# Colour Brightness & Angular Distance

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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.

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## Description

#### Colour Brightness & Angular Distance

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
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.
Brightness usually refers to the level light whilst colour brightness refers to the level of saturation of a colour.

###### Overview of diagram
• There is no property belonging to electromagnetic radiation that causes a rainbow to appear as bands of colour to an observer.
• The fact that we do see distinct bands in the arc of a rainbow is often described as an artefact of human colour vision.
• This diagram deals with a related phenomenon, the fact that some of the bands of colour within a rainbow appear brighter and more intense than others.
• The diagram plots the differences in the apparent brightness of each colour as it appears to an observer looking at a primary rainbow.
• The plot of each curve shows that as angular distance increases, brightness also slowly increases.
• At an angular distance of 40.70 the brightness of violet suddenly increases to a peak and then quickly declines to zero.
• Each subsequent band undergoes a similar sudden increase towards its own peak at a progressively larger angular distance.
• Having reached peak brightness, each band quickly declines to zero.
• Remember that the angular distance of any colour can be measured vertically from the rainbow axis to the apex of the arcs or horizontally to left or right.
###### Discs of colour
• It is the slow increase in brightness of each band of colour from the anti-solar point (the centre of a rainbow) towards the circumference that suggests that each band can be thought of as a separate disc.
• Each disc is composed of a band of wavelengths and each has a different diameter.
• Each band of wavelengths appear to be a distinctly different colour to an observer.
• The circumference of each disc marks the region of peak brightness.
• The sharp outer edge of each disc corresponds with the point at which its brightness quickly drops to zero.
• This diagram plots the brightness (y axis) against angular distance (x axis) of the different bands of colour in a primary rainbow.
• The main diagram is a graph showing:
• x axis = A scale with angular distance increasing from left to right
• y axis = A scale with relative peak brightness increasing from bottom to top
• The plots for the different bands of colour colour show that their brightness increases and peaks at different angular distances.
• The diagram suggests that the relative brightness of each bans in ascending order in violet, blue, red, orange, yellow and green.
• The inset diagram in the top left shows a side-on view of an observer and rainbow to remind viewers that the angular distance of any colour can be measured vertically from the rainbow axis to the apex of the arcs or horizontally to left or right.

Rainbow colour refers to the colours seen in rainbows and other situations where visible light separates into its component wavelengths and the corresponding hues become visible to the human eye.

• Rainbow colour (also called spectral colour) is a colour model.
• A colour model is a theory of colour that establishes terms, definitions, rules and conventions for understanding and describing colours and their relationships with one another.
• A spectral colour is a colour evoked in normal human vision by a single wavelength of visible light (or by a narrow spread of adjacent wavelengths).
• When all the spectral colours are mixed together in equal amounts and at equal intensities, they produce white light.
• In order of wavelength, the rainbow colours (ROYGBV) are red (longest visible wavelength), orange, yellow, green, blue and violet (shortest visible 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 and produce 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 commonplace colour names associated with rainbows such as yellow or blue defy easy definition. These names are concepts related to subjective impressions.
• Modern portrayals of rainbows show six colours – ROYGBV. This leaves out other colours such as cyan and indigo.
• Atmospheric rainbows actually contain millions of spectral colours. Measured in nanometres there are around 400 colours between red and violet, measured in picometres there are 400,000.

Angular distance is the angle between the rainbow axis and the direction in which an observer must look to see a specific colour within the arcs of a rainbow.

• Angular distance, viewing angle and angle of deflection all produce the same value measured in degrees.
• Angular distance is a measurement on a ray-tracing diagram that represents the Sun, an observer and a rainbow in side elevation.
• Think of angular distance as an angle between the centre of a rainbow and its coloured arcs with red at 42.40 and violet at 40.70.
• Angular distances for different colours are constants determined by the laws of refraction and reflection.
• The elevation of the Sun, the location of the observer and exactly where rain is falling are all variables that determine where a rainbow will appear to an observer.
• The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share a common centre.
• The angular distance to any specific colour is the same whatever point is selected on the circumference.
• The angular distance for any observed colour in a primary bow is between 42.40 and violet at 40.70.
• The angular distance for any observed colour in a secondary bow is between 53.40 and 50.40 from its centre.
• The angular distance can be calculated for any specific colour visible within a rainbow.
• Considered from an observer’s viewpoint, it is clear that all incident rays seen by an observer run parallel with each other as they approach a raindrop.
• Most of the observable incident rays that strike a raindrop follow paths that place them outside the range of possible viewing angles. The unobserved rays are all deflected towards the centre of a rainbow.
###### Viewing angle, angular distance and angle of deflection
• The term viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head to see a specific colour within the arcs of a rainbow.
• The term angular distance refers to the same measurement when shown in side elevation on a diagram.
• The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection towards an observer.
• The term rainbow ray refers to the path taken by the deflected ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
• The term angle of deviation measures the degree to which the path of a light ray is bent back by a raindrop in the course of refraction and reflection towards an observer.
• In any particular example of a ray of light passing through a raindrop, the angle of deviation and the angle of deflection are directly related to one another and together add up to 1800.
• The angle of deviation is always equal to 1800 minus the angle of deflection. So clearly the angle of deflection is always equal to 1800 minus the angle of deviation.
• In any particular example, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow are all approaching on a trajectory running parallel with the rainbow axis.

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#### Some key terms

The visible part of the electromagnetic spectrum is called the visible spectrum.

• The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.
• As light travels through the air it is invisible to our eyes.
• Human beings don’t see wavelengths of light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
• The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.
• The visible spectrum is often divided into named colours, though any division of this kind is somewhat arbitrary.
• Traditional colours referred to in English include red, orange, yellow, green, blue, and violet.

The amplitude of a wave is a measurement of the distance from the top of a crest through the centre line  (the still position, zero-point, mid-point) to the bottom of a trough.

ROYGBV is an acronym for the sequence of hues (colours) commonly described as making up a rainbow: red, orange, yellow, green, blue, and violet.

• A rainbow spans the continuous range of spectral colours that make up the visible spectrum.
• The human eye is tuned to the visible spectrum and so to spectral colours between red and violet.
• ROYGBV are colours associated with a range of wavelengths rather than with unique values.
• The visible spectrum is the small band of wavelengths within the electromagnetic spectrum that corresponds with all the different colours we see in the world.
• The fact that we see the distinct bands of colour in a rainbow is an artefact of human colour vision.

On a sunny day, stand with the Sun on your back and look at the ground, the shadow of your head coincides with the antisolar point.

• The anti-solar point is the position on the rainbow axis 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 anti-solar point – the geometric centre of a rainbow.
• The idea that a rainbow has a centre corresponds with what an observer sees in real-life.
• As seen in side elevation, the centre-point of a rainbow is called the anti-solar point.
• ‘Anti’, because it is opposite the Sun with respect to the location of an observer.
• Unless seen from the air, the anti-solar point is always below the horizon.
• The centre of a secondary rainbow is always on the same axis as the primary bow and shares the same anti-solar point.
• First, second, fifth and sixth-order bows all share the same anti-solar point.

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