Rainbows as Cones of Colour

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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.
  • For quick reference don’t miss the summaries of key terms further down each page.

Description

Rainbows as Cones of Colour

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Red is always on the outside edge of a primary rainbow.
It is useful to think of the bands that form a rainbow as discs of colour because the brightness of any specific colour seen by an observer drops off to nothing at the circumference but drops off more slowly towards the centre.
Yes! If droplets are large, 1 millimetre or more in diameter, red, green, and violet are bright but blue is hardly visible.
No! The outermost colour on a secondary rainbow is violet because the colours of a secondary rainbow are reversed.
Yes! Each colour in a rainbow between red and violet is a spectral colour.

About the diagram

Overview of rainbows

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.
Thinking of rainbows as cones of colour

Rainbows can be modelled as a set of six nested cones with the apex of each aligned with the lenses of an observer’s eyes.

  • Each cone has a different radius and each is composed of a narrow spread of wavelengths of light that determines its apparent colour. Red fills the cone with the largest radius and violet fills the smallest.
  • The cones do not have a simple 2D base. At their nearest, droplets may be within reach of an observer. At the other extreme, distant raindrops also refract and reflect light back towards an observer.
  • Modelling a rainbow as a cone that shows depth, as well as height and width, demonstrates that all the raindrops contained within one of the cones at any moment can contribute to the visual experience of an observer regardless of how far they are away.
  • Whilst modelling rainbows as discs corresponds with what an observer sees, the idea that rainbows are formed from cones of colour corresponds with a diagram showing a side elevation with the Sun, observer and rainbow arranged along the rainbow’s axis.

 

Some key terms

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

  • In the presence of visible light, an observer perceives colour because the retina at the back of the human eye is sensitive to wavelengths of light that fall within the visible part of the electromagnetic spectrum.
  • The visual experience of colour is associated with words such as red, blue, yellow, etc.
  • The retina’s response to visible light can be described in terms of wavelength, frequency and brightness.
  • Other properties of the world around us must be inferred from light patterns.
  • An observation can take many forms such as:
    • Watching an ocean sunset or the sky at night.
    • Studying a baby’s face.
    • Exploring something that can’t be seen by collecting data from an instrument or machine.
    • Experimenting in a laboratory setting.

 

On a sunny day, if you stand with the Sun at your back and look at the ground, the shadow of your head will align with the antisolar point.

  • The antisolar point is the position directly opposite the Sun, around which the arcs of a rainbow appear. An imaginary straight line can always be drawn that passes through the Sun, the eyes of an observer, and the antisolar point, which is the geometric centre of a rainbow.
  • This concept corresponds with what an observer sees in real life: the idea that a rainbow has a center. From a side view, the centre of a rainbow is called the antisolar point, so named because it is opposite the Sun relative to the observer’s position.
  • Unless observed from the air, the antisolar point is always below the horizon. Both primary and secondary rainbows share the same antisolar point, as do higher-order bows, such as fifth and sixth-order rainbows.

A rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflection, refraction (bending) and dispersion (spreading out) of light in individual droplets and result in the appearance of an arc of spectral colours.

  • Atmospheric rainbows only appear when weather conditions are ideal and an observer is in the right place at the right time.
  • Waterfalls, lawn sprinklers and other things that produce air-borne water droplets can produce a rainbow.
  • An atmospheric rainbow is formed from countless individual droplets each of which reflects and refracts a tiny coloured image of the Sun towards the observer.
  • As white light passes through water droplets, refraction causes the light to disperse and separate into the different colours seen by an observer.
  • If the sun is behind an observer then the rainbow will appear in front of them.
  • When a rainbow is produced by sunlight, the angles between the sun, each droplet and the observer determine which ones will form part of the rainbow, the colour each droplet will produce and the sequence in which they appear.
  • The observer effect is a principle of physics and states that any interaction between a particle and a measuring device will inevitably change the state of the particle. This is because the act of measurement itself imposes a disturbance on the particle’s wave function, which is the mathematical description of its state.
  • The concept of observation refers to the act of engaging with an electron or other particle, achieved through measuring its position or momentum.
  • In the context of quantum mechanics, observation isn’t a passive undertaking, observation actively alters a particle’s state.
  • This means that any kind of interaction with an atom, or with one of its constituent particles, that provides insight into its state results in a change to that state. The act of observation is always intrusive and will always change the state of the object being observed.
  • It can be challenging to reconcile this with our daily experience, where we believe we can observe things without inducing any change in them.

A light source is a natural or man-made object that emits one or more wavelengths of light.

  • The Sun is the most important 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 of the most simple type include natural tars and resins, wax candles, lamps that burn oil, fats or paraffin and gas lamps.
  • Modern man-made light sources include tungsten light sources. 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 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 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. These lamps are very efficient at emitting visible light, produce less waste heat, and typically last much longer than incandescent lamps.
  • An LED (Light Emitting Diode) is an electroluminescent light source. It produces light by passing an electrical charge across the junction of a semiconductor.
  • Made-made lights can emit a single wavelength, bands of wavelengths or combinations of wavelengths.
  • An LED light typically emits a single colour of light which is composed of a very narrow range of wavelengths.

Rainbow colours are the colours seen in rainbows and in other situations where visible light separates into its different wavelengths and the spectral colours corresponding with each wavelength become visible to the human eye.

  • The rainbow colours (ROYGBV) in order of wavelength are red (longest wavelength), orange, yellow, green, blue and violet (shortest wavelength).
  •  It is the sensitivity of the human eye to this small part of the electromagnetic spectrum that results in our perception of colour.
  • The names of rainbow colours are a matter more closely related to the relationship between perception and language than anything to do with physics or scientific accuracy. While the spectrum of light and the colours we see are both determined by wavelength, it’s our eyes and brains that turn these differences in light into the colours we experience.
  • In the past, rainbows were sometimes portrayed as having seven colours: red, orange, yellow, green, blue, indigo and violet.
  • Modern portrayals of rainbows reduce the number of colours to six spectral colours, ROYGBV.
  • In reality, the colours of a rainbow form a continuous spectrum and there are no clear boundaries between one colour and the next.

 

 

The spectral colour model represents the range of pure colours that correspond to specific wavelengths of visible light. These colours are called spectral colours because they are not created by mixing other colours but are produced by a single wavelength of light. This model is important because it directly reflects how human vision perceives light that comes from natural sources, like sunlight, which contains a range of wavelengths.

  • The spectral colour model is typically represented as a continuous strip, with red at one end (longest wavelength) and violet at the other (shortest wavelength).
  • Wavelengths and Colour Perception: In the spectral colour model, each wavelength corresponds to a distinct colour, ranging from red (with the longest wavelength, around 700 nanometres) to violet (with the shortest wavelength, around 400 nanometres). The human eye perceives these colours as pure because they are not the result of mixing other wavelengths.
  • Pure Colours: Spectral colours are considered “pure” because they are made up of only one wavelength. This is in contrast to colours produced by mixing light (like in the RGB colour model) or pigments (in the CMY model), where a combination of wavelengths leads to different colours.
  • Applications: The spectral colour model is useful in understanding natural light phenomena like rainbows, where each visible colour represents a different part of the light spectrum. It is also applied in fields like optics to describe how the eye responds to light in a precise, measurable way.

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