Now if you are anything like me then you would have at some point looked up at wonder at the awesome site of a rainbow. As a child you may have been told that there is a pot of gold at the end of the rainbow or you may have been told that they never actually end. Funny side story to this. When my dad was a kid, he was told that there was a pot of gold at the end of the rainbow. So on one sunny but rainy afternoon, he actually decided to go and find this pot of gold, only to get very lost for several days. Apparently they had the police looking for him everywhere and were almost coming to the conclusion that he was lost for good 😀 but I digress.
Here I am going to explain exactly what a rainbow is and how they come to form. There will, as always be some pictures and a very informative video (from the early 90s which is pretty retro baby).
The Basics of a Rainbow
A rainbow is light split into it’s separate colours as the light passes through droplets of water. An example of this is when it is raining but the Sun is still shining. As the light from the Sun passes through the rain droplets, the light is refracted (split) and depending on the angle of the light shining on the single rain drop will determine the colour that is viewed.
The technical details of rainbow formation were first analyzed by Isaac Newton in 1665. His brilliant optics work concerning reflection and refraction certainly does not detract from the beauty and promise of the rainbow. On the contrary, Newton’s scientific insights show the marvelous complexity of creation. The rainbow is a gracious pledge that God will not destroy the earth a second time with a worldwide flood (Genesis 9:11-17):
“I have set my rainbow in the clouds, and it will be the sign of a covenant between me and the earth… Never again will the waters become a flood to destroy all life.” (Genesis 9:13,15).
A rainbow occurs when raindrops and sunshine cross paths. Sunlight consists of all the colors of light, which add together to make white illumination. When sunlight enters water drops, it reflects off their inside surfaces. While passing through the droplets, the light also separates into its component colors, which is similar to the effect of a glass prism. Each falling water drop actually flashes its colors to the observer for just an instant, before another drop takes its place.
A rainbow is usually seen in the opposite direction in the sky from the sun. The rainbow light is reflected to the eye at an angle of 42 degrees to the original ray of sunlight. The bow shape is actually part of a cone of light that is cut off by the horizon. If you travel toward the end of a rainbow, it will move ahead of you, maintaining its shape. Thus, there is no real end to a rainbow, and no pot of gold waiting there. Because the 42 degree angle is measured from each individual observer’s eye, no two people see exactly the same rainbow. Every person is at the center of his or her own particular cone of colored light. From the high vantage point of a mountaintop or an airplane a complete circle of rainbow light sometimes can be seen.
The bright, primary rainbow has red on the outer edge and blue within. Higher in the sky there is always another, dimmer rainbow with the order of colors reversed. This secondary rainbow results from additional reflection of sunlight through the raindrops. It is most visible when there are dark clouds behind it. Look for the second bow high in the sky the next time rainbow colors appear. Some observers have even reported seeing third and fourth rainbows above the first two.
The Colours of a Rainbow
> A rainbow is a multi-colored arc that forms in the sky.
> Rainbows are created by both reflection and refraction (bending) of light in water droplets in the atmosphere, which results in a spectrum of light appearing.
> A rainbow is in fact a full circle of light. However, due to most people viewing a rainbow on the ground we only see a semi-circle or arc of the rainbow.
> A rainbow is not situated at a specified distance, instead it will always be visible to a person at the precise angle freshwater droplets reflect the light which is 42 degrees in the opposite direction of the sun.
> A rainbow is not an object, it cannot be approached or physically touched.
> No two people see the same rainbow, in fact even our individual eyes see slightly different rainbows. If someone appears to be standing under a rainbow you can see, they will see a different rainbow at the same angle but further away.
> Rainbows can be seen not just in rain but also mist, spray, fog, and dew, whenever there are water drops in the air and light shining from behind at the right angle.
> Sir Isaac Newton identified the 7 colors of the visible spectrum that together make up white light. All of which are present in a rainbow in the order red, orange, yellow, green, blue, indigo and violet (the acronym or name ROY G BIV is a good way to remember these colors and their order).
> Most rainbows we see will be a “primary rainbow” whereby the color red can be seen on the outer edge through to violet on the inner edge.
> The sky within a primary rainbow is brighter than the sky outside of the arc. This is due to the fact that the millions of droplets needed to make a rainbow are spherical and overlap to create white light. At the edge however, these colored discs don’t overlap so display their individual colors producing the rainbow arc.
> A “double rainbow” is where a second, much fainter arc can be seen outside of the primary arc. This is caused by the light reflecting twice inside the water droplets. As a result of this double reflection the colors of the second arc are inverted with violet on the outer edge and red on the inner edge.
> The dark, unlit sky between the primary arc and secondary arc is called Alexander’s band, after Alexander of Aphrodisias who first described it in 200 AD.
> Very rarely, light can be reflected 3 or 4 times within a water droplet which produces even fainter tertiary (third) and quaternary (fourth) rainbows in the direction of the sun.
> A “moonbow” is a rare lunar rainbow or night time rainbow produced by light from the moon. Our eyes see it as white even though all colors are faintly present.
> A “fogbow” is formed by cloud and fog droplets, they are almost white with very faint colors visible. Fogbows are quite large and much broader than a rainbow.
Rainbows in a little More Detail
A rainbow is an optical and meteorological phenomenon that is caused by both reflection and refraction of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be full circles, however, the average observer sees only an arc, formed by illuminated droplets above the ground and centred 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 (bent) 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, red facing toward the other one in both rainbows. This second rainbow is caused by light reflecting twice inside water droplets.
A rainbow is not located at a specific distance from the observer, but comes from an optical illusion caused by any water droplets viewed from a certain angle relative to a light source. Thus, a rainbow is not an object and cannot be physically approached. Indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems “under” or “at the end of” a rainbow, the second observer will see a different rainbow—farther off—at the same angle as seen by the first observer.
Rainbows span a continuous spectrum of colours. Any distinct bands perceived are an artefact of human colour vision, and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side. For colours seen by the human eye, the most commonly cited and remembered sequence is Newton’s sevenfold red, orange, yellow, green, blue, indigo and violet, remembered by the mnemonic, Richard Of York Gave Battle In Vain (ROYGBIV). 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 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.
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 lens with a focal length of 19 mm or less wide-angle lens would be required. Now that powerful 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 an aeroplane, it is possible to see the whole circle of the rainbow, with the plane’s shadow in the centre. This phenomenon can be confused with the glory, but a glory is usually much smaller, covering only 5–20°.
At good visibility conditions (for example, a dark cloud behind the rainbow), the second arc can be seen, with inverse order of colours. At the background of the blue sky, the second arc is barely visible.
As is evident by the photos on this page, the sky inside of a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light in a many-layered stack of coloured discs over an entire circular disc in the sky, but only the edge of the disc, which is coloured, is what is called a rainbow. Alistair Fraser, coauthor of The Rainbow Bridge: Rainbows in Art, Myth, and Science, explains: “Each color has a slightly different-sized disc and since they overlap except for the edge, the overlapping colors give white, which brightens the sky on the inside of the circle. On the edge, however, the different-sized colored discs don’t overlap and display their respective colors—a rainbow arc.”
Light of primary rainbow arc is 96% polarised tangential to the arch. Light of second arc is 90% polarised.
When sunlight encounters a raindrop, part is reflected but part enters, being refracted at the surface of the raindrop. When this light hits the back of the drop, some of it is reflected off the back. When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop. (The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow.) The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°. This angle is independent of the size of the drop, but does depend on its refractive index. Seawater has a higher refractive index than rain water, so the radius of a “rainbow” in sea spray is smaller than a true rainbow. This is visible to the naked eye by a misalignment of these bows.
The reason the returning light is most intense at about 42° is that this is a turning point – light hitting the outermost ring of the drop gets returned at less that 42°, as does the light hitting the drop nearer to its centre. There is a circular band of light that all gets returned right around 42°. If the sun were a laser emitting parallel, monochromatic rays, then the luminance (brightness) of the bow would tend toward infinity at this angle (ignoring interference effects). (See Caustic (optics).) But since the sun’s luminance is finite and its rays are not all parallel (it covers about half a degree of the sky) the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its wavelength, and hence its colour. This effect is called dispersion. Blue light (shorter wavelength) is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside. The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. (A “rainbow” formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow.)
The light at the back of the raindrop does not undergo total internal reflection, and some light does emerge from the back. However, light coming out the back of the raindrop does not create a rainbow between the observer and the sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow.
A rainbow does not exist at one particular location. Many rainbows exist; however, only one can be seen depending on the particular observer’s viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer’s eye. This light is what constitutes the rainbow for that observer. The whole system composed by the sun’s rays, the observer’s head, and the (spherical) water drops has an axial symmetry around the axis through the observer’s head and parallel to the sun’s rays. This already explains the circular arc shape of the rainbow: whatever is the effect of any water’s drop on the observer, rotating around the axis must leave it unchanged. Therefore, the bow appears to be centered on the shadow of the observer’s head, or more exactly at the antisolar point (which is below the horizon during the daytime, unless the observer is sufficiently far above the earth’s surface), and forms a circle at an angle of 40–42° to the line between the observer’s head and its shadow. As a result, if the sun is higher than 42°, then the rainbow is below the horizon and usually cannot be seen as there are not usually sufficient raindrops between the horizon (that is: eye height) and the ground, to contribute. Exceptions occur when the observer is high above the ground, for example in an aeroplane (see above). Alternatively, you might see the full circle in a fountain or waterfall spray if you have the right vantage point.
Secondary rainbows are caused by a double reflection of sunlight inside the raindrops, and appear at an angle of 50–53°. As a result of the second reflection, the colours of a secondary rainbow are inverted compared to the primary bow, with blue on the outside and red on the inside. The secondary rainbow is fainter than the primary because more light escapes from two reflections compared to one and because the rainbow itself is spread over a greater area of the sky. The dark area of unlit sky lying between the primary and secondary bows is called Alexander’s band, after Alexander of Aphrodisias who first described it.
In 2010, a viral video of a double rainbow was posted on YouTube by Paul “Bear” Vasquez. The clip, filmed in his front yard just outside Yosemite National Park in the U.S. state of California, shows his ecstatic reaction to a double rainbow. As of April 2014, the video has accumulated more than 39.5 million views on YouTube.
Unlike a double rainbow that consists of two separate and concentric rainbow arcs, the very rare twinned rainbow appears as two rainbow arcs that split from a single base. The colours in the second bow, rather than reversing as in a double rainbow, appear in the same order as the primary rainbow. It is sometimes even observed in combination with a double rainbow. The cause of a twinned rainbow is the combination of different sizes of water drops falling from the sky. Due to air resistance, raindrops flatten as they fall, and flattening is more prominent in larger water drops. When two rain showers with different-sized raindrops combine, they each produce slightly different rainbows which may combine and form a twinned rainbow.
Until recently, scientists could make only an educated guess as to why a twinned rainbow does appear, even though extremely rarely. It was thought that most probably non-spherical raindrops produced one or both bows, with surface tension forces keeping small raindrops spherical, while large drops were flattened by air resistance; or that they might even oscillate between flattened and elongated spheroids. However, in 2012 a new technique was used to simulate rainbows, enabling the accurate simulation of non-spherical particles. Besides twinned rainbows, this technique can also be used to simulate many different rainbow phenomena including double rainbows and supernumerary bows.
Full circle rainbow
A complete rainbow’s shape appears as a circle, though it is by definition a cone. A full circle rainbow can be seen only from above, as from an aircraft. The height of the sun when the rainbow appears determines how much of the circle can be seen; as the sun approaches the horizon, more of the circle comes into view, whereas the higher the sun is in the sky, the smaller the arch of the rainbow becomes.
Alexander’s Dark Band
Alexander’s band or Alexander’s dark band is an optical phenomenon associated with rainbows which was named after Alexander of Aphrodisias who first described it in 200 AD. It occurs due to the deviation angles of the primary and secondary rainbows. Both bows exist due to an optical effect called the angle of minimum deviation. The refractive index of water prevents light from being deviated at smaller angles. The minimum deviation angle for the primary bow is 137.5°. Light can be deviated up to 180°, causing it to be reflected right back to the observer. Light which is deviated at intermediate angles brightens the inside of the rainbow.
The minimum deviation angle for the secondary bow is about 230°. The fact that this angle is greater than 180° makes the secondary bow an inside-out version of the primary. Its colors are reversed, and light which is deviated at greater angles brightens the sky outside the bow.
Between the two bows lies an area of unlit sky referred to as Alexander’s band. Light which is reflected by raindrops in this region of the sky cannot reach the observer, though it may contribute to a rainbow seen by another observer elsewhere.