A rainbow is a colourful bow or arc of light that appears in the sky after or during rain. A rainbow is one of the prime examples of various physical phenomena such as reflection, refraction, and dispersion of light. It also helps to verify that the sunlight is not white in colour, but consists of a spectrum of colours having different wavelengths. To understand how a rainbow is formed, one must have a basic understanding of light. The light obtained from the sunlight appears to be white in colour, but it contains a number of colours. The speed of light is approximately equal to 3 x 10^8 m/sec. The light radiations emitted by the sun are arranged according to their respective wavelengths and are represented with the help of an electromagnetic spectrum. The gamma radiations emitted by the sun have the highest wavelength and least frequency, while radio waves have the lowest wavelength and highest frequency. The light waves existing within the wavelength range 380-740 nanometres are visible to the human eye. This band of light is known as white light.
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Formation of a Rainbow
The formation of a rainbow is a meteorological phenomenon. The basic process of rainbow formation includes a light wave that gets split into multiple colours after passing through a water droplet. Here, each water droplet of the rain shower acts as a small prism. In detail, the formation of a rainbow can be described as a three-step process. The first step starts with the light wave striking the face or the front surface of the raindrop. This causes the wave to undergo the dispersion phenomenon and get split into seven different colours. The dispersed wave is also subjected to refraction due to the change in medium. The second step of rainbow formation is the total internal reflection of the wave, which takes place when the refracted wave proceeds further and strikes the back surface of the raindrop. This causes the spectrum of light to escape the raindrop and emerge out. The third and final step involves refraction of the light wave due to a change in medium.
Colours in a Rainbow
A rainbow consists of seven colours that are arranged with respect to their wavelengths. The red colour appears on the top or on the outer perimeter of the rainbow because it gets refracted at a steeper angle as compared to other colours. Similarly, the violet colour is seen on the bottom or on the inner boundary of the rainbow as it tends to experience the least steep angle of refraction out of all the colours. If the colours present in a rainbow are seen from the bottom to the top, then the set of seven colours is abbreviated as VIBGYOR. Here, V stands for violet, I stands for indigo, B means blue, G represents green, Y signifies yellow, O is for orange, and R means the red colour.
Viewing Conditions of a Rainbow
To get a clear view of a rainbow one must ensure that the following conditions are properly met:
1. The back of the viewer must face the sun.
2. The angle of elevation must be more than or equal to 40 degrees.
3. For a better view, the person must stand under the sky between the sun and the rain shower at a location that has minimum obstacles.
Why are Rainbows Curved?
A rainbow appears to be a half or semi-circle when seen from the ground; however, in reality, a rainbow is a complete circle of seven colours. This can be observed easily while looking at a rainbow from an aeroplane. The bottom half of the full rainbow gets blocked due to the ground, and only the top half curve of the circle is visible, which is why rainbows appear to be curved. The refraction, dispersion, and total internal reflection phenomena responsible for the formation of a rainbow happens all across the horizon. Most of the refracted white light gets scattered in the atmosphere and is not visible to the human eye. Only the light that is bent at an angle of 40 or 42 degrees is perceivable. The angle formed between the source of light, i.e., the sun, the observer, and the water droplets is majorly responsible for the curved or semi-circle shape of the rainbow. The low angle of the sun causes the rainbow to be more curved, while the high angle of the sun is responsible for the formation of a shallow rainbow.
Moonbow
A moonbow is a rainbow that usually emerges out during the night. Moonbows are observed when the moon is almost completely illuminated, i.e., the brightness level of the moon is approximately 85 per cent. The moon rarely gets lit up to this level, which means that the chances of viewing a moonbow are very low. The physical process of formation of a moonbow is similar to that of a rainbow. The only difference is that a moonbow makes use of moonlight as the illumination source rather than using the sunlight. Moonbows can be observed even in the absence of a rain shower. In such a case, the water droplets of melting hail and fog or the mould spores serve to be the prism that split moonlight into a multicoloured curve.
Nitpick: The formation of a rainbow is an optical phenomenon. The conditions that create it are meteorological.
The actual process is best envisioned not as a single ray, but as a wavefront hitting a spherical drop. Like a water wave hitting a floating beach ball, and then following this line as it enters the ball. The colors in each “single ray” in that wavefront do separate as you describe, but most re-combine with colors from other rays to make white light. You can see this inside the rainbow in your pictures, most notably in the lower-right of the first.
The drop acts more like a lens than a prism, which depends on recombination not happening. The three steps are:
(1) The light transmits into the drop (“refraction” means it changes direction as it transmits). This causes the wavefront to become focused onto the back of the drop. The extent of the wavefront is reduced to about a third of its original length. But the focused length depends on wavelength (“dispersion” does not mean “separation,” it means the results become a function of wavelength).
(2) MOST OF THE LIGHT TRANSMITS OUT OF THE DROP. Total Internal Reflection is impossible, because the angle of incidence on the back of the drop is equal to the angle of refraction as it entered. But some does reflect. The reflected wavefront is distorted slightly, but increases in extent.
(3) The process in step 2 is repeated, in theory indefinitely. At each encounter, the wavefront that is transmitted is bent back on itself at either end, like a used staple. After one internal reflection, it exits the drop in a cone about 40° wide from the original path of the light.
The interesting part is the bend in the staple-shape. There is much more light in this part, making the reflection brightest there. This is what makes the bright bands. Dispersion means the bright band is at a different angle for each color. But there is light of all colors inside the colored bands, so the sky between the bow and its center is brighter.
The secondary bow is about 130° wide, and centered on the sun. Since this is more than 90°, the secondary bow “wraps” around the top of the sky and is seen about 10° above the primary. The white part is above it; this can be seen in your picture of the full-circle bows. The colors are not reversed, they are seen upside-down.
Similar descriptions get passed from teacher to student because they seem so obviously correct. They aren’t.
Since the surface normal of a sphere includes a radius of that sphere, the path taken by any ray of light inside a spherical raindrop forms an isosceles triangle with the surface normal at either end of the path. So the angle of refraction as the light enters the drop – which by definition is less than the critical angle – is equal to the angle of incidence at the back of the drop. Total Internal Reflection is impossible.
You can’t explain rainbows by comparing them to how colors separate when a single ray of white light hits a prism. Because the ray right next to any one will separate differently in the drop, and the colors will recombine. Instead, think of the light like a wave in a pool that hits a floating ball.
The net effect on the line of this wave, after refracting as it enters the drop, reflecting off of the back, and refracting again as it exits, is to bend that line like a used staple. Because there is much more of the staple’s length in the part where it bends, the “staple of light” makes the reflection much brighter at the bend. That’s 40° for violet light, and 42° for red. This brightness is what makes the bright bands, but the band of each color inside the red contains dimmer portions of all the colors towards the red end of the spectrum. And inside the violet band, if you can see it at all, the rainbow still exists as white all the way to the horizon. This is clear in your photographs.