Optical illusion

Optical illusions and other visual anomalies result from the way the human visual system processes information.

Types of illusion include:

Physical illusions

Physical illusions seem to be hard-wired into the way that the human eye and brain process visual stimuli. Examples include:

  • The Sun and Moon appear much larger when close to the horizon than when high in the sky.
  • Rainbows are composed of a continuous range of wavelengths across the visible spectrum but appear to be formed from bands of colour.
Physiological illusions

Physiological illusions are often connected with the different attributes of visual perception and occur when a visual stimulation is beyond our eyes’/brain’s processing ability. Examples include:

  • The effects of excessive stimulation produced by brightness or hue that result in after-images.
  • Moiré patterns are produced when an area of parallel dark lines with interspersed white spaces is overlaid on another similar pattern that is slightly displaced or rotated.
Cognitive illusions

Cognitive illusions intentionally or accidentally induce ambiguity or confusion about how a visual stimulus should be interpreted. Examples include:

  • Ambiguous illusions are pictures or objects that elicit a perceptual “switch” between alternative interpretations.
  • Distorting or geometrical illusions are characterized by size, length, position or curvature distortions.
  • Paradox illusions are generated by objects that contain visual clues that contradict one another or conflict with deeply embedded ways that we understand the visual world.
  • Fictions are a type of illusion produced when a visual stimulus creates the impression of additional visual content beyond what is present in a scene.

Amplitude, brightness, colour brightness & intensity

About amplitude, brightness, colour brightness and intensity

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

Amplitude
Brightness
  • Brightness is related to how things appear from the point of view of an observer.
    • When something appears bright it seems to radiate or reflect more light or colour than something else.
    • Brightness may refer to a light source, an object, a surface, transparent or translucent medium.
    • The brightness of light depends on the intensity or the amount of light an object emits( eg. the Sun or a lightbulb).
    • The brightness of the colour of an object or surface depends on the intensity of light that falls on it and the amount it reflects.
    • The brightness of the colour of a transparent or translucent medium depends on the intensity of light that falls on it and the amount it transmits.
    • Because brightness is related to intensity, it is related to the amplitude of electromagnetic waves.
    • Brightness is influenced by the way the human eye responds to the colours associated with different wavelengths of light. For example, yellow appears relatively brighter than reds or blues to an observer.
Colour brightness
  • Colour brightness refers to the difference between the way a colour appears to an observer in well-lit conditions compared with its subdued appearance when in shadow or when poorly illuminated.
    • In a general sense, brightness is an attribute of visual perception and produces the impression that something is radiating or reflecting light and/or colour.
    • Colour brightness increases as lighting conditions improve, whilst the vitality of colours decreases when a surface is poorly lit.
    • Optical factors affecting colour brightness include:
    • Material properties affecting the colour brightness of a medium, object or surface include:
      • Chemical composition
      • Three-dimensional form
      • Texture
      • Reflectance
    • Perceptual factors affecting colour brightness include:
    Intensity
    • 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.

Amacrine cell functions

About amacrine cell functions

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.

Adobe RGB colour space

About the Adobe RGB colour space
  • The Adobe RGB (1998) colour space is designed to encompass the colours that can be reproduced 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 Adobe RGB (1998) colour space was developed 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.

Angle of deflection

When discussing the formation of rainbows, the angle of deflection measures the angle between the original path of an incident ray of 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 case, 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 light as it exits a raindrop.
  • Because of the optical properties of primary rainbows, no rays of light within the visible part of the electromagnetic spectrum exit a raindrop at an angle of deflection larger than 42.40.
  • Because of the optical properties of secondary rainbows, no rays of light within the visible part of the electromagnetic spectrum exit a raindrop at an angle of deflection larger than 50.40.
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 42.40. This corresponds with the minimum angle of deviation.
    • 42.40 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 = 42.40 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.
About rainbows: 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.

Additive colour and the RGB colour model

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 in equal amounts, 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 implementations of RGB colour models can produce millions of 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.

Amacrine cells

Amacrine cells

Amacrine cells interact with bipolar cells and/or ganglion cells. They are a type of interneuron that monitor and augment the stream of data through bipolar cells and also control and refine the response of ganglion cells and their subtypes.

Amacrine cells are in a central but inaccessible region of the retinal circuitry. Most are without tale-like axons. Whilst they clearly have multiple connections to other neurons around them, their precise inputs and outputs are difficult to trace. They are driven by and send feedback to the bipolar cells but also synapse on ganglion cells, and with each other.

Amacrine cells are known to serve narrowly task-specific visual functions including:

  • Efficient transmission of high-fidelity visual information with a good signal-to-noise ratio.
  • Maintaining the circadian rhythm, so keeping our lives tuned to the cycles of day and night and helping to govern our lives throughout the year.
  • Measuring the difference between the response of specific photoreceptors compared with surrounding cells (centre-surround antagonism) which enables edge detection and contrast enhancement.
  • Object motion detection which provides an ability to distinguish between the true motion of an object across the field of view and the motion of our eyes.

Centre-surround antagonism refers to the way retinal neurons organize their receptive fields. The centre component is primed to measure the sum-total of signals received from a small number of cones 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 agree or disagree.

Accommodation

Accommodation

The distance between the retina (the detector) and the cornea (the refractor) is fixed in the human eyeball. The eye must be able to alter the focal length of the lens in order to accurately focus images of both nearby and far away objects on the retinal surface. This is achieved by small muscles that alter the shape of the lens. The distance of objects of interest to an observer varies from infinity to next to nothing but the image distance remains constant.

The ability of the eye to adjust its focal length is known as accommodation. The eye accommodates by assuming a lens shape that has a shorter focal length for nearby objects in which case the ciliary muscles squeeze the lens into a more convex shape. For distant objects, the ciliary muscles relax, and the lens adopts a flatter form with a longer focal length.

Aurora

Aurora (also known as the polar lights) are a natural display of curtains, rays, spirals, and flickering patterns of light in the northern polar latitudes (Aurora Borealis) and southern polar latitudes (Aurora Australis). They are most prominent after dark.

  • Aurora are the result of charged particles (electrons) produced by the Sun (solar wind) interacting with Earth’s magnetosphere.
  • The magnetosphere accelerates electrons as they plunge into the atmosphere during their final few 10,000 km journeys from the Sun.
  • The colour and pattern of aurora depend partly upon the amount of acceleration imparted to the precipitating particles.
Related diagrams

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

Electron

An electron is a subatomic particle with a negative  charge.

  • Electrons are thought to be elementary particles because they have no known components or substructure.
  • Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light.
  • Since an electron has a negative charge, it has a surrounding electric field, and in motion generates a magnetic field.
  • Electrons radiate or absorb energy in the form of photons when they are accelerated.
  • Electrons play an essential role in numerous physical phenomena, such as electricity, magnetism, chemistry and thermal conductivity, and they also participate in gravitational, electromagnetic and weak interactions.

Anti-solar point

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.

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.

Angular distance

When discussing rainbows, 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.
About viewing angles, angular distance and angles of deflection

Angular distance

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.

Atmospheric rainbows summary

  • 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 distinct red, orange, yellow, green, blue and violet rays.
  • Rainbows can be described as being both atmospheric and optical phenomena.
Remember that:
  • If the Sun is directly behind you, rain is falling in front of you, and you look straight ahead, then you will see that the rainbow forms around a centre-point.
  • The centre-point of a rainbow is often referred to as 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 to the Sun as seen by 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 light in the sky.
  • Rainbows only form a complete circle when the ground doesn’t get in the way. This only happens when you are on a plane.
  • Whenever something blocks sunlight then a shadow forms and a portion of 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.
  • Seen from the air, the shadow of your plane is often visible at the centre of the rainbow. The further away the curtain of rain is on which the bow forms, the smaller the plane appears.
  • At ground level, the main reason rainbows don’t form a complete circle is because when droplets hit the ground they stop reflecting light so the rainbow comes to an end.

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.

Cones of colour

Rainbows can be modelled as a set of six nested cones with the apex of each aligned with the lenses of an observer’s eyes.

  • Each cone has a different radius and each is composed of a narrow spread of wavelengths of light that determines its apparent colour. Red fills the cone with the largest radius and violet fills the smallest.
  • The cones do not have a simple 2D base. At their nearest, droplets may be within reach of an observer. At the other extreme, distant raindrops also refract and reflect light back towards an observer.
  • Modelling a rainbow as a cone that shows depth, as well as height and width, demonstrates that all the raindrops contained within one of the cones at any moment can contribute to the visual experience of an observer regardless of how far they are away.
  • Whilst modelling rainbows as discs corresponds with what an observer sees, the idea that rainbows are formed from cones of colour corresponds with a diagram showing a side elevation with the Sun, observer and rainbow arranged along the rainbow’s axis.

Discs of colour

Rainbows can be modelled as six concentric two-dimensional discs as seen from the point of view of an observer. Each disc has a different radius and contains a narrow spread of colours. The red disc has the largest radius and violet the smallest.

  • The colour of each disc is strongest and most visible near its outer edge because this is the area into which light is most concentrated from the point of view of an observer.
  • This concentration of light near the outer edge of each disc results from the path of rainbow rays.
  • The term rainbow ray describes the path that produces the most intense experience of colour for any particular wavelength of light passing through a raindrop.
  • The intensity of the colour of each disc reduces rapidly away from the rainbow angle because other rays passing through each raindrop diverge from one another and so are much less concentrated.
  • The divergence of rays of light after exiting a raindrop is often called scattering.
  • From the point of view of an observer, the six discs are superimposed upon one another and appear to be in the near to middle distance in the opposite direction to the Sun.
  • There is no property belonging to electromagnetic radiation that causes a rainbow to appear as bands or discs of colour to an observer. The fact that we do see distinct bands of colour in the arc of a rainbow is often described as an artefact of human colour vision.
  • To model rainbows as discs allows us to think of them as forming on flat 2D curtains of rain.
  • 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 three-dimensional form.
  • Each member of the set of discs has a different radius due to the spread 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 at a larger angle (42.40) than violet (40.70).
  • From the point of view of an observer, refraction stops abruptly at 42.40 and results in a sharp boundary between the red band and the sky outside a primary rainbow.
  • The idea of rainbows being composed of discs of colour fits well with the fact that there is a relatively clear outer limit to any observed band of colour.