Understanding rainbows

To properly understand rainbows involves referring to different fields of enquiry and areas of knowledge.

  • The field of optics tells us that rainbows are about the paths that light takes through different media and are the result of reflection, refraction and dispersion of light in water droplets.
  • A weather forecaster might explain rainbows in meteorological terms because they depend on sunlight and only appear in the right weather conditions and times of the 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.

Our DICTIONARY OF LIGHT COLOUR AND VISION assembles terms drawn from these different fields to explore our central interest at lightcolourvision.org which is the interconnections between these three topics.
Whenever terms that appear in the DICTIONARY are used on pages within our LIBRARY OF DIAGRAMS, a blue link appears in the text.

Viewing angle

The viewing angle of a rainbow is the angle between a line extended from an observer’s viewpoint to the bow’s anti-solar point and a second line extended towards the coloured arcs of its bow.

  • Viewing angle, angular distance and angle of deflection all produce the same value measured in degrees.
  • To locate the viewing angle as you look at a rainbow, trace two lines away from your eyes, one to the anti-solar point (the centre of the rainbow) and the other to one of the coloured arcs of the rainbow. The viewing angle is between those two lines, which intersect within the lenses of your eyes.
  • To establish where the anti-solar point of a rainbow is, imagine extending the ends of the bow until they meet and form a circle. The anti-solar point is right in the middle and is always below the horizon.
  • The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share centres at their anti-solar point.
  • The viewing angle is the same whatever point is selected on the section of the circumference of the circular arcs of the rainbow visible above the horizon.
  • The viewing angle for a primary bow is between approx. 40.70 and 42.40 from its centre. The exact angle depends upon the rainbow colour selected.
  • The viewing angle for a secondary bow is between approx. 50.40 and 53.40 when you are looking at its centre.
  • The viewing angle can be calculated for any specific colour within a rainbow.
  • The centre of a rainbow is always on its axis. The rainbow axis is an imaginary straight line that connects the light source, observer and anti-solar point.
  • Most incident rays striking a raindrop will follow paths that place them outside the viewing angle. The resulting deflected rays pass by an observer and play no part in their observation.
  • The viewing angle for all rainbows is a constant 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.

Viewing angle, angular distance and angle of deflection

Viewing angle, angular distance and angle of deflection all produce the same value measured in degrees.

    • The viewing angle as described above is a measurement taken from an observer’s point of view and conceives of a rainbow as a three-dimensional object in the real world.
    • The viewing angle is the angle to which an observer looks regardless of whether they look towards the top of a rainbow to see a specific colour or sideways to look at the same colour near the horizon.
    • Angular distance refers to a measurement on a ray-tracing diagram that represents a rainbow as a two-dimensional object.
    • Angular distance measures the same angle as the viewing angle so between the rainbow axis and the position of any specific rainbow colour as it appears on the drawing.
    • The angle of deflection also refers to a measurement on a ray-tracing diagram. It takes the same measurement but at a different intersection of lines.
    • 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.

Viewing angle

The viewing angle of a rainbow is the angle between a line extended from an observer’s eyes to a bow’s centre point and a second line extended out towards the coloured arcs.

  • Viewing angle, angular distance and angle of deflection all produce the same value measured in degrees.
Viewing angle and rainbows
  • Viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head.
  • On the vertical plane, the viewing angle is a measure of how far an observer must raise their eyes or head to look from the centre of a rainbow out to the coloured arcs.
  • On the horizontal plane, the viewing angle is a measure of how far an observer must look from the centre out to the side to see the coloured arcs.
Viewing angle and raindrops
  • The idea of a viewing angle for a specific raindrop within a rainbow is nonsense really because they are too small to see. However, the viewing angle for a specific raindrop can be derived from the angle of deflection.
  • 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.
  • Of all the rays deflected towards an observer by a single raindrop, there is always one that produces the most intense impression of colour for an observer at any specific moment. It is often called the rainbow ray.
  • 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.
  • A ray-tracing diagram can calculate which of the rays of a specific wavelength, exiting a raindrop is the rainbow ray.
  • If an observer could watch a single raindrop as it falls, they would see its viewing angle decrease and its colour change from red, through intermediate colours, to violet. With each change of viewing angle, colour and wavelength the exact trajectory of the rainbow ray must be recalculated.
Find the viewing angle
  • To find the viewing angle as you look at a rainbow, trace two lines away from your eyes, one to the centre of the rainbow, and the other to any point on the coloured arcs. The viewing angle is between those two lines, which intersect within the lenses of your eyes.
  • If you are not sure where the centre of the rainbow is, imagine extending the ends of the bow until they meet and form a circle. The centre (the anti-solar point) is right in the middle.
  • For atmospheric rainbows seen from the ground, the anti-solar point is always below the horizon.
  • The coloured arcs of a rainbow form the circumference of circles (discs or cones) and share centres at their anti-solar point.
  • The viewing angle is the same whatever point is selected on the circumference of the circular arcs of the rainbow visible above the horizon.
  • The viewing angle for a primary bow is between approx. 40.70 and 42.40 from its centre. The exact angle depends on which rainbow colour is selected.
  • The viewing angle for a secondary bow is at an angle of between approx. 50.40 and 53.40 when you are looking outwards from its centre.
  • The viewing angle can be calculated for any specific colour within a rainbow.
  • The centre of a rainbow is always on its axis. The rainbow axis is an imaginary straight line that connects the light source, observer and anti-solar point.
  • 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.
  • The viewing angles for all rainbow 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.
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.

Visible light

Visible light is the range of wavelengths of electromagnetic radiation perceived as colour by human observers.

Visible light

Visible light is the range of wavelengths of electromagnetic radiation perceived as colour by human observers.

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.

  • Human beings don’t see wavelengths of visible 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 is somewhat arbitrary.
  • Traditional colours in English include: red, orange, yellow, green, blue, and violet.
  • The visible spectrum is continuous, and the human eye can distinguish many thousands of spectral colours.
  • The fact that we see distinct bands of colour in a rainbow is an artefact of human colour vision.
  • The visible spectrum is a small part of the electromagnetic spectrum.

https://en.wikipedia.org/wiki/Visible_spectrum

Visible spectrum

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.

Vision

Human vision starts with the light emitted or reflected by an object or scene entering our eyes through the cornea, pupil and lens.

Vision

  • The cornea and the lens help to concentrate and focus light onto the retina – the photosensitive layer of cells at the back of the eyeball.
  • The amount of light that reaches the retina is regulated by changing the size of the pupil, which is a hole in the iris which in terms sits between the cornea and the lens.
  • The retina is responsible for translating the differences in light wavelength (colour) and brightness into biological signals.
  • This signal is transmitted through the optic nerve and neuronal pathways to the visual processing areas of the brain.

Visual perception

  • Vision, as experienced by human beings, provides the basis for visual perception.
  • Visual perception is associated with eyesight but also refers to the brain’s ability to make sense of what our eyes see.
  • Visual perception augments the physiological sensitivity of our eyes to light with all the inferences from which our understanding of the world is derived.

Light, colour and vision

  • The human eye and so human vision are tuned and respond to the visible spectrum and so to colours between red and violet.
  • Light is rarely of a single wavelength, so an observer will usually be exposed to a range of different wavelengths of light or a mixture of wavelengths from different areas of the spectrum.
  • There are no properties of electromagnetic radiation that distinguish visible light from other parts of the electromagnetic spectrum.
  • Colour is not a property of electromagnetic radiation, but a feature of vision and the visual perception of an observer.
  • Colour is what human beings see in the presence of light.
  • Objects appear to be different colours to an observer depending on the wavelengths and intensity of light at the moment it strikes the retina at the back of the eye.

Trichromatic colour vision (Trichromacy)

The trichromatic colour theory explains the system the human eye uses to see colour.

  • Trichromatic colour theory is based on the presence of three types of light-sensitive cone cells in the retina at the back of our eyes, each sensitive to a different spread of colour.
  • All the colours we observe result from the simultaneous response of all three types of cones.
  • The sensitivity of cone cells is the physiological basis for trichromatic colour vision in humans.
  • The fact that we see colour is, in the first instance, the result of interactions among the three types of cones, each of which responds with a bias towards its favoured wavelength within the visible spectrum.
  • The result is that the L, M and S cone types respond best to light with long wavelengths (biased towards 560 nm), medium wavelengths (biased towards 530 nm), and short wavelengths (biased towards 420 nm) respectively.

Visual perception

Visual perception is the human ability to see and make sense of our surrounding environment by virtue of the sensitivity of our eyes to wavelengths of light corresponding with all the colours we see between red and violet.

Visual perception, light and colour
References
  • https://en.wikipedia.org/wiki/Visual_perception

Visual perception

Colour is not a property of electromagnetic radiation, but a feature of visual perception by an observer.

Wave

A wave can be thought of as a disturbance that travels through a medium from one location to another location. Waves are produced as energy is transmitted through a medium such as air or water. Electricity produces microscopic waves that travel through a conductor such as a copper wire.

About waves
  • Waves propagate through a medium as atoms and molecules bump into each other producing a domino affect.
  • Waves share common features such as amplitude, crests, direction of travel, frequency and wavelength.
About waves in water
  • If you throw a stone into a pond it produces a series of ripples (waves) that spread out in concentric circles before crashing against obstacles.
  • Seen from a boat at sea, waves form as the wind and tide apply forces that disturb the water.
  • In general terms:
    • The frequency of waves in water can be counted as individual waves rise to a crest at any given point.
    • Wavelength can be calculated by looking at the distance from the crest of one wave to the crest of the next.
    • Amplitude can be measured by looking at the distance from the top of a crest of a wave to the bottom of the next trough.
    • When looking at waves on water it is easy to see in what direction they are travelling.
    • The energy carried by waves at the beach is obvious when you go for a swim and are thrown head-over-heels.
Electromagnetic waves
  • Electromagnetic waves are invisible either because they are too small to see or because our eyes don’t respond to them:
    • The wavelength of some radio waves can be measured in metres but our eyes are not tuned to see them.
    • When we see colours around us electromagnetic waves are entering our eyes but their amplitude, frequency and wavelength are too small to see.
    • Whilst we may not be able to see electromagnetic waves we may be able to sense them as heat or feel a buzz in a wire.
  • Electromagnetic waves can vary in size so much that their wavelength may need to be measured in kilometres or trillions of picometres (1012) .
  • The frequency of electromagnetic waves may be as infrequent as 1 per second (1 hz per second) or as frequent as a quadrillion per second (1015).
References
  • https://en.wikipedia.org/wiki/Wave

Wave-cycle

A wave-cycle refers to the path of a wave measured from any point through the course of a single oscillation to the same point on the next oscillation.

  • Imagine a wave-cycle as a series of points marked on the path of the wave between one crest and the next.
  • All electromagnetic waves share features such as crests, troughs, oscillations, wavelength, frequency, amplitude, direction of travel.
  • Whilst a wave-cycle is the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon along the axis of the wave.

http://www.imagewheel.org/knowledge-base/wave-cycles/

Wave-cycle

A wave-cycle refers to the path of a wave measured from any point through the course of a single oscillation to the same point on the next oscillation.

  • Imagine a wave-cycle as a series of points marked on the path of the wave between one crest and the next.
  • All electromagnetic waves share features such as crests, troughs, oscillations, wavelength, frequency, amplitude, direction of travel.
  • As a wave oscillates (vibrates), it can be viewed as a series of individual oscillations measured from one crest to the next crest, one trough to the next trough, or from the start of a wave-cycle to the next starting point.
  • Whilst wave-cycle refers to the path from one point on a wave during a single oscillation to the same point on completion of that oscillation, wavelength is a measurement of the same phenomenon along the axis of the wave.

http://www.imagewheel.org/knowledge-base/wave-cycles/

Wave-particle duality

Wave–particle duality is the concept in quantum mechanics that every particle can be partly described in terms of particles, but also in terms of waves.

  • The dual wave-like and particle-like nature of light is known as the wave-particle duality.
    • Electromagnetic radiation is often described in terms of waves. However, the energy imparted by these waves is absorbed at single locations the way particles are absorbed.
    • The absorbed energy of an electromagnetic wave is called a photon and represents the quanta of light.
    • When a wave of light is absorbed as photons, the energy of the wave collapses to specific locations, and these locations are where the photons “arrive”. This is called the wave function collapse.
  • Albert Einstein wrote:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

Wavelength

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation. The measurement is made parallel to the centre-line of the wave.

  • Wavelength can be measured from any point on a wave. To avoid confusion, it is best to measure wavelength from the top of a crest to the top of the next crest, or from the bottom of a trough to the bottom of the next trough so that the measurement is of the length of a single complete oscillation.
  • The wavelength of an electromagnetic wave is measured in metres.
  • Each type of electromagnetic radiation, such as radio waves, visible light and gamma waves,  forms a band of wavelengths on the electromagnetic spectrum.
  • The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency — the higher the frequency, the shorter the wavelength — it follows that short wavelengths are more energetic than long wavelengths.
  • The visible part of the electromagnetic spectrum is composed of the range of wavelengths that correspond with all the different colours we see in the world.
  • Human beings don’t see wavelengths of visible light, but they do see the spectral colours that correspond with each wavelength and the other 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 of light.
  • The wavelength of visible light is measured in nanometres.
  • The wavelength of visible light is measured in nanometres. There are 1,000,000,000 nanometres in a metre.
  • The visible spectrum is often divided into named colours, though any division is somewhat arbitrary.
  • Traditional colour names in English include red, orange, yellow, green, blue, and violet. But the visible spectrum is, in fact, continuous, and the human eye can distinguish many thousands of intermediary spectral colours.
  • Wavelengths corresponding with the colours of the visible spectrum are usually measured in nanometres. There are therefore 300 different colours between 400 nanometres (violet) and 700 nanometres (red). But if picometres are used instead, then there are 300,000 different wavelengths each of which corresponds with a different colour.
  • The perceived colour (hue) of a light stimulus depends on its wavelength.
  • A colour produced by a single wavelength is called a pure spectral colour.
  • Light is rarely of a single wavelength. Light is usually a mixture of several different wavelengths.
  • The greater number of spectral colours associated with a light source, the lower the saturation, so light of mixed wavelengths produces duller more neutral colours.

https://en.wikipedia.org/wiki/Wavelength

Wavelength

Wavelength is a measurement from any point on the path of a wave to the same point on its next oscillation. The measurement is made parallel to the centre-line of the wave.

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 a vacuum or a medium it is described as white light if it contains all the wavelengths of visible light.
  • As light travels through the air it is invisible to our eyes.
  • When we look around we see through the air because it is very transparent and light passes through it.
  • The term white light doesn’t mean light is white as it travels through the air.
  • One situation in which light becomes visible is when it reflects off the surface of an object.
  • When white light strikes a neutral coloured object and all wavelengths are reflected then it appears white to an observer.