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
Rainbows appear as bands of colour because our eyes tend to see some wavelengths of light as being brighter and so more distinct than others.
Yes! A rainbow can form a complete circle when seen from a plane.
Rainbows appear when bright sunshine is refracted, reflected and dispersed in raindrops in the presence of an observer.
Rainbows are sometimes represented as cones of colour because raindrops from directly in front of an observer to those in the far distance can all help to produce the resulting bows of colour.
Yes! Other common media that produce rainbow-like effects include: Paraffin Benzene Plate glass Other glass

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 boundary between one transparent medium and another.

  • Light bends towards the normal and slows down when it moves from a fast medium (like air) to a slower medium (like water).
  • Light bends away from the normal and speeds up when it moves from a slow medium (like diamond) to a faster medium (like glass).
  • These phenomena are governed by Snell’s law, which describes the relationship between the angles of incidence and refraction.
  • The refractive index (index of refraction) of a medium indicates how much the speed and direction of light are altered when travelling in or out of a medium.
  • It is calculated by dividing the speed of light in a vacuum by the speed of light in the material.
  • Snell’s law relates the angles of incidence and refraction to the refractive indices of the two media involved.
  • Snell’s law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices.

Reflection is the process where light rebounds from a surface into the medium it came from, instead of being absorbed by an opaque material or transmitted through a transparent one.

  • The three laws of reflection are as follows:
    • When light hits a reflective surface, the incoming light, the reflected light, and an imaginary line perpendicular to the surface (called the “normal line”) are all in the same flat area.
    • The angle between the incoming light and the normal line is the same as the angle between the reflected light and the normal line. In other words, light bounces off the surface at the same angle as it came in.
    • The incoming and reflected light are mirror images of each other when looking along the normal line. If you were to fold the flat area along the normal line, the incoming light would line up with the reflected light.

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

  • In the presence of visible light, an observer perceives colour because the retina at the back of the human eye is sensitive to wavelengths of light that fall within the visible part of the electromagnetic spectrum.
  • The visual experience of colour is associated with words such as red, blue, yellow, etc.
  • The retina’s response to visible light can be described in terms of wavelength, frequency and brightness.
  • Other properties of the world around us must be inferred from light patterns.
  • An observation can take many forms such as:
    • Watching an ocean sunset or the sky at night.
    • Studying a baby’s face.
    • Exploring something that can’t be seen by collecting data from an instrument or machine.
    • Experimenting in a laboratory setting.

 

In the field of optics, dispersion is shorthand for chromatic dispersion which refers to the way that light, under certain conditions, separates into its component wavelengths, enabling the colours corresponding with each wavelength to become visible to a human observer.

  • Chromatic dispersion refers to the dispersion of light according to its wavelength or colour.
  • Chromatic dispersion is the result of the relationship between wavelength and refractive index.
  • When light travels from one medium (such as air) to another (such as glass or water) each wavelength is refracted differently, causing the separation of white light into its constituent colours.
  • When light undergoes refraction each wavelength changes direction by a different amount. In the case of white light, the separate wavelengths fan out into distinct bands of colour with red on one side and violet on the other.
  • Familiar examples of chromatic dispersion are when white light strikes a prism or raindrops and a rainbow of colours becomes visible to an observer.

Incident light refers to light that is travelling towards an object or medium.

  • Incident light refers to light that is travelling towards an object or medium.
  • Incident light may come from the Sun, an artificial source or may have already been reflected off another surface, such as a mirror.
  • When incident light strikes a surface or object, it may be absorbed, reflected, refracted, transmitted or undergo any combination of these optical effects.
  • Incident light is typically represented on a ray diagram as a straight line with an arrow to indicate its direction of propagation.
  • The observer effect is a principle of physics and states that any interaction between a particle and a measuring device will inevitably change the state of the particle. This is because the act of measurement itself imposes a disturbance on the particle’s wave function, which is the mathematical description of its state.
  • The concept of observation refers to the act of engaging with an electron or other particle, achieved through measuring its position or momentum.
  • In the context of quantum mechanics, observation isn’t a passive undertaking, observation actively alters a particle’s state.
  • This means that any kind of interaction with an atom, or with one of its constituent particles, that provides insight into its state results in a change to that state. The act of observation is always intrusive and will always change the state of the object being observed.
  • It can be challenging to reconcile this with our daily experience, where we believe we can observe things without inducing any change in them.

Rainbow colours are the colours seen in rainbows and in other situations where visible light separates into its different 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).
  •  It is the sensitivity of the human eye to this small part of the electromagnetic spectrum that results in our perception of colour.
  • The names of rainbow colours are a matter more closely related to the relationship between perception and language than anything to do with physics or scientific accuracy. While the spectrum of light and the colours we see are both determined by wavelength, it’s our eyes and brains that turn these differences in light into the colours we experience.
  • In the past, rainbows were sometimes portrayed as having seven colours: red, orange, yellow, green, blue, indigo and violet.
  • Modern portrayals of rainbows reduce the number of colours to six spectral colours, ROYGBV.
  • In reality, the colours of a rainbow form a continuous spectrum and there are no clear boundaries between one colour and the next.

 

 

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