Rainbows - How Are They Formed?

Rainbows are one of the most admired meteorological phenomena across the globe, but how are they formed?
Rainbows are formed when light from the sun is scattered by water droplets (e.g. raindrops or fog) through a process called refraction. Refraction occurs when the light from the sun changes direction when passing through a medium denser than air, such as a raindrop. Once the refracted light enters the raindrop, it is reflected off the back and then refracted again as it exits and travels to our eyes.

But how does refraction result in a rainbow’s colours?


Sunlight is made of many different wavelengths, or colours, that travel at different speeds when passing through a medium. This causes the white light to split into different colours. Longer wavelengths appear as red and shorter wavelengths appear as blue or violet. We see the colour spectrum of the rainbow as the light passes through the raindrop at different angles of approximately two degrees, from red to violet. This is not a true spectrum as the colours mix and blur throughout the spectacle. The angle of scatter from raindrops is different for everyone which means that every rainbow is unique to the observer.
However, for the observer to see a rainbow, they must be in a specific position relative to the sun and water droplets -
The observer must be positioned so the sun is behind them.
The lower the sun in the sky, the more of an arc of a rainbow the observer will see – it must be less than 42° in the sky.
Water droplets such as rain or fog must be in front of the observer.

Why do rainbows form instead of just straight bands of colors? And why do they appear to touch the ground?

Sunlight passing through raindrops causes rainbows via a process called refraction, which is the bending of light as it passes from one medium to another. This is analagous to pushing a shopping cart at the edge of a parking lot: if the wheels on one side roll off the pavement onto an adjacent area of grass, the cart will start to turn toward the grass. This is because the wheels moving on the pavement are able to roll faster than the wheels on the grass.

In the case of a rainbow, when sunlight hits a raindrop it does not move as fast through the water as it does through the atmosphere, so it bends a little. The light then turns again as it moves out of the raindrop and back into the air at its original speed. When light hits the rain at just the right angle, it is refracted through a raindrop and into our eyes, causing us to see a rainbow.

But how does the "white" sunlight produce a multicolored rainbow? Sunlight, or "white" light, is actually made up of continuous bands of different colored light--red, orange, yellow, green, blue, indigo and violet. Each color has a different wavelength, or frequency, which refracts slightly differently when it passes from one medium to another. As a result, white light can be broken up into its component colors by being passed through certain medium. For example, a prism can also create rainbows because the glass, like the raindrop, bends the different colors of light at slightly different angles.

Longer wavelengths are bent at larger angles, so longer wavelengths are bent less than shorter wavelengths. When sunlight hits a raindrop, the red light waves are bent at an angle of 42 degrees from their original direction from the sun. Shorter violet light waves are only bent at an angle of 40 degrees. The other colored light frequencies are bent at angles in between these two. This is why we see rainbows as a continuous band of colors with red on top and violet on the bottom.

A typical raindrop is also spherical and therefore its effect on sunlight is symmetrical about an imagined axis connecting the center of the drop and the sun. Because of this symmetry, so long as the raindrop is viewed along a line of sight that makes a 40- to 42-degree angle with the direction of the sun, the various colors of light will be visible. Thus, a rainbow is actually a circle centered on the point directly opposite the sun from the observer--the so-called antisolar point--with an angular radius of 42 degrees.

We don't actually see the full circle because the earth gets in the way. The closer the sun is to the horizon, the more of the circle we see. Right at sunset, we would see a full semicircle of a rainbow with the top of the arch 42 degrees above the horizon. The higher the sun is in the sky, the less of a rainbow is visible above the horizon.

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.
Eruption of Castle Geyser, Yellowstone National Park, with double rainbow seen in the mist
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.
Rainbow

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.
Light of primary rainbow arc is 96% polarised tangential to the arch. Light of second arc is 90% polarised.

Why Do Rainbows Appear?

What color is sunshine? When we see the light of the Sun streaming through the windows, it appears colorless. Even though we can't see it, this “white" light is actually made up of many different colors of light. Each of these colors has a different wavelength.
In 1666, the famous scientist Isaac Newton discovered that if sunlight passed through a triangular piece of glass called a prism, the white light would split into a band of colors. This band of colors was made up of red, orange, yellow, green, blue, indigo, and violet light. These are the colors of the rainbow in order. Some people remember them by the name ROY G. BIV.
The “birth" of a rainbow after a rainstorm works in a similar way. After it rains, the air in the atmosphere is filled with raindrops. Each raindrop acts like a tiny prism. If sunlight passes through raindrops at just the right angle, the light is split into an arc of colors with red on the outside of the band and violet on the inside.
The most brilliant rainbow displays occur when part of the sky is still dark with rainclouds and the viewer is in a sunny spot facing the Sun. This creates a very bright and vivid rainbow against the darkened background.
Sometimes it is possible to see a second arc or “double rainbow." This is caused by a double reflection of sunlight inside the raindrops. The double reflection causes the colors of a second rainbow to arrange in the opposite order of the colors on a primary arc.
Secondary rainbows are fainter than primary rainbows for two reasons. First, the double reflection allows more light to escape. Second, a double rainbow arcs above the primary rainbow, which means it is spread out over a greater area of sky.
If you're hoping to find a pot of gold at the end of the rainbow, you may be disappointed to find out there is no real end of the rainbow. This is because rainbows do not actually exist in a particular location in the sky. A rainbow's position depends on the location of the observer and the position of the Sun.
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