An Introduction to Rainbows

Description

An Introduction to Rainbows

Here are all the diagrams in our Rainbow Series.
Each one appears on its own page with a full explanation.
AND
Did you know that all our diagrams are free to download!

Take a Photo of a Rainbow
How to See a Rainbow
Rainbows Seen From the Air Form a Circle
Rainbows Seen From the Ground Form an Arc
A Rainbow is an Optical Phenomenon
Sun, Observer and Rainbow Share a Common Axis
The Lower the Sun, the Higher the Rainbow
The Higher the Sun, the Lower the Rainbow
Rainbows Appear as Bands of Spectral Colour
The Angle Between Incident and Refracted Rays
The Apparent Position of a Rainbow
Angular Distance Determines Raindrop Colour
Reflection and Refraction in a Raindrop
Dispersion of White Light in a Raindrop
Reflection and Refraction in a Raindrop
The Path of Red Ray Through a Raindrop in Detail
Parallel Light Rays Incident to a Raindrop
Light Rays from a Point Source Incident to a Raindrop
Non-parallel Light Rays Incident to a Raindrop
The Position of Raindrops Determine Their Colour
The Position of Each Raindrop Determines its Colour
Intensity of Rainbow Colours
Paths of Polarized Light in a Raindrop
Rainbows and the Polarization of Light
Drawing Rainbow Diagrams
Rainbows as Superimposed Disks of Colour
Rainbows as Superimposed Cones of Colour
To find out more about the diagrams above . . . . read on!

About the Diagrams

What is a rainbow?

  • A rainbow takes the form of arcs or circles of spectral colour that appear in the sky in the presence of strong sunshine and rain.
  • Rainbows often appear as a rain shower is approaching, or has just passed over, and the falling rain forms a curtain of droplets.
  • To see a rainbow, the rain must be in front of an observer and the Sun must be in the opposite direction, at their back.
  • Rainbows are caused by sunlight reflecting, refracting and dispersing inside water droplets before they are seen by an observer.
  • A rainbow is produced when millions of raindrops reproducing the same optical effects, direct wavelengths of light within the visible spectrum towards an observer.
  • Rainbows are curved because light is reflected, refracted and dispersed symmetrically about an imagined axis that passes through the Sun, the eyes of an observer and the anti-solar point – the geometric centre of the rainbow.
  • Rainbows can sometimes be produced by waterfalls, lawn sprinklers and other things that create a spray of water.

A rainbow is an optical effect

  • A rainbow isn’t an object in the sense that we see and recognise most things in the world around us.
  • A rainbow is an optical effect, a trick of the light, and is caused by the behaviour of light waves travelling through transparent spherical droplets of water.
  • Rainbows only appear at certain times and have no fixed location. Where they appear depends on the location of the light source and the observer.

Preconditions for seeing a rainbow

There are three basic preconditions for seeing a rainbow:

  • An observer who is in the right place at the right time.
  • Bright sunlight shining through a clear air.
  • A curtain of falling rain.

The best conditions for seeing rainbows

  • The right weather conditions are important if you hope to see a rainbow.
  • Rainbows are rare in areas with little or no rainfall such as dry, desert conditions with few clouds.
  • Hills and mountains often create ideal conditions because clouds form quickly, and the weather can change several times a day – especially during spring and autumn.
  • Too much cloud is not good for seeing rainbows because it blocks direct sunlight.
  • The best rainbows appear in the morning and evening when the Sun is strong but low in the sky.
  • Far northern and southern latitudes are good for rainbows because the days are longer and the Sun remains lower in the sky all day.
  • Winter is not the best season for rainbows because the days are shorter, the Sun isn’t as strong and there can be too much cloud.
  • Rainbows are less common around midday because the whole bow may be below the horizon.

Rainbow colours

  • Rainbow colours are the colours seen in rainbows and in other situations where visible light separates into its component wavelengths and the colours corresponding with each wavelength become visible to the human eye.
  • Rainbow colours are spectral colours. A spectral colour is a colour evoked in normal human vision by a single wavelength of visible light, or by a narrow band of adjacent wavelengths. When spectral colours are mixed together in equal amounts, they produce white light.
  • 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. Whilst the visible spectrum and its spectral colours are determined by wavelength, and corresponding frequency, it is our eyes and brains that interpret these differences in electromagnetic radiation to produce our colour perceptions.
  • Naming rainbow colours is a matter more closely related to the relationship between perception and language than anything to do with physics or optics. Even the commonplace colour names associated with rainbows such as yellow or blue defy easy definition. Because rainbow colours are produced by narrow bands of wavelengths, their names are concepts we generally agree on but are not strictly defined by anything in the nature of light itself.
  • Modern portrayals of rainbows show six colours – ROYGBV. This leaves out other colours such as indigo and cyan. In reality, rainbows contain all spectral colours and which ones appear to be the most intense varies depending upon conditions at the time of observation.

Bands of colour

  • The visible spectrum is made up of a smooth and continuous range of wavelengths that correspond with a smooth and continuous range of colours. There is no property belonging to electromagnetic radiation that causes bands of colour to appear to a human observer.
  • The fact that we see distinct curved bands of colour in a rainbow is often described as an artefact of human colour vision. We see them because the human eye distinguishes between some ranges of wavelengths of visible light better than others. It is the relationship between our eyes and brain that produces the impression of different bands of colour.

Primary rainbow

  • The most common rainbow is a primary bow that appears when sunlight is refracted as it enters raindrops, reflects once off the opposite interior surface, is then refracted again as it escapes back into the air and travels towards the observer.
  • The colours in a primary rainbow are always arranged with red on the outside and violet on the inside.
  • The outside edge of a primary rainbow forms an angle of approx. 420 to its axis.The inside edge forms at an angle of approx. 400.
  • The axis of a rainbow is an imaginary straight line that passes through the light source, the eyes of an observer and the centre-point of the bow.

Secondary rainbow

  • A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface and is then refracted again as it escapes back into the air.
  • A secondary rainbow usually appears alongside a primary rainbow and forms a second larger arc with the colours reversed. A secondary rainbow has violet on the outside and red on the inside.
  • When both primary and secondary bows are visible at the same time they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between 500 to 530 to its axis.
  • The axis of a rainbow is an imaginary straight line passing through the light source, the eyes of an observer and the centre-point of the bow.

Understanding rainbows

  • To fully understand rainbows involves referring to different fields of enquiry and areas of knowledge.
  • The field of optics tells us that rainbows are all about the paths that light rays take through different media and are principally caused by the reflection, refraction and dispersion of different wavelengths of light in water droplets.
  • A weather forecaster might explain rainbows in meteorological terms because they depend on sunlight and only appear in certain weather conditions and times of day.
  • A hydrologist who studies the movement and distribution of water around the planet might refer to the water-cycle and so to things like evaporation, condensation and precipitation.
  • A vision scientist will need to refer to visual perception in humans and the biological mechanisms of the eye.
  • An optometrist may check for colour blindness or eye disease.

A light source for rainbows

  • The best light source for rainbows is a strong point-source such as sunlight.
  • A human observer with binocular vision has a 1200 field of view from side to side. In clear conditions, the Sun can be considered to be a point-source filling only 0.50 of an observer’s horizontal field of view.
  • A wide range of visible wavelengths of light is needed to produce all the rainbow colours. The Sun produces a continuous range of wavelengths across the entire visible spectrum.
  • When atmospheric conditions defuse sunlight, it causes too much scattering of rays before they reach raindrops, so no bow is formed.

Rainbows are reflections of the Sun

  • To properly understand the formation of rainbows it is important to remember that what an observer sees is a tiny coloured reflection of the Sun mirrored by every one of the millions of droplets that form its coloured arcs.
  • It is the position of each individual droplet within the bow that determines exactly which spectral colour is observed.
  • The area inside a rainbow also reflects spectral colours but the light is scattered so that the individual colours combine to produce a white appearance.

Water droplets

  • When a raindrop is in free-fall and not buffeted by the wind, it forms a sphere. The more perfect the sphere the better the rainbow because each droplet affects incoming sunlight in a consistent way.
  • The size of raindrops is important. When all the droplets are the same size, they produce rainbows with intense bands of colour. If the droplets are too large (over 3 to 4 mm) then air resistance affects their shape and causes a blurring of colours. If the droplets are too small they float in the air and form mist or fog and produce faint, fuzzy rainbows.
  • The spacial distribution of raindrops is important. If a curtain of rain is crossing an observer’s entire field of view, the rainbow may appear continuous from end to end. Where and when rain falls is however the result of endless changes in atmospheric conditions as air and clouds are blown across the landscape, so long arcs may shrink down to nothing in seconds.
  • The temporal distribution of raindrops is important. A rainbow that at one moment looks almost close enough to touch may be visible for minutes on end before receding slowly into the distance. In other situations a rainbow may appear one moment and be gone the next.

Reflection off the outside of a raindrop

  • Not all incident light striking a raindrop crosses the boundary into the watery interior of a droplet. Some light is reflected off the surface facing the observer.
  • Incident light reflected off the surface facing an observer undergoes neither refraction nor dispersion.
  • Because the outside surface of a raindrop is convex it reflects white light in every possible direction.
  • All incident light reflected off the top half of a raindrop from an observer’s point of view is directed downwards. Light reflected off the lower half is directed upwards.
  • The fact that light is directed upwards above the centre-line of a droplet, reflection stops abruptly at the outer edge of a rainbow.
  • Raindrops anywhere within a cone centred on the eye of an observer, and the circumference of the base extending to an angle of 420 from its axis, can reflect white light from the Sun towards an observer.
  • In part, white light reflected towards and observer off the outside of raindrops accounts for the sky within a rainbow appearing brighter and lighter than the area of sky outside.

The areas inside and outside a rainbow

  • The area inside the arc of a rainbow, from its centre out to the band of colour, often appears tonally lighter than the area of sky outside. There are four reasons for this:
    • The area inside the arc of a rainbow contains light that has been reflected off the front surface of raindrops relative to an observer.
    • The maximum angle from the axis of a rainbow at which any light is reflected, refracted and dispersed by raindrops towards an observer corresponds with the outside edge of the red arc.
    • The light reflected off the front of raindrops has not undergone diffusion so reflects white light towards an observer.
    • The area inside the arc of a rainbow contains lots of randomly scattered light that appears colourless to an observer
  • The angle between the axis of a rainbow and the angle at which the red arc appears to an observer is 420.
  • The 420radius of a rainbow is determined by the refractive index of water droplets. The refractive index of a medium determines how much a ray of light refracts (bends) as it passes from one to another. In the case of a primary rainbow, refraction occurs twice.
  • From the point of view of an observer, all reflected, refracted and dispersed light is produced by incident rays striking the top half of droplets and exiting from the bottom half.
  • Incident rays that strike the bottom half of a droplet are all directed upwards away from an observer.

Remember that:

  • White light containing all wavelengths within the visible part of the electromagnetic spectrum separates into spectral colour as diffusion takes place. Similarly, when all the different wavelengths of the visible spectrum are mixed together they produce white light.
  • White light is the name given to visible light that contains all wavelengths of the visible spectrum at equal intensities. As light travels through the air it is invisible to our eyes. White light is what an observer sees when all the colours that make up the visible spectrum strike a white or neutral coloured surface.

Think of rainbows as discs or cones of colour

Let’s think of rainbows as discs of colour first:

  • Rainbows can be thought of as being composed of a set of six concentric two-dimensional discs as seen from the point of view of an observer. Each disc within the set contains a narrow band of colour – red, orange etc.
  • There is no property belonging to electromagnetic radiation that causes bands of colour to appear to an observer. The fact that we do see distinct bands of colour in a rainbow is often described as an artefact of human colour vision.
  • To model rainbows as six discs allows us to think of them forming on flat 2D curtains of rain. In this case, all the raindrops are imagined to be equidistant from an observer.
  • 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 shape in three-dimensions.
  • Each member of the set of discs has a different radius due to the band 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 over a larger angle (420) than violet light (400).
  • In every case, it is around the edges of each coloured disc that an observer sees the most intense coloured arcs.
  • From the point of view of an observer, refraction stops abruptly at 420, this results in a sharp boundary between the red arc and the sky outside the rainbow.
  • The notion of rainbows being composed of discs of colour fits well with the fact that whilst there is a sharp outer limit to any observed colour, scattering results in all wavelengths being present in reduced amounts across the entire disk. Because scattering effects every wavelength, their associated colours are distributed randomly causing the sky within the bow to appear lighter and brighter than on the outside.

Now let’s think of rainbows as cones of colour:

  • Rainbows can be thought of as being composed of sets of six concentric two-dimensional discs or three-dimensional cones, as seen from the point of view of an observer. The discs and cones within each set contain a narrow band of colour – red, orange etc.
  • To model rainbows as six cones of colour allows us to think of rainbows as forming within a 3D cone reaching from the eye of an observer at its apex and away into the distance. In this case, all raindrops within the set of cones contribute to the rainbow regardless of how far they are away from the observer.
  • Each member of the sets of discs has a different radius. The radius of each coloured disc depends on the band of wavelengths of light. The angle of refraction as light enters and exits the raindrop determines the radius with red refracted over a larger angle than blue light.
  • In every case, it is around their edges that an observer sees the most intense colours. Colour drop away sharply on the outside but more slowly towards their centres.
  • To model rainbows as six discs allows us to think of them forming on flat 2D curtains of rain. In this case, all the raindrops are imagined to be equidistant from an observer.
  • 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 shape in three-dimensions.
  • To model rainbows as six cones of colour allows us to think of rainbows as forming within a 3D cone reaching from the eye of an observer at its apex and away into the distance. In this case, all raindrops within the set of cones contribute to the rainbow regardless of how far they are away from the observer.

 

  • Because the discs overlay one another, the resulting interference affects an observer’s impression of colour. Within the bow the interference produced by the whole set of discs makes the sky appear brighter and lighter than it appears on the outside.
  • /conesoverlapping colours give white, which brightens the sky on the inside of the circle. On the edge, however, the different-sized coloured discs don’t overlap and display their respective colours — a rainbow arc

Rainbows and electromagnetic waves

 

It is also useful to realise that the image of the Sun produced by each droplet is composed of polarized light waves and that in every case, the light reflected towards an observer is polarized on a plane bisecting each droplet and at a tangent to the arc of the rainbow. This happens because the rear hemisphere of a raindrop forms a concave mirror in which an observer sees a reflection of the Sun.

To understand this it helps to review what we mean when we talk about a light wave, which is to say, an electromagnetic wave.

EM-Wave

Electromagnetic waves consist of coupled oscillating electric and magnetic fields orientated at 900 to one another. (Credit: https://creativecommons.org/licenses/by-sa/4.0)

Electromagnetic waves can be imagined as oscillating electric (E) and magnetic (B) fields arranged at right angles to each another. In the diagram above, the coupled electric and magnetic fields follow the y-axis and z-axis and propagate along the x-axis. This arrangement is known as a transverse wave which means the oscillations are perpendicular to the direction of travel. By convention, the electric field is shown in diagrams aligned with the vertical plane and the magnetic field on the horizontal plane. However, in normal atmospheric conditions the geometric orientation of any particular electromagnetic wave is random, so the coupled fields EB can be rotated to any angle.

Polarization of an electromagnetic wave refers to a situation in which the rotation of all the coupled electric and magnetic fields are restricted to a single plane from the point of view of an observer. It is the electric field that aligns with the plane. This phenomenon is known as plane polarization. Plane polarization filters out all the waves where the electric field is not orientated with the plane.

To visualize plane polarization, imagine trying to push a large sheet of card through a window fitted with close-fitting vertical bars. Only by aligning the card with the slots between the bars can it be pushed inside. Align the card at any other angle and its path is blocked. Now substitute the alignment of the electric field of an electromagnetic wave for the sheet of card.

Polarizing lenses in sunglasses work in this way. The polarizing plane is orientated horizontally and cuts out glare by blocking all but horizontally aligned waves.

In the case of a rainbow, its is the position of each raindrop on the arc of the bow, with respect to the observer, that determines the angle of the polarizing plane.

Raindrops polarize light

Rainbows form in the presence of sunlight, raindrops and an observer, and involve a combination of refraction, reflection and chromatic dispersion. It is during reflection off the back of a droplet that the light becomes polarized with respect to the observer.

To understand why raindrops polarize light, remember first that reflection involves a mirrored surface. In this case the mirror is provided by the inside face of the back of a raindrop.

Now recall that to see yourself in a normal flat mirrored surface it has to be aligned perpendicular to your eyes. Get it right and you see your eyes right in the middle. If it’s not perpendicular, then you see your image off centre because the mirror is not aligned with your eyes in both horizontal and vertical planes.

The back of a raindrop forms a hemispherical mirrored surface. Align a raindrop perfectly and a reflection of the Sun appears right in the centre from the point of view of an observer. Get it wrong and the reflection of the Sun misses you completely.

Given that an ideal raindrop forms a perfect sphere, it is not the orientation of the droplet that is important here, it is a question of where of where rays of light strike the hemispherical mirror on the horizontal and vertical planes. Only rays that strike at the point where the horizontal and vertical planes intersect reflect towards the observer.

The position of a raindrop in the sky along with the effects of reflection, refraction and dispersion all determine which raindrops contribute to an observed rainbow.

The correct alignment of a raindrop involves the vertical axis of the hemispherical mirror being at exactly 900 with respect to a plane the includes your eyes, the centre of the droplet, and, the electric field of the electromagnetic waves from the Sun. To see a primary rainbow the hemisphere has to be titled upward by 410 on its horizontal axis to allow for the effects of refraction.

When an observer sees a rainbow the light is 96% polarized by raindrops.

 

 

Raindrops polarise the light seen by an observer.

  • The diagram shows each raindrop in cross section. Each one has been cut in half right through the centre.
  • The cross cut produces either a vertical or horizontal plane.
  • The incident light rays enter, are reflected and exit each droplet in line with the surface formed by the plane.
  • The sequence in each case is that incident light strikes the droplet and is refracted, it then
  • through the is why the diagram shows half of each raindrop as a hemi-spherical cross-section. The cross-section in this diagram forms a plane that includes the light source, the centre of the raindrop and the eye of the observer. It is positioned at the apex of the observed rainbow.

 

 

In the field of optics

The process for a primary rainbow is as follows:

The front half of every raindrop that contributes to an observer’s rainbow refracts rays of incident light as they cross the boundary from air to water and then again as they exit.

The back half acts as a semi-hemispherical concave reflector

If In the case of a primary rainbow, incident light enters the raindrop above halfway

Follow the blue links for definitions . . . . or check the summaries of key terms below!

Supernumerary rainbow

  • Supernumerary rainbows are faint bows that appear just inside a primary rainbow. Several supernumerary rainbows can appear at the same time with a small gap between each one.
  • The word supernumerary means additional to the usual number. The first supernumerary rainbow forms near the edge of the primary bow and is normally the sharpest. Each subsequent supernumerary bow is a little fainter. They often look like fringes of pastel colours and can change in size, intensity and position from moment by moment.
  • Supernumerary rainbows are clearest when raindrops are small and of equal size.
  • On rare occasions, supernumerary rainbows can be seen on the outside a secondary rainbow.
  • Supernumerary rainbows are produced by water droplets with a diameter of around 1 mm or less. The smaller the droplets, the broader the supernumerary bands become, and the less saturated are their colours.
  • Supernumerary rainbows are caused by interference between light waves that contribute towards the main bow but are out of phase with one another by the time they leave a raindrop and travel towards the observer.
  • The theory is that rays of a similar wavelength have slightly different distances to travel through misshapen droplets affected by turbulence, and this can cause them to get slightly out of phase with one another. When rays are in phase, they reinforce one another, but when they get out of phase they produce an interference pattern that appears inside the primary bow.

Fogbows, dewbows, moonbows and more

There are many optical effects similar to rainbows.

  • A fogbow is a similar phenomenon to a rainbow. As its name suggests, they are associated with fog rather than rain. Because of the very small size of water droplets that cause fog a fogbow has only very weak colours.
  • A dewbow can form where dewdrops reflect and disperse sunlight. Dewbows can sometimes be seen on fields in the early morning when the temperature drops below the dew point during the night, moisture in the air condenses, falls to the ground, and covers cobwebs.
  • A moonbow is produced by moonlight rather than sunlight but appears for the same reasons. Moonbows are often too faint to excite the colour receptors (cone cells) but sometimes appear in photographs taken at night with a long exposure.
  • Twinned rainbows are produced when two rain showers with different sized raindrops overlap one another. Both raindows have red on the outside and violet on the inside. The two bows often intersect at one end.
  • A reflection rainbow is produced when light reflects off large lakes or the ocean before striking a curtain of rain. The conditions must be ideal with no wind so that the reflecting water acts like a mirror. A reflected rainbow appears to be similar to a primary bow but has a higher arc. Don’t get confused between a reflection rainbow which appears in the sky and a rainbow reflected in water.
  • A glory is a circle of bright white light that appears around the anti-solar point.
  • A halo is a circle of bright multicoloured light caused by ice crystals that appears around the Sun or the Moon.
  • A monochrome rainbow only occurs when the Sun is on the horizon. When an observer sees a sunrise or sunset, light is travelling horizontally through the atmosphere for several hundred kilometres. In the process, atmospheric conditions cause all but the longest wavelengths to scatter so the Sun appears to be a diffuse orange/red oval. Because all other wavelengths are absent from a monochrome  rainbow, the whole scene may appear to be tinged with a fire-like glow.

Some Key Terms

Move to the next level! Check out the following terms.

Angle of incidence

The angle of incidence measures the angle at which incoming light strikes a surface. The angle of incidence is measured ...
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Angle of reflection

The angle of reflection measures the angle at which reflected light bounces off a surface. The angle of reflection is ...
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Angle of refraction

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media ...
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Dispersion

Dispersion (or chromatic dispersion) refers to the way that light, under certain conditions, separates into its component wavelengths and the ...
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Electromagnetic radiation

Electromagnetic radiation is a type of energy more commonly simply called light. Detached from its source, it is transported by ...
Read More

Electromagnetic spectrum

The electromagnetic spectrum includes electromagnetic waves with all possible wavelengths of electromagnetic radiation, ranging from low energy radio waves through ...
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Frequency

The frequency of electromagnetic radiation (light) refers to the number of wave-cycles of an electromagnetic wave that pass a given ...
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Internal reflection

Internal reflection takes place when light travelling through a medium such as water fails to cross the boundary into another ...
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Law of refraction

As light crosses the boundary between two transparent media, the law of refraction (Snell's law) states the relationship between the ...
Read More

Reflection

Reflection takes place when incoming light strikes the surface of a medium, obstructing some wavelengths which bounce back into the ...
Read More

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