# Angular Distance Determines Raindrop Colour

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## Description

To find out more about the diagram above . . . . read on!

#### Angular Distance Determines Raindrop Colour

Look carefully at the diagram at the top of the page. Now check out the following questions (and answers)!

Introducing the diagram! Read back and forward between the image at the top of the page and the explanation below!

Have you already checked out An Introduction to Rainbows?

It is the opening page of our Rainbow Series and contains masses of useful information. This is the table of contents:

A rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflection, refraction and dispersion of light in individual droplets of rain and results in the appearance of an arc of spectral colours across the sky.

• 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 water droplets can produce a rainbow.
• A rainbow is formed from millions of individual water droplets each of which reflects and refracts a tiny coloured image of the sun towards the observer.
• It is the dispersion of light as refraction takes place that produces the rainbow 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 a rainbow and which colour each will produce.
• Rainbows always form arcs around a centre point (called the anti-solar point).
• The axis of a rainbow is an imaginary line drawn between the light source and observer during the period the bow is visible. The anti-solar point is on the same axis.
• If you can see your own shadow and a rainbow at the same time, then the anti-solar point (the centre of the rainbow) is aligned with the shadow of your head.
• Seen from the air a rainbow can appear as a complete circle. It is only because the ground around the observer gets in the way that a rainbow produced by sunlight is reduced from a circle to a semi-circle or an arc.
• The sky inside a rainbow is brighter than on the outside because raindrops direct light there too.
• When you see a primary rainbow, the band of red appears on the outside, followed by orange, yellow, green, blue, with violet on the inside.
• When you see a double rainbow then the secondary rainbow is above the primary bow, it is usually less intense, and the colours are in reverse order with violet on the outside.

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.

• 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 gets 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.

Now let’s look at all this in more detail!

What is a rainbow

• Natural 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 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 to each and every wavelength.
• Each droplet of rain can only direct one refracted and dispersed 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.

A rainbow is an optical effect

• A rainbow is an optical effect, a trick of the light, so there must always be an observer present to see a rainbow.
• A rainbow isn’t an object in the sense that we see and recognise most things in the world around us.
• A rainbow can’t be approached because it has no fixed location. As an observer move so does the rainbow.
• Where a rainbow appears depends on the position of the sun and where the observer is standing.
• A rainbow is caused by the behaviour of light waves travelling through transparent spherical droplets of water.

Rainbow axis and anti-solar point

• If the Sun is directly behind you, a curtain of rain is falling in front of you, and you look straight ahead, then you will see that a rainbow forms around a centre-point.
• The centre-point of a rainbow is called the anti-solar point. The anti-solar point, your eyes and the Sun are always in line with one another – on the same axis.
• Anti means opposite, opposed, or at 1800. So anti-solar means a point opposite the Sun as seen from the viewpoint of an observer.
• The axis of a rainbow is an imaginary line drawn between the Sun, observer and anti-solar point.
• When sunlight and raindrops combine to make a rainbow, they can make a whole circle of coloured rings in the sky.
• Rainbows only form a complete circle when the ground doesn’t get in the way.
• At ground level, the main reason rainbows don’t form a complete circle is because when droplets hit the ground they stop reflecting light.
• Whenever something blocks sunlight then a shadow forms and a rainbow disappears.
• Even if you stand on a mountain peak, the bow forms less than a circle because the mountain creates a shadow.
• Your own shadow can get in the way of a rainbow formed by the spray from a hose or lawn sprinkler.

Light source

• Rainbows are produced by electromagnetic radiation (light).
• 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, whilst in clear conditions, the Sun can be considered a point-source because it fills only 0.50 of the sky.
• When atmospheric conditions defuse sunlight, it causes too much scattering of rays before they reach raindrops, so no bow is produced.
• A wide range of visible wavelengths of light is needed to produce a rainbow with a full range of intense colours.
• The Sun produces a continuous range of wavelengths across the entire visible spectrum.
• The Sun emits radiation throughout the electromagnetic spectrum from gamma rays to radio waves. The visible spectrum is a tiny part of the whole.
• Atmospheric conditions can scatter some wavelengths without affecting others such as at sunset. As a result, some colours may seem very faint or disappear completely as conditions change.

Rays of light

• Light can be described as photons, waves or rays depending on the context.
• The idea of rays is useful when dealing with optics because it allows the path of light through different media to be described.
• The diagram above starts by showing parallel rays of sunlight travelling through the air past an observer and forming a rainbow.

Light and raindrops

• Sunlight has to strike a raindrop at the right point and the right angle to reach an observer.
• If a raindrop is in the right position it reflects a tiny image of the sun towards the observer.
• The position of falling raindrops determines the refracted colour an observer sees.
• For a raindrop to refract red on a primary rainbow, it has to be at an angle of 420 from the anti-solar point.
• For a raindrop to refract violet on a primary rainbow, it has to be at an angle of 400 from the anti-solar point.

Bands of colour

• There is no property belonging to electromagnetic radiation that causes bands of colour to appear to a human observer. The visible spectrum is made up of a smooth and continuous range of wavelengths that correspond with a smooth and continuous range of colours.
• The fact that we do see distinct bands is often described as an artefact of human colour vision.
• We see bands of colour because the human eye can distinguish between some ranges of wavelengths of visible light better than others because they appear more intense.
• It is our eyes in conjunction with our brain that sees a boundary between different bands of colour and gives each band a different name.

Reflection, refraction and dispersion

• Raindrops form as warm air cools and condenses, first producing vapour, then mist, then droplets.
• In calm conditions, the result is tiny spheres that are all the same size and so affect light in an optically consistent way.
• The drops start to fall because they are denser than the surrounding air.
• Their optical density is higher the air around them causing them to refract and disperse sunlight that crosses their path.
• As a ray of light strikes a drop it undergoes refraction as it crosses the boundary from air to water.
• Refraction causes a ray of light to decrease in speed and the path of the ray to bend.
• Once a ray crosses the boundary between air and water it travels on its new course through the interior of the droplet disperses slightly before striking the other side.
• The boundary between water and air inside a raindrop acts as a mirror so rays bounce off the interior surface and set off in the opposite direction at a new angle.
• When a ray within a raindrop hits the boundary for the second time it is refracted again and exits the droplet with the third change of angle.
• As light passes back into the air from a raindrop it speeds up again.
• The raindrop causes a different amount of deviation in the path of each ray of light depending on its wavelength.
• As rays of every possible wavelength of visible light enter and exit a droplet the process causes each associated colour to take a slightly different path and so separate into the full range of rainbow colours.

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

#### Some Key Terms

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

#### Bands of colour

An observer perceives bands of colour when visible light separates into its component wavelengths and the human eye distinguishes between ...

#### Colour

Things appear coloured because colour corresponds with a property of light that is visible to the human eye. The visual ...

#### Colour vision

Colour vision is the ability of an organism or machine to distinguish objects based on the wavelengths (or frequencies) of ...

#### Internal reflection

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

#### Light source

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

#### Observer

A human observer is a person who engages in observation or watches something. In the presence of light, an observer ...

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