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Variations Double rainbows "Double rainbow" redirects here. For other uses, see Double Rainbow. Double rainbow with Alexander's band visible between the primary and secondary bows. Also note the pronounced supernumerary bows inside the primary bow.
Physics of a primary and secondary rainbow and Alexander's dark band  The term double rainbow is used when both the primary and secondary rainbows are visible.
In theory, all rainbows are double rainbows, but since the secondary bow is always fainter than the primary, it may be too weak to spot in practice.
Secondary rainbows are caused by a double reflection of sunlight inside the water droplets. As a result of the "inside" of the secondary bow being "up" to the observer, the colours appear reversed compared to those of the primary bow.
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.
Each rainbow reflects white light inside its coloured bands, but that is "down" for the primary and "up" for the secondary. A "normal" secondary rainbow may be present as well.
Twinned rainbows can look similar to, but should not be confused with supernumerary bands. The two phenomena may be told apart by their difference in colour profile: 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. That small difference in droplet size resulted in a small difference in flattening of the droplet shape, and a large difference in flattening of the rainbow top.
Viewing the rainbow's lower half requires the presence of water droplets below the observer's horizon, as well as sunlight that is able to reach them. These requirements are not usually met when the viewer is at ground level, either because droplets are absent in the required position, or because the sunlight is obstructed by the landscape behind the observer.
From a high viewpoint such as a high building or an aircraft, however, the requirements can be met and the full-circle rainbow can be seen.
In the right circumstances, a glory and a circular rainbow or fog bow can occur together. Supernumerary rainbows Contrast-enhanced photograph of a rainbow with additional supernumerary bands inside the primary bow In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i.
These extra bands are called supernumerary rainbows or supernumerary bands; together with the rainbow itself the phenomenon is also known as a stacker rainbow. The supernumerary bows are slightly detached from the main bow, become successively fainter along with their distance from it, and have pastel colours consisting mainly of pink, purple and green hues rather than the usual spectrum pattern.
The alternating faint bands are caused by interference between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in phasereinforcing each other through constructive interferencecreating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interferenceand creating a gap.
Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow. Supernumerary rainbows are clearest when raindrops are small and of uniform size.
The very existence of supernumerary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in Their names are slightly different. A reflected rainbow may appear in the water surface below the horizon.
The reflected rainbow is frequently visible, at least partially, even in small puddles. A reflection rainbow may be produced where sunlight reflects off a body of water before reaching the raindrops see diagram and if the water body is large, quiet over its entire surface, and close to the rain curtain.
The reflection rainbow appears above the horizon. It intersects the normal rainbow at the horizon, and its arc reaches higher in the sky, with its centre as high above the horizon as the normal rainbow's centre is below it.From the Pythagorean theorem we have the relationship: a² + b² = c² In our case we will let c = R+δ; b=R; a=d; where R is the radius of the Earth (we will use miles), d is our distance, and δ which is our unknown quantity (the drop height) so we can put these into the equation as follows.
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