Apparent Position of a Rainbow

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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.

  • Follow the links embedded in the text for definitions of all the key terms.
  • For quick reference don’t miss the summaries of key terms further down each page.

Description

Apparent Position of a Rainbow

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Red is always on the outside edge of a primary rainbow.
Yes! 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.drops.
No! Rainbows are not always visible at midday because their whole circumference can be below the horizon when the sun is high in the sky.

About the diagram

An overview of rainbows

An atmospheric rainbow is an arc or circle of spectral colours and appears in the sky when an observer is in the presence of strong sunshine and rain.

  • Atmospheric rainbows:
    • Are caused by sunlight reflecting, refracting and dispersing inside raindrops before being seen by an observer.
    • Appear in the section of the sky directly opposite the Sun from the point of view of an observer.
    • Become visible when millions of raindrops reproduce the same optical effects.
  • Atmospheric rainbows often appear as a shower of rain is approaching, or has just passed over. The falling raindrops form a curtain on which sunlight falls.
  • To see an atmospheric rainbow, the rain must be in front of the observer and the Sun must be in the opposite direction, at their back.
  • A rainbow can form a complete circle when seen from a plane, but from the ground, an observer usually sees the upper half of the circle with the sky as a backdrop.
  • Rainbows are curved because light is reflected, refracted and dispersed symmetrically around their centre-point.
  • The centre-point of a rainbow is sometimes called the anti-solar point. ‘Anti’, because it is opposite the Sun with respect to the observer.
  • 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.
  • A section of a rainbow can easily disappear if anything gets in the way and forms a shadow. Hills, trees, buildings and even the shadow of an observer can cause a portion of a rainbow to vanish.
  • Not all rainbows are ‘atmospheric’. They can be produced by waterfalls, lawn sprinklers and anything else that creates a fine spray of water droplets in the right conditions.
Overview of diagram
Visual processing

Visual processing is a complex and dynamic process that involves interactions between various retinal cells, neural pathways, and brain regions, ultimately leading to conscious visual perception.

Visual processing begins the moment light enters the human eye. It then progresses through multiple stages as signals travel towards the visual cortex, where the neural activity is integrated, resulting in conscious visual experience.

As visual processing begins the retina starts to process information about colors, as well as basic information about the shape and movement associated with those colors. By the end of this stage, multiple forms of information about a visual scene are ready to be conveyed to higher brain regions.

Let’s examine two major forms of processing, trichromatic and opponent-processing, which occur within the eyeball as visual information is gathered from light entering our eyes.

Trichromacy, also known as the trichromatic theory of colour vision, explains how three types of cone receptors in the retina work together with bipolar cells to perform their role in the initial stage of colour processing. Rod cells also play a significant role in this form of processing visual information, particularly in low-light conditions.

Opponent-processing, also known as the opponent-process theory of colour vision, explains the second form of processing. Opponent-processing involves ganglion cells that process the data received from trichromatic processing and combine it with other intercellular activities.

It is interesting to note that as both trichromatic and opponent-process theories developed over the last century, researchers and authors have often pitted one theory against the other. However, both processes are crucial for understanding how colour vision occurs.

Trichromatic theory explains the encoding of visual information when light hits the retina, while opponent-processing explains a subsequent stage of information convergence, assembly, and coding before the data leaves the retina via the optic nerve.

Note that:

  • Both trichromatic and opponent-processing occur independently within each retina, without comparing with the other.
  • Each eye gathers information from a specific viewpoint, approximately 50 mm to the left or right of the nose.
  • The two impressions are later compared and combined to provide us with a single three-dimensional, stereoscopic view of the world, rather than two flattened images.

We can consider the layers of retinal cells involved in trichromatic and opponent-processing as examining, interpreting, and transmitting visually relevant information. However, it would be incorrect to view this as a straightforward linear process due to the intricate neural networking, cross-referencing, and feedback loops within the retina.

About the diagram

The important points this diagram makes are that:

  • All raindrops that form part of a rainbow appear the same colour to an observer regardless of distance.
  • The raindrops that form part of a rainbow at any particular moment can be anywhere within a cone centred on the eyes of an observer.
  • If raindrops are close by, and in the right position to reflect light into the eyes of an observer, a rainbow may seem almost close enough to touch.
  • If there are raindrops close by and others in the middle distance (and in the right position), they will all contribute to a rainbow regardless of its apparent distance from the observer.
  • Rainbows don’t have qualities like size or distance because they are simply the impression produced by millions of individual droplets of rain reflecting and refracting light in every possible direction.
  • Whilst raindrops scatter light everywhere, only those rays that enter and exit at exactly the right points and at the right moment direct light towards an observer.
  • This diagram shows an observer looking up towards droplets of rain as parallel rays of white light from the Sun are reflected back towards them.
  • The diagram is a cross-section and shows the observer looking up towards the top of the rainbow.
  • The observer sees coloured droplets at different elevations with red at the top and violet at the bottom.
  • The raindrops are all of a similar size and shape but are falling across the observer’s field of view.
  • As raindrops pass an elevation of 42.20 from the axis they appear red. As they continue to fall each one changes colour, first to orange then yellow, green, blue and finally at 400, violet.
  • Each colour of visible light corresponds with a different wavelength but instead of seeing a smooth and continuous range of colours the observer can see distinct bands of colour.
Angle between incident and refracted rays

When light strikes a raindrop, the angle between the incident and refracted rays is often called angular distance.

  • Angular distance is usually measured between the axis of a rainbow and the elevation of those raindrops seen by an observer.
  • Angular distance can also be measured using the angle between the path of an incident ray of light before it strikes a raindrop and its path after it leaves the raindrop and is approaching the observer. See our diagram Path of a Red Ray Through a Raindrop for more details.
  • In diagrams showing the Sun, observer and rainbow, angular distance is often shown as an angle between the axis and a point at the apex of a rainbow. In reality, the angular distance for any colour is the same at every position on the arc or entire circumference of a rainbow due to polarization.

Some Key Terms

Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the interface between one transparent medium and another.

  • As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
  • As light passes from a slow medium such as diamond to a faster medium such as glass it bends away from the normal and speeds up.
  • In a diagram illustrating optical phenomena like refraction or reflection, the normal is a line drawn at right angles to the boundary between two media.
  • A fast (optically rare) medium is one that obstructs light less than a slow medium.
  • A slow (optically dense) medium is one that obstructs light more than a fast medium.
  • The speed at which light travels through a given medium is expressed by its index of refraction.
  • If we want to know in which direction light will bend at the boundary between transparent media we need to know:
  • Which is the faster, less optically dense (rare) medium with a smaller refractive index?
  • Which is the slower, more optically dense medium with the higher refractive index?
  • The amount that refraction causes light to change direction, and its path to bend, is dealt with by Snell’s law.
  • Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.

A human observer is a person who engages in observation by watching things.

Reflection takes place when incoming light strikes the surface of a medium, obstructing some wavelengths which bounce back into the medium from which they originated.

Reflection takes place when light is neither absorbed by an opaque medium nor transmitted through a transparent medium.

If the reflecting surface is very smooth, the reflected light is called specular or regular reflection.

Specular reflection occurs when light waves reflect off a smooth surface such as a mirror. The arrangement of the waves remains the same and an image of objects that the light has already encountered become visible to an observer.

Diffuse reflection takes place when light reflects off a rough surface. In this case, scattering takes place and waves are reflected randomly in all directions and so no image is produced.

Rainbow colours are the bands of colour seen in rainbows and in other situations where visible light separates into its component wavelengths and the spectral colours corresponding with each wavelength become visible to the human eye.

  • The rainbow colours (ROYGBV) in order of wavelength are red (longest wavelength), orange, yellow, green, blue and violet (shortest wavelength).
  • The human eye, and so human perception, is tuned to the visible spectrum and so to spectral colours between red and violet. It is the sensitivity of the eye to this small part of the electromagnetic spectrum that results in the perception of colour.
  • Defining rainbow colours is a question more closely related to the relationship between perception and language than to anything to do with physics or scientific accuracy.
  • Even the commonplace colours associated with the rainbow defy easy definition. They are concepts we generally agree on, but are not strictly defined by anything in the nature of light itself.
  • Whilst the visible spectrum and spectral colour are both determined by wavelength and frequency it is our eyes and brains that interpret these and create our perceptions after a lot of processing.

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