Angular Distance & Raindrop Colour


This is one of a set of almost 40 diagrams exploring Rainbows.

Each diagram appears on a separate page and is supported by a full explanation.

  • Follow the links embedded in the text for definitions of all the key terms.
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Angular Distance & Raindrop Colour

The red band of colour on a primary rainbow appears at an angular distance of 42.4 degrees from the centre of the bow.
Angular distance is the angle between the rainbow axis and the direction in which an observer must look to see the coloured arcs of a rainbow.

About the diagram

Overview of raindrops

An idealized raindrop forms a sphere. These are the ones that are favoured when drawing diagrams of both raindrops and rainbows because they suggest that when light, air and water droplets interact they produce predictable and replicable outcomes.

  • In real-life, full-size raindrops don’t form perfect spheres because they are composed of water which is fluid and held together solely by surface tension.
  • In normal atmospheric conditions, the air a raindrop moves through is itself in constant motion, and, even at a cubic metre scale or smaller, is composed of areas at slightly different temperatures and pressure.
  • As a result of turbulence, a raindrop is rarely in free-fall because it is buffeted by the air around it, accelerating or slowing as conditions change from moment to moment.
  • The more spherical raindrops are, the better defined is the rainbow they produce because each droplet affects incoming sunlight in a consistent way. The result is stronger colours and more defined arcs.
Real-life raindrops
  • Raindrops start to form high in the atmosphere around tiny particles called condensation nuclei — these can be composed of particles of dust and smoke or fragments of airborne salt left over when seawater evaporates.
  • Raindrops form around condensation nuclei as water vapour cools producing clouds of microscopic droplets each of which is held together by surface tension and starts off roughly spherical.
  • Surface tension is the tendency of liquids to shrink to the minimum surface area possible as their molecules cohere to one another.
  • At water-air interfaces, the surface tension that holds water molecules together results from the fact that they are attracted to one another rather than to the nitrogen, oxygen, argon or carbon dioxide molecules also present in the atmosphere.
  • As clouds of water droplets begin to form, they are between 0.0001 and 0.005 centimetres in diameter.
  • As soon as droplets form they start to collide with one another. As larger droplets bump into other smaller droplets they increase in size — this is called coalescence.
  • Once droplets are big and heavy enough they begin to fall and continue to grow. Droplets can be thought to be raindrops once they reach 0.5mm in diameter.
  • Sometimes, gusts of wind (updraughts) force raindrops back into the clouds and coalescence starts over.
  • As full-size raindrops fall they lose some of their roundness, the bottom flattens out because of wind resistance whilst the top remains rounded.
  • Large raindrops are the least stable, so once a raindrop is over 4 millimetres it may break apart to form smaller more regularly shaped drops.
  • In general terms, raindrops are different sizes for two primary reasons,  initial differences in particle (condensation nuclei) size and different rates of coalescence.
  • As raindrops near the ground, the biggest are the ones that bump into and coalesce with the most neighbours.
Overview of diagram
  • Rainbows form when sunlight encounters a curtain of rain.
  • The sunlight enters raindrops at one angle and then emerges at another.
  • The water droplets have to be in just the right place to reflect coloured rays into an observer’s eyes.
  • Each raindrop is made of liquid water and acts as a tiny prism.
  • Raindrops break sunlight into spectral colours and so into red, orange, yellow, green, blue and violet.
  • The visible spectrum is composed of wavelengths between approximately 380 and 740 nanometres and each corresponds with a different colour.
  • Although we recognise the rainbow colours ROYGBV there is a colour corresponding with each and every wavelength.
  • Each droplet of rain can only direct one colour towards an observer’s eyes. All the other colours exit at the wrong angle and go off in other directions.
  • Rainbows are described as being both atmospheric and optical phenomena.
About the diagram
  • This diagram shows an observer looking towards the anti-solar point at the centre of a rainbow.
  • The rainbow forms a complete circle as if seen from a plane.
  • A rainbow only forms a complete circle when the ground around an observer doesn’t get in the way.
  • Normally, a rainbow produced by sunlight is reduced from a circle to a semi-circle or an arc.
  • The diagram shows two raindrops, one is above (red) and one is below (violet) the rainbow’s axis.
  • Both the raindrops are of a similar size and shape and are within a curtain of rain falling across the observer’s field of view.
  • It is the difference in angular distance from the axis that determines their colour.
  • As raindrops that are in the right position at the right moment pass an elevation of 42.20 from the axis they appear red. As their angular distance decreases, they appear orange then yellow, green, blue and finally at 400, violet.
  • Once the angular distance drops below 400 raindrops don’t contribute colour to a rainbow.
  • Each colour of visible light corresponds with a different wavelength but instead of seeing a smooth and continuous range of colours the observer can see distinct bands of colour.
The angle between incident and refracted rays
  • The angle between incident and refracted rays is often called the angular distance. Angular distance is usually measured between the axis and the elevation of coloured raindrops as seen by an observer.
  • Angular distance can also be measured using the angle between the path of an incident ray of light before it strikes a raindrop and its path after it leaves the raindrop and is approaching the observer. See our diagram The Path of a Red Ray Through a Raindrop for more details.
  • For convenience and consistency angular distance is often shown in rainbow diagrams measured between the axis and the top of the rainbow as seen by an observer. In reality the angular distance for any colour is the same at every position on the arc or entire circumference of a rainbow.

Some key terms

The perception of colour by an observer results from properties of light that are visible to the human eye. The visual experience of colour is associated with terms like red, blue and yellow.

A human observer is a person who engages in observation by watching things.

  • A light source is a natural or man-made object that emits one or more wavelengths of light.
  • Natural light sources include:
    • The Sun is the most important natural light source in our lives and emits every wavelength of light in the visible spectrum.
    • Celestial sources of light include other stars, comets and meteors.
    • Other natural sources of light include lightning, volcanoes and forest fires.
  • There are also bio-luminescent light sources including some species of fish and insects as well as types of bacteria and algae.
  • Man-made light sources include:
    • Man-made light sources of the most simple type include natural tars and resins, wax candles, lamps that burn oil, fats or paraffin and gas lamps
    • Tungsten lights: These are a type of incandescent source which means they radiate light when electricity is used to heat a filament inside a glass bulb.
    • Halogen bulbs: These are more efficient and long-lasting versions of incandescent tungsten lamps and produce a very uniform bright light throughout the bulb’s lifetime.
    • Fluorescent lights: These are non-incandescent sources of light. They generally work by passing electricity through a glass tube of gas such as mercury, neon, argon or xenon instead of a filament. Fluorescent lamps are very efficient at emitting visible light, produce less waste heat, and typically last much longer than incandescent lamps.
    • LED lights: An LED (Light Emitting Diode) is an electroluminescent light source. It produces light by passing an electrical charge across the junction of a semiconductor. An LED light typically emits a single colour of light which is composed of a very narrow range of wavelengths.
  • Made-made lights can emit a single wavelength, bands of wavelengths or combinations of wavelengths.
  • Colour vision is the human ability to distinguish between objects based on the wavelengths of the light they emit, reflect or transmit. The human eye and brain together translate light into colour.
  • Colour is not a property of electromagnetic radiation, but a feature of visual perception.
  • The human eye, and so human perception, is tuned to the range of wavelengths of light that make up the visible spectrum and so to the corresponding spectral colours between red and violet.
  • Light, however, is rarely of a single wavelength, so an observer will usually be exposed to a spread of different wavelengths of light or a mixture of wavelengths from different areas of the spectrum.
  • An observer’s perception of colour is a subjective process as the eyes and brain respond together to stimuli produced when incoming light reacts with light-sensitive cells within the retina at the back of the eye.
  • The perception of colour can be influenced by various factors, such as lighting conditions, surrounding colours, and individual differences in colour perception.

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