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The Three-Step Magic Behind Every Rainbow
Rainbows are optical phenomena caused by refraction, internal reflection and dispersion of light in water droplets. When sunlight hits a water droplet, it doesn’t just pass straight through. The formation of a rainbow begins with the refraction of sunlight as it enters a raindrop, which is the change in direction of lightwaves as it passes from one medium to another caused by its change in speed. Think of it like a ball bouncing off a wall at an angle – except here, light is bending as it moves from air into water.
White light from the Sun is composed of different colors of the visible spectrum that each have different wavelengths, and in a process known as dispersion, each color of light is bent at a slightly different angle due to its different wavelengths. When the refraction process occurs, the light breaks up into seven colors inside the water droplet, and the light is refracted again when it exits the droplet, further emphasizing the dispersion.
Why Water Droplets Act Like Tiny Prisms
When light meets a water droplet, it is refracted at the boundary of air and water, and enters the droplet, where the light is dispersed into the seven colors, then the rainbow effect occurs because the light is reflected inside the droplet and finally refracted out again into the air. Under the right conditions, each water droplet acts like a prism, which means that when a beam of sunlight hits the droplet, the light will bend, bounce off the surface, and then bend again as it comes out, dispersing the white light into the seven visible colors.
The refractive index of water to the orange sodium-vapor light emitted by streetlamps is 1.33, while to violet, which has a short wavelength, is nearly 1.34, and to red light, which has a long wavelength, the refractive index of water is almost 1.32. This difference might seem tiny, but it’s exactly what creates the beautiful color separation we see.
The Critical 42-Degree Angle That Makes Rainbows Possible
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°, and this angle is independent of the size of the drop, but does depend on its refractive index. Sunlight most strongly reflects at a 42-degree angle, and if we were hovering in the air, we could see that rainbow as a 42-degree circle, but because we’re usually on the ground, we see the rainbow as a curved arc that intersects with the ground.
A primary rainbow, created when a light source shines on water droplets, always creates a 42 degree arc, offset with respect to the light source that creates it, and the 42 degree angle is universal to rainbows created in air by fresh water droplets. You can see rainbows when the sun is located right behind you, and the main rainbow becomes visible at an angle of around 40 degrees from the horizon.
The Surprising Truth About Rainbow Shapes
A rainbow is not actually shaped like a semicircle or an arc; that is simply the shape that we see, as in fact, a rainbow is a circle, but we can’t see the full shape because the horizon cuts off the lower half. Rainbows can be full circles, however, the observer normally sees only an arc formed by illuminated droplets above the ground, and centered on a line from the Sun to the observer’s eye.
From above the Earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle, though this phenomenon can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°. A rainbow is not just a half circle or an arch but a full circle, and the only way to see it in its full circular shape is to observe it from up in the air because the horizon blocks our view of the other half.
Why Every Rainbow Forms a Perfect Cone
The rainbow is curved because the set of all the raindrops that have the right angle between the observer, the drop, and the Sun, lie on a cone pointing at the sun with the observer at the tip. Raindrops glint rainbow rays at an angle of 42 degrees from the point directly opposite the sun, and all the drops glinting the rainbow are on the surface of a cone with its point at your eye.
This process occurs simultaneously in countless droplets across a rain-filled sky, however, only those droplets positioned at the correct angle with respect to the observer’s line of sight reflect light that reaches the eye, and these droplets lie on the surface of an imaginary cone, with the observer’s eye at the tip and the cone pointing away from the Sun. It’s remarkable to realize that because rainbows aren’t physically real – they’re just optical phenomena, like shadows – that if you could simply add more “mist particles” for the sunlight to reflect off of in the right locations, you’d be able to see the true shape of a rainbow every time: a full circle.
The Personal Nature of Rainbow Viewing
A rainbow does not exist at one particular location, as many rainbows exist; however, only one can be seen depending on the particular observer’s viewpoint as droplets of light illuminated by the sun, since all raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer’s eye. The appearance of a rainbow all depends on where you stand, and if you move, then the rainbow moves, as for every single person, the view will be different.
Rainbows aren’t physically “real objects,” in the sense that if you move toward or away from one, the rainbow will shift in response to your motion, as each observer at each unique location sees their own individual rainbow, which is why any attempt to find the proverbial “pot of gold at the end of the rainbow” will always fail.
Understanding Double Rainbows and Color Reversal
The secondary rainbow is distinct from the primary rainbow in several ways, as it is positioned outside the primary rainbow and has a radius of approximately 51 degrees, lying about 9 degrees beyond the primary bow. Sometimes the light reflects twice off the back of the raindrop; this leads to the secondary rainbow, and the second reflection causes the order of the colors in the bow to reverse.
The secondary bow is formed by two internal reflections within raindrops, resulting in rays that are deviated more than 180 degrees, and unlike the primary bow, which has a radius of approximately 42 degrees, the secondary bow has a larger radius of 51 degrees, attributed to the minimum deviation angle of about 231 degrees. The secondary rainbow is nearly always fainter than the primary, and its colours are reversed and more widely separated.
When Rainbow Conditions Come Together
The formation of rainbows, including double rainbows, hinges upon specific weather conditions, as there must be sunlight and rain simultaneously present, with the angle of the sun crucial, as rainbows typically form when the sun is low in the sky, such as during or shortly after a rain shower in the late afternoon or early morning. The range of angles at which raindrops reflect is the real reason why rainbows are curved, and for you to view a rainbow properly, you have to be standing with the sun behind you and it must be low in the sky.
The size of raindrops also plays a crucial role in determining the visibility and clarity of double rainbows, as larger raindrops tend to produce more prominent and vivid rainbows, while smaller droplets may result in fainter or less distinct arcs, because larger droplets have a greater capacity to refract and disperse sunlight.
The Mysterious World of Supernumerary Rainbows
Supernumerary rainbows are additional, faint bands that can be seen just inside the primary rainbow, caused by interference patterns resulting from the wave nature of light, typically appearing when small, uniformly sized water droplets are present, and can create a series of closely spaced arcs that enhance the visual effect of the primary bow. In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow, these extra bands are called supernumerary rainbows, and the supernumerary bows are slightly detached from the main bow, become successively fainter, and have pastel colours rather than the usual spectrum pattern.
The effect becomes apparent when water droplets are involved that have a diameter of about 1 mm or less; the smaller the droplets are, the broader the supernumerary bands become, and due to their origin in small droplets, supernumerary bands tend to be particularly prominent in fogbows.
Scientific History Behind Rainbow Understanding
Isaac Newton demonstrated that white light was composed of the light of all the colours of the rainbow, which a glass prism could separate into the full spectrum of colours, and he also showed that red light is refracted less than blue light, which led to the first scientific explanation of the major features of the rainbow. Newton’s corpuscular theory of light was unable to explain supernumerary rainbows, and a satisfactory explanation was not found until Thomas Young realised that light behaves as a wave under certain conditions, with Young’s work refined in the 1820s by George Biddell Airy, and modern physical descriptions of the rainbow are based on Mie scattering, work published by Gustav Mie in 1908.
Roger Bacon studied rainbows in medieval times, though the first accurate calculation of the angular size came later, and Theodoric of Freiberg is known to have given an accurate theoretical explanation of both the primary and secondary rainbows in 1307.
Beyond Traditional Rainbows – Rare Phenomena
Monochrome rainbows appear in a single color rather than the full spectrum, and are most commonly seen in red, especially during sunrise or sunset when the light has to travel a longer distance through the atmosphere. Twinned rainbows consist of two separate rainbows that appear side by side, occurring when light undergoes multiple internal reflections within the raindrops, with the secondary rainbow typically fainter than the primary one and having its colors reversed.
The quinary rainbow lies partially in the gap between the primary and secondary rainbows and is far fainter than even the secondary, and in a laboratory setting, it is possible to create bows of much higher orders, with Felix Billet depicting angular positions up to the 19th-order rainbow, a pattern he called a “rose of rainbows”.
The Mathematical Beauty of Rainbow Geometry
Since raindrops are spherical, they reflect light in a cone shape, making rainbows appear circular, meanwhile, the sunlight reflects most strongly at a 42-degree angle, which can be observed if we hover in the air, but because we are usually on the ground, we see this color spectrum as a curved arc intersecting with the ground. 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.
There is a circular band of light that all gets returned right around 42°, and if the Sun were a laser emitting parallel, monochromatic rays, then the luminance of the bow would tend toward infinity at this angle if interference effects are ignored, but since the Sun’s luminance is finite and its rays are not all parallel the luminance does not go to infinity. Did you expect that such a simple display of nature would involve such intricate physics and mathematics?
