A rainbow is an optical effect

A rainbow is an optical effect, a trick of the light, caused by the behaviour of light waves travelling through transparent water droplets towards an observer.

  • Sunlight and raindrops are always present when a rainbow appears but without an observer, there is nothing, because eyes are needed to produce the visual experience.
  • A rainbow isn’t an object in the sense that we understand physical things in the world around us. A rainbow is simply light caught up in raindrops.
  • A rainbow has no fixed location. Where rainbows appear depends on where the observer is standing, the position of the Sun and where rain is falling.
  • The exact paths of light through raindrops is so critical to the formation of rainbows that when two observers stand together their rainbows are produced by different sets of raindrops.

About this dictionary

This DICTIONARY OF LIGHT, COLOUR & VISION contains a vocabulary of closely interrelated terms that underpin all the resources you will find here at lightcolourvision.org.

  • Each term has its own page in the DICTIONARY and starts with a DEFINITION.
  • Bullet points follow that provide both context and detail.
  • Links embedded in the text throughout the site (highlighted in blue) take you directly to DICTIONARY entries.
  • Shorter SUMMARIES of terms appear on DIAGRAM PAGES under the heading SOME KEY TERMS. These entries strip definitions back to basics and can be viewed without leaving the page.
Why a dictionary of light, colour & vision
  • One of the practical objectives of this website is to make the connections between the topics of light, colour and vision accessible to students and researchers of all ages.
  • Our DICTIONARY aims to avoid a problem faced by websites such as Wikipedia where articles are often composed by contributors with narrow specialisation and their own topic-specific vocabulary.
  • The layout of the DICTIONARY also aims to avoid situations where a single unknown word or phrase makes it difficult, if not impossible, for our visitors to find the information they need (as explained below).
Terms, definitions and explanations
  • All the terms we have selected for the DICTIONARY are widely used and are applied consistently across the topics of light, colour and vision.
  • The aim is to avoid definitions and explanations with different meanings in different fields.
  • As far as possible definitions contain no more than two short sentences.
  • The explanations that follow each definition are arranged as short bullet points that avoid paragraphs of information completely.
  • Each bullet makes a stand-alone point and is intended to deal with a single piece of information that we believe is likely to be important to our readership.
  • The writing style across all terms aims to be clear, accessible and engaging.
  • The idea is to enable our visitors to find and digest information quickly and to confirm facts one at a time.
  • Because our readership and their concerns are diverse, bullet points sometimes provide different perspectives on a single term or topic.

Show me the DICTIONARY OF LIGHT, COLOUR & VISION

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Absorption

When light strikes an object, some wavelengths are absorbed and their energy is converted to heat, others undergo reflection or transmission.

About absorption
  • When light is absorbed by an object or medium, its energy is transferred to electrons and emitted as heat.
  • Absorption of a particular wavelength of light into a material takes place when the frequency of the wave matches the frequency of electrons orbiting atomic nuclei.
  • Electrons selectively absorb photons with matching frequencies.
  • As electrons orbiting atomic nuclei absorb energy, they vibrate more vigorously causing atoms to collide with one which produces heat.
  • When light is reflected off a surface it bounces off at the same wavelength with little or no change in energy.
Related diagrams

Each diagram can be viewed on its own page with a full explanation.

Accommodation

Accommodation refers to the way our eyes keep things in focus by simultaneously changing the shape of each lens. The result is sharp images of the world regardless of whether things are close by or in the distance.

About accommodation
  • If you look into a mirror, the lens in each eye is located just behind the pupil. The lens shape is controlled by ciliary muscles.
  • The distance of objects of interest to an observer varies from infinity to next to nothing but the image distance always remains the same.
  • Image distance is measured between the retina (the light-sensitive surface at the back of the eye) and the cornea (the transparent surface at the front of the eye) and is fixed in the case of the human eyeball.
  • Because the image distance is fixed, our eyes accommodate for this by using the ciliary muscle to alter the focal length of the lens. This enables images of both nearby and far away objects to be brought into sharp focus on the retinal surface.
  • The ciliary muscle forms a ring of flexible tissue around the edge of each lens in the eye’s middle vascular layer.
  • Our eyes accommodate nearby objects by forming each lens into a shape with a shorter focal length. In this case, the ciliary muscles squeeze the lens into a more convex form.
  • Our eyes accommodate distant objects, by relaxing the ciliary muscles, causing the lens to adopt a flatter and less convex shape with a longer focal length.

Achromatic

Achromatic means without colour so refers to surfaces or objects that appear white, grey or black. Achromatic colours can be described in terms of their apparent brightness but are without hue or saturation.

About achromatic colours
  • Near-neutral colours (very light tints or very dark tones) are also sometimes described as achromatic.
  • Unsaturated achromatic hues include browns, tans, pastel tints and equivalent darker tones.
  • When mixing paint, achromatic hues are produced by adding black and/or white until the original colour almost disappears.
  • Achromatic colours are produced on TV, computer and phone screens by mixing RGB colours in equal proportions. The RGB colour model produces a middle grey with the hexadecimal colour value #808080.
  • The way achromatic hues appear to an observer often depends on adjacent more saturated colours. So next to a bright red couch, a grey wall will appear distinctly greenish – green and red being complementary colours.
  • Saturated colours are colours produced by a single wavelength (or a small band of wavelengths) of light.

Additive colour

Additive colour refers to the way any two or more wavelengths of light can be combined to produce other colours.  The RGB colour model, HSB colour model and Spectral colour model use different methods to produce systematic ranges of colour.

About additive colour
  • Additive colour is the method used to mix wavelengths of light, whilst subtractive colour is the method used when mixing pigments such as dyes, inks and paints.
  • An additive approach to colour is used to control the emission of light by television, computer and phones screens.
  • A colour model can be thought of as a theory of colour whilst additive colour and subtractive colour refer to the method used in practice.
About additive colour and the RGB colour model

The RGB colour model used by TV, computer and phone screens involves additive colour mixing. The RGB colour model produces all the colours seen by an observer simply by combining the light emitted by arrays of red, green and blue pixels (picture elements) in different proportions.

  • RGB colour is an additive colour model that combines wavelengths of light corresponding with red, green and blue primary colours to produce all other colours.
  • Red, green and blue are called additive primary colours in an RGB colour model because just these three component colours can produce any other colour if mixed in the right proportion.
  • Different colours are produced by varying the intensity of the component colours between fully off and fully on.
  • When fully saturated red, green and blue primary colours are combined, they produce white.
  • A fully saturated colour is produced by a single wavelength (or narrow band of wavelengths) of light.
  • When any two fully saturated additive primary colours are combined, they produce a secondary colour: yellow, cyan or magenta.
  • Some RGB colour models can produce over 16 million colours by varying the intensity of each of the three primary colours.
  • The additive RGB colour model cannot be used for mixing pigments such as paints, inks, dyes or powders.

Adobe RGB colour space

The aim of a colour space is to ensure that a colour produced by a colour model is accurately reproduced when displayed on-screen, printed or made into paint. The Adobe RGB (1998) colour space is an RGB colour space developed by Adobe Systems, Inc.

About colour spaces
  • A colour space aims to accurately define the relationship between any selected colour and how it will be perceived by the human eye when it is reproduced by a specific digital display, printer or paint mixing machine.
  • The Pantone colour collection defines its colour space by:
    • Establishing a set of inter-related colour swatches
    • Giving each swatch a name or code
    • Calibrating a paint machine (or other types of equipment) to accurately reproduce the colour of each swatch.
  • When an artist chooses a limited number of oil paints to add to their palette they establish a colour space within which they plan to work.
  • Digital colour spaces are often used to define the range (gamut) of colours that will be produced by a particular device or file type.
  • Each digital colour space is programmatically defined to produce a specific gamut of colours and accurately display them when paired with a type of equipment or when paired with a specific colour profile.
  • A colour profile is a program that allows a piece of equipment to know how to handle and process the information it receives so that it can produce the intended colour output.
About the Adobe RGB colour space
  • The Adobe RGB (1998) colour space is designed to encompass the colours that can be output by CMYK colour printers.
  • When the RGB colour model is used on a modern computer screen, the Adobe RGB (1998) colour space aims to reproduce roughly 50% of the range of colours that an observer is capable of seeing in ideal conditions.
  • The purpose of the  Adobe RGB (1998) colour space was to improve on the gamut of colours that could be produced by the earlier sRGB colour space, primarily in the reproduction of cyan-green hues.

Alexander’s band

Alexander’s band (Alexander’s dark band) is an optical effect associated with rainbows. It refers to the area between primary and secondary bows that often appears to be noticeably darker to an observer than the rest of the sky.

About Alexander’s band
  • Alexander’s band is named after Alexander of Aphrodisias, an ancient Greek philosopher who commented on the effect in his writing.
  • The darker area between primary and secondary rainbows can be explained by the fact that fewer photons are directed from that area of the sky toward an observer.
  • The raindrops that form a primary rainbow all direct exiting light downwards towards an observer so away from Alexander’s band.
  • The raindrops that form a secondary bow all direct light upwards, so away from Alexander’s band, before a second internal reflection directs light downwards towards an observer.
  • Plenty of light is scattered into the area between primary and secondary rainbows but very little of it travels towards an observer.

Amacrine cells

Amacrine cells are interneurons in the human retina that interact with retinal ganglion cells and/or bipolar cells.

About amacrine cells
  • Amacrine cells are a type of interneuron within the human retina.
  • Amacrine cells are embedded in the retinal circuitry.
  • Amacrine cells are activated by, and feedback to, bipolar cells. They also have junctions with ganglion cells, as well as with each other.
  • Amacrine cells are known to add information to the stream of data travelling through bipolar cells and then to control and refine the way ganglion cells (and their subtypes) respond to it.
  • Most amacrine cells don’t have tale-like axons. But whilst they clearly have multiple connections to other neurons around them, research into their precise inputs and outputs is ongoing.
  • Axons are the part of neurons that transmit electrical impulses to other neurons.
  • Neurons are the nerve cells that the human central nervous system is composed of.
About the functions of amacrine cells

Amacrine cells are known to contribute to narrowly task-specific visual functions such as:

  • Efficient transmission of high fidelity visual information with a good signal-to-noise ratio.
  • Maintaining the circadian rhythm which keeps our lives tuned to the cycles of day and night and helps to govern our lives throughout the year.
  • Measuring the difference between the response of specific photoreceptors compared with surrounding cells (centre-surround antagonism), so enabling edge detection and contrast enhancement.
  • Motion detection and the ability to distinguish between the movement of things across the field of view and our own eye movements.
Centre-surround antagonism

Centre-surround antagonism refers to the way retinal neurons organize their receptive fields.

  • Centre-surround antagonism refers to the way that light striking the human retina is processed by groups of light-sensitive cone cells in the retina.
  • The centre component is primed to measure the sum-total of signals received from a small number of cone cells directly connected to a bipolar cell.
  • The surround component is primed to measure the sum of signals received from a much larger number of cones around the centre point.
  • The two signals are then compared to find the degree to which they disagree.

Amplitude

The amplitude of an electromagnetic wave is a measurement of the distance from the centre line (or the still position) to the top of a crest or to the bottom of a corresponding trough. The greater the distance the more energy the wave carries.

About amplitude
  • In any particular situation, the relative amplitude of an electromagnetic wave correlates with the relative intensity of light falling on a surface and the relative brightness of the colour perceived by an observer.
  • As the amplitude of an electromagnetic wave increases so does the overall distance between the peak and a corresponding trough.
  • The greater the amplitude of a wave, the more energy it carries.
  • The energy carried by an electromagnetic wave is proportional to the amplitude squared.
  • The amplitude of the electric field of an electromagnetic wave is measured in volts per metre and the magnetic field in amperes per metre.
About amplitude, brightness, colour brightness and intensity

The terms amplitude, intensity and colour brightness are sometimes confused.

Amplitude is a feature of electromagnetic waves. Other features include:

Brightness is used alongside hue and saturation in the HSB colour model.

Colour brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it.

Intensity measures the energy carried by a light wave or stream of photons:

  • When light is modelled as a wave, intensity is directly related to amplitude.
  • When light is modelled as a particle, intensity is directly related to the number of photons present at any given point in time.
  • The intensity of light falls exponentially as the distance from a point light source increases.
  • Light intensity at any given distance from a light source is directly related to its power per unit area (when the area is measured on a plane perpendicular to the direction of propagation of light).
  • The power of a light source describes the rate at which light energy is emitted and is measured in watts.
  • The intensity of light is measured in watts per square meter (W/m2).
  • Cameras use a light meter to measure the light intensity within an environment or reflected off a surface.

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

https://www.physicsclassroom.com/getattachment/reasoning/light/src35.pdf

Analogous colours

Analogous colours are colours that are very similar to one another and appear next to each other on a colour wheel.

About analogous colours
  • Analogous colours are colours of similar hue.
  • An example of a set of analogous colours is red, reddish-orange, orange, yellow-orange.
  • An analogous colour scheme creates a rich, smooth look but is less vibrant than a complementary colour scheme.
  • Increasing the number of segments on a colour wheel shows analogous colours more clearly as the gradation between colours becomes finer.

Angle of deflection

The angle of deflection measures the angle between the original path of a ray of incident light prior to striking a raindrop and the angle of deviation which measures the degree to which the ray is bent back on itself in the course of refraction and reflection towards an observer.

  • The angle of deflection and the angle of deviation are always directly related to one another and together add up to 1800.
  • The angle of deflection is equal to 1800 minus the angle of deviation. So clearly the angle of deviation is always equal to 1800 minus the angle of deflection.
  • 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 all approach on a trajectory running parallel with the rainbow axis.
Remember that:
  • Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
  • When light travels from a vacuum or from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.
  • The more a ray changes direction as it passes through a raindrop the smaller will be the angle of deflection.
  • It is the optical properties of raindrops that determine the angle of deflection of incident light as it exits a raindrop.
  • It is the optical properties of raindrops that prevent any ray of visible light from exiting a primary raindrop at an angle of deflection larger than 42.70.
Now consider the following:
  •  For a single incident ray of light of a known wavelength striking a raindrop at a known angle:
    • To appear in a primary rainbow it cannot exceed an angle of deflection of more than 42.70. This corresponds with the minimum angle of deviation.
    • 42.70 is the angle of deflection that produces the appearance of red along the outside edge of a primary rainbow from the point of view of an observer.
    • 1800 – 137.60 = 42.0 4 is the maximum angle of deflection for any ray of visible light if it is to appear within a primary rainbow.
    • 1800 -139.30 =  40.70 is the angle of deflection for a ray that appears violet along the inside edge of a primary rainbow.
    • Angles of deviation between 137.60 and 139.30 correspond with viewing angles and angles of deflection between 42.40 (red) and 40.70 (violet).
    • An angle of deviation of 137.60 (so viewing angles of 42.40) corresponds with the appearance of red light with a wavelength of approx. 720 nm.
  • The range of angles of deflection that create the impression of colour for an observer is not related to droplet size.
  • The laws of refraction (Snell’s law) and reflection and the law of reflection can be used to calculate the angle of deviation of white light in a raindrop.
  • The angle of deviation can be fine-tuned for any specific wavelength by fine adjustment of the refractive index.
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 angle between the original path of a ray of incident light prior to striking a raindrop and the angle of deviation.
  • 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.

Angle of deviation

(1) The angle of deviation measures the angle between the direction of an incident ray and the direction of a refracted ray when light travels from one medium to another

(2) The angle of deviation measures the degree to which the path of light through a raindrop is altered in the course of refraction and reflection towards an observer.

About the angle of deviation (Raindrops)
  • The angle of deviation is measured between the path of light incident to a raindrop and its path after it exits the raindrop back into air.
  • In any particular example 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 light that forms a rainbow, if thought of in terms of rays, is approaching on trajectories running parallel with the rainbow axis.
Remember that:
  • Any ray of light (stream of photons) travelling through empty space, unaffected by gravitational forces, travels in a straight line forever.
  • When light leaves  a vacuum or travels from one transparent medium into another, it undergoes refraction causing it to change both direction and speed.
  • The more a ray changes direction as it passes through a raindrop the greater will be its angle of deviation.
  • Amongst the optical properties of air and water, absorption, reflection, refraction, and scattering of light are the most important.
  • It is the optical properties of raindrops that determine the angle of deviation of incident light as it exits a raindrop.
  • It is the optical properties of raindrops that prevent any ray of visible light from exiting a primary raindrop at an angle of deviation less than 137.60.
Now consider the following:
  • For a single incident ray of light of a known wavelength striking a raindrop at a known angle:
    • To appear in a primary rainbow it must reach an angle of deviation of at least 137.60 if it is to be visible to an observer.
    • 137.60 is the angle of deviation that produces the appearance of red along the outside edge of a primary rainbow from the point of view of an observer.
    • 137.60 is the minimum angle of deviation for any ray of visible light if it is to appear within a primary rainbow.
    • 139.30 is the angle of deviation for a ray that appears violet along the inside edge of a primary rainbow.
    • Angles of deviation between 137.60 and 139.30 correspond with viewing angles between 42.40 (red) and 40.70 (violet).
    • For any raindrop to form part of a primary rainbow it must be between the viewing angles of 42.40 (red) and 40.70 (violet)
    • An angle of deviation of 137.60 (so viewing angles of 42.40) corresponds with the appearance of red light with a wavelength of approx. 720 nm.
  • The range of angles of deviation that create the impression of colour for an observer is not related to droplet size.
  • The laws of refraction (Snell’s law) and reflection can be used to calculate the angle of deviation of white light in a raindrop.
  • The angle of deviation can be fine-tuned for any specific wavelength by making a small adjustment to the refractive index of water.
Minimum angle of deviation
  • The optical properties of an idealised spherical raindrop mean that no light of any specific wavelength can deviate less than its minimum angle of deviation.
  • The minimum angle of deviation for red light with a wavelength of approx. 720 nm is always 137.60 but similar rays with other points of impact can deviate up to a maximum of 1800.
  • Imagine a falling raindrop:
    • At a specific moment, the droplet is at an angle of 500 from the rainbow axis as seen from the point of view of an observer. This corresponds with an angle of deviation of 1300 which is insufficient to be visible to an observer.
    • A moment later the droplet is at an angle of 42.40 which is the viewing angle for red in a primary rainbow so the droplet becomes visible to the observer.
    • 42.40 corresponds with the rainbow angle for light with a wavelength of 720 nm, so at this moment the droplet appears red at maximum intensity.
    • As the droplet continues to fall, the minimum angle of deviation for red is passed and so that colour fades just as the minimum angle of deviation for orange arrives. For a second the same droplet now appears intensely orange.
    • The sequence repeats for yellow, green, blue and then violet at which point the viewing angle drops below 40.70. A moment later, it briefly produces ultra-violet light.
    • As soon as the minimum angle of deviation for violet is exceeded, increasing towards 1800, it no longer forms part of the arcs of colour seen by an observer, but continues to scatter light into the area between the bow and anti-solar point.
By way of summary
  • Raindrops emit no light of any particular wavelength at an angle less than its minimum angle of deviation.
  • The minimum angle of deviation for any wavelength of visible light is never less than 137.60  whilst the maximum is always 1800.
  • When the angle of deviation is 1800, the angles or refraction (on the entry and exit of a raindrop) = 00 and the angle of reflection = 1800.

Angle of incidence

The angle of incidence measures the angle at which incoming light strikes a surface.

About the angle of incidence
  • The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to (at 900 to), the boundary between two media.
  • If the boundary between two media is curved then the normal is drawn perpendicular to the boundary.
References

https://en.wikipedia.org/wiki/Angle_of_incidence_(optics)

Angle of reflection

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

  • The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
  • If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

Angle of reflection

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

About the angle of reflection
  • The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to (at 900 to), the boundary between two media.
  • If the boundary between two media is curved then the normal is drawn perpendicular to the boundary.

Angle of refraction

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

  • The angle of refraction is measured between a ray of light and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
  • If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.
  • Snell’s law is a formula used to describe the relationship between the angles of incidence and refraction when referring to light passing across the boundary between two different transparent media, such as water, glass, or air.
  • In optics, the law is used in ray diagrams to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a medium.