Rainbows as Discs of Colour

An atmospheric rainbow is an arc or circle of spectral colours and appears in the sky when an observer is in the presence of strong sunshine and rain.

• Atmospheric rainbows:
  • Are caused by sunlight reflecting, refracting and dispersing inside raindrops before being seen by an observer.
  • Appear in the section of the sky directly opposite the Sun from the point of view of an observer.
  • Become visible when millions of raindrops reproduce the same optical effects.
• Atmospheric rainbows often appear as a shower of rain is approaching, or has just passed over. The falling raindrops form a curtain on which sunlight falls.
• To see an atmospheric rainbow, the rain must be in front of the observer and the Sun must be in the opposite direction, at their back.
• A rainbow can form a complete circle when seen from a plane, but from the ground, an observer usually sees the upper half of the circle with the sky as a backdrop.
• Rainbows are curved because light is reflected, refracted and dispersed symmetrically around their centre-point.
• The centre-point of a rainbow is sometimes called the anti-solar point. ‘Anti’, because it is opposite the Sun with respect to the observer.
• An imaginary straight line can always be drawn that passes through the Sun, the eyes of an observer and the anti-solar point – the geometric centre of a rainbow.
• A section of a rainbow can easily disappear if anything gets in the way and forms a shadow. Hills, trees, buildings and even the shadow of an observer can cause a portion of a rainbow to vanish.
• Not all rainbows are ‘atmospheric’. They can be produced by waterfalls, lawn sprinklers and anything else that creates a fine spray of water droplets in the right conditions.

Rainbows can be modelled as six concentric two-dimensional discs as seen from the point of view of an observer. Each disc has a different radius and contains a narrow spread of colours. The red disc has the largest radius and violet the smallest.

• The colour of each disc is strongest and most visible near its outer edge because this is the area into which light is most concentrated from the point of view of an observer.
• This concentration of light near the outer edge of each disc results from the path of rainbow rays.
• The term rainbow ray describes the path that produces the most intense experience of colour for any particular wavelength of light passing through a raindrop.
• The intensity of the colour of each disc reduces rapidly away from the rainbow angle because other rays passing through each raindrop diverge from one another and so are much less concentrated.
• The divergence of rays of light after exiting a raindrop is often called scattering.
• From the point of view of an observer, the six discs are superimposed upon one another and appear to be in the near to middle distance in the opposite direction to the Sun.
• There is no property belonging to electromagnetic radiation that causes a rainbow to appear as bands or discs of colour to an observer. The fact that we do see distinct bands of colour in the arc of a rainbow is often described as an artefact of human colour vision.
• To model rainbows as discs allows us to think of them as forming on flat 2D curtains of rain.
• Rainbows are often modelled as discs for the same reason the Sun and Moon are represented as flat discs – because when we look into the sky, there are no visual cues about their three-dimensional form.
• Each member of the set of discs has a different radius due to the spread of wavelengths of light it contains. This can be explained by the fact that the angle of refraction of rays of light as they enter and exit a droplet is determined by wavelength. As a result, the radius of the red disc is the largest because wavelengths corresponding with red are refracted at a larger angle (42.4⁰) than violet (40.7⁰).
• From the point of view of an observer, refraction stops abruptly at 42.4⁰ and results in a sharp boundary between the red band and the sky outside a primary rainbow.
• The idea of rainbows being composed of discs of colour fits well with the fact that there is a relatively clear outer limit to any observed band of colour.