, and also appear to viewers facing the sun. They are even fainter and broader than tertiary rainbows.

Beyond quaternary rainbows, higher-order rainbows are named by their reflective number, or order. In the lab, scientists have detected a 200th-order rainbow.

Twinned Rainbow

A twinned rainbow is two distinct rainbows produced from a single endpoint. Twinned rainbows are the result of light hitting an air mass with different sizes and shapes of water droplets—usually a raincloud with different sizes and shapes of raindrops.

Supernumerary Rainbow

A supernumerary rainbow is a thin, pastel-colored arc usually appearing below the inner arch of a rainbow. Supernumeraries are the result of the complex interaction of light rays in an air mass with small, similarly sized water droplets.

In supernumerary formation, reflected rays interact in ways called constructive and destructive interference. Light is either reinforced (constructive interference) or canceled out (destructive interference). Interference is responsible for the lighter hues and narrower bands of supernumeraries.

Reflection Rainbow

A reflection rainbow appears above a body of water. A primary rainbow is reflected by the water, and the reflected light produces a reflection rainbow. Reflection rainbows do not mirror the primary rainbow—they often appear to stretch above it.

Reflected Rainbow

A reflected rainbow appears directly on the surface of a body of water. A reflected rainbow is created by rays of light reflected by the water surface, after the rays have have passed through water droplets. Reflected rainbows to not appear to form a circle with a primary rainbow, although their endpoints seem to meet in an almond-shaped formation.

Red Rainbow

A red rainbow, also called a monochrome rainbow, usually appears at sunrise or sunset. During this time, sunlight travels further in the atmosphere, and shorter wavelengths (blue and violet) have been scattered. Only the long-wavelength red colors are visible in this rainbow.

Fogbow

A fogbow is formed in much the same way as a primary rainbow. Light in a fogbow is refracted and reflected by fog (water droplets suspended in air). A fogbow seen in the clouds is called a cloudbow.

Because the water droplets in fog are much smaller than raindrops, fogbows have much fainter colors than rainbows. In fact, some fogbows have few detectable colors at all and appear mostly white, with a reddish tinge on their outer edge and a bluish tinge on their inner edge.

Moonbow

A moonbow, also called a lunar rainbow, is a rainbow produced by light reflected by the moon.

The moon itself does not emit light, of course. Moonlight is reflected sunlight, as well as some starlight and "Earthlight." Because moonlight is so much fainter than sunlight, moonbows are dimmer than rainbows.

Rainbows in Myth

Rainbows are part of the myths of many cultures around the world. Rainbows are often portrayed as bridges between people and supernatural beings. In Norse mythology, for instance, a rainbow called the Bifrost connects Earth with Asgard, where the gods live. In the ancient beliefs of Japan and Gabon, rainbows were the bridges that human ancestors took to descend to the planet.

The shape of a rainbow also resembles the bow of an archer. Hindu culture teaches that the god Indra uses his rainbow bow to shoot arrows of lightning.

Rainbows are usually positive symbols in myths and legends. In the Epic of Gilgamesh and, later, the Christian Bible, the rainbow is a symbol from a deity (the goddess Ishtar and the Hebrew God) to never again destroy Earth with floods.

Sometimes, however, rainbows are negative symbols. In parts of Burma, for instance, rainbows are considered demons that threaten children. Tribes throughout the Amazon Basin associate rainbows with disease.

Perhaps the most famous piece of mythology surrounding rainbows is the Irish legend of the pot of gold at the end of a rainbow. The gold is guarded by a tricky leprechaun, but—because no one sees the same rainbow and rainbows don't "end" (they're circles)—no one ever finds the gold or the magical creature.

Rainbow Flags

Rainbow flags usually appear as stripes (bands) of at least five different colors. Rainbow flags have long represented groups championing diversity, respect, and inclusiveness.

The Wiphala is a type of rainbow flag. It is a symbol of communities indigenous to the Andes, stretching from modern-day Ecuador to Chile. A Wiphala has been an official flag of Bolivia since 2009, when the nation elected its first indigenous president, Evo Morales. The Wiphala features a diagonal patchwork design with squares in different rainbow colors. Different arrangements of patchwork squares represent different Andean communities.

The Buddhist flag, designed in the 19th century, is flown by Buddhists around the world. It is a vertical arrangement of six bands, each representing a different aspect of Buddhism, from kindness to moderation, blessings to wisdom.

The Jewish Autonomous Oblast, a community on Russia's border with China, is represented by a seven-banded rainbow flag. The seven bands symbolize the seven branches of a menorah.

Additional Information - I

A rainbow is a series of concentric coloured arcs that may be seen when light from a distant source—most commonly the Sun—falls upon a collection of water drops—as in rain, spray, or fog. The rainbow is observed in the direction opposite to the Sun.

The coloured rays of the rainbow are caused by the refraction and internal reflection of light rays that enter the raindrop, each colour being bent through a slightly different angle. Hence, the composite colours of the incident light will be separated upon emerging from the drop. The most brilliant and most common rainbow is the so-called primary bow, which results from light that emerges from the drop after one internal reflection.

Although light rays may exit the drop in more than one direction, a high density of the rays emerge at a minimum angle of deviation from the direction of the incoming rays. The observer thus sees the highest intensity looking at the rays that have minimum deviation, which form a cone with the vertex in the observer’s eye and with the axis passing through the Sun. Light emerging from raindrops after one internal reflection has a minimum deviation of about 138° and thus the greatest intensity in the directions forming a cone with an angular radius of about 42°, with arcs (from inside to outside) of violet, indigo, blue, green, yellow, orange, and red.

Occasionally, a secondary bow may be observed, which is considerably less intense than the primary bow and has its colour sequence reversed. The secondary rainbow has an angular radius of about 50° and hence is seen outside of the primary bow. This bow results from light that has undergone two internal reflections within the water drop. Higher-order rainbows, resulting from three or more internal reflections, are exceedingly weak and hence are rarely observed.

Occasionally, faintly coloured rings are seen just inside of the primary bow. These are called supernumerary rainbows; they owe their origin to interference effects on the light rays emerging from the water droplet after one internal reflection.

Additional Information - II

A rainbow is a multicolored arc, or curved line, in the sky. Most rainbows form when the Sun’s rays strike raindrops falling from faraway rain clouds. Rainbows appear in the part of the sky opposite the Sun, usually in the early morning or late afternoon. From inside to outside, the colors of a rainbow are violet, indigo, blue, green, yellow, orange, and red.

Sunlight travels through space in the form of waves. Scientists use an idea called wavelength to describe these waves. Some light waves have long wavelengths, while others have short wavelengths. Light waves with different wavelengths appear as different colors. Usually all light waves blend together to form white light. But when light waves pass through raindrops, they separate. This happens because the raindrops bend light waves with different wavelengths by a different amount. The separated light waves appear as the colors of a rainbow.

The brightest and most common type of rainbow is called a primary bow. Sometimes a fainter rainbow forms outside the primary bow. This is called a secondary bow or, sometimes, a double rainbow. A secondary bow forms when the light bends twice inside the water drops. The first bend makes the primary bow, and the second bend makes the secondary bow. The colors in the secondary bow appear in the opposite order of the colors in the primary bow.