Rainbows & the Polarization of Light

Rainbows & the Polarization of Light

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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.
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Description

RAINBOWS & THE POLARIZATION OF LIGHT

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Are the Sun, observer and anti-solar point all on the rainbow axis?
Yes! When drawing a diagram showing where a rainbow will appear, the Sun, observer and anti-solar point are all on the rainbow axis.
Does every observer have a unique view of the world?
Yes! Every observer has a unique view of the world because: Each one of us sees the world from a different physical location and so has a unique point of view Every one of us has different life experiences including educational, social and cultural factors that affect how we see the world.
Is every observer’s experience of colour different?
Yes! Colour is a visual experience unique to each of us at any given moment because of our different points of view, so we share our experiences of colour using language and by way of examples.
How is wavelength affected as light travel from air into raindrops?
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
Does light travel faster in air than in raindrops?
Yes! Light travels faster in air than in water.

About the diagram

About rainbows and light

Rainbows result from light encountering raindrops in the presence of an observer. The phenomenon of rainbows offers many clues as to the nature of light.

  • Light is a form of radiation, a type of energy that travels in the form of electromagnetic waves and can also be described as a flow of particle-like ‘wave-packets’, called photons.
  • Radiation, electromagnetic waves and photons are all concepts that are interchangeable with the more general concept of light.
Theories of light

There are four principal theories that underpin our understanding of the physical properties of light as it relates to rainbows:

  • Wave theory – the idea that light is transmitted from luminous bodies in an undulatory wave-like motion.
  • Particle theory – the idea that the constitution and properties of light can be described in terms of the interactions of elementary particles.
  • Electromagnetic theory – the classical theory of electromagnetism that describes light as coupled electric and magnetic fields, transporting energy as it propagates through space as a wave. The energy is stored in its electric and magnetic fields and can be measured in terms of its intensity.
  • Quantum theory – explains the interactions of light with matter (atoms, molecules etc.) and describes light as consisting of discrete packets of energy,  photons. Quantum physics suggests that electromagnetic radiation behaves more like a classical wave at lower frequencies and more like a classical particle at higher frequencies, but never completely loses all the qualities of one or the other.
These theories tell us things about the properties of light
  • Light is electromagnetic radiation, the force carrier of radiant energy.
  • Whilst it carries energy and has momentum, light has no mass and so is not matter.
  • Light is the result of the interaction and oscillation of electric and magnetic fields.
  • Light is a microscopic phenomenon that needs macroscopic metaphors such as waves and particles to describe it.
  • Once emitted at its source, light can propagate indefinitely through a vacuum in a straight line at the speed of light (299,792,458 metres a second) but can be deflected by gravity.
  • In any specific instance, light can be described in terms of the inter-relationship of its wavelength, frequency and energy.
  • Light slows down and is deflected as it propagates through air, water, glass and other transparent media as photons interact with matter.
Phenomena associated with light include:
Some facts about electromagnetic waves
  • An electromagnetic wave carries electromagnetic radiation.
  • Electromagnetic radiation is measured in terms of the amount of electromagnetic energy carried by an electromagnetic wave.
  • Electromagnetic waves can be imagined as synchronised oscillations of electric and magnetic fields propagating at the speed of light in a vacuum.
  • The kinetic energy carried by electromagnetic waves is often simply called radiant energy or light.
  • Electromagnetic waves are similar to other types of waves in so far as they can be measured in terms of wavelength, frequency and amplitude.
  • Other terms for the amplitude of light are intensity and brightness.
  • Another term for the speed at which light travels is its velocity.
  • We can feel electromagnetic waves release energy when sunlight warms our skin.
  • The position of an electromagnetic wave within the electromagnetic spectrum can be identified by its frequency, wavelength or energy.
Some facts about photons
  • Photons are the elementary building blocks and so the smallest unit used to describe light.
  • Photons are the carriers of electromagnetic force and travel in harmonic waves.
  • Photons are zero mass bosons.
  • Photons have no electric charge.
  • The amount of energy a photon carries can make it behave like a wave or a particle. This is called the “wave-particle duality” of light.
Facts about the electromagnetic spectrum
  • Visible light is just one tiny part of the electromagnetic spectrum.
  • Our eyes only respond to the visible light which we see as colours between red and violet.
  • The electromagnetic spectrum includes, in order of increasing frequency and decreasing wavelength: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.
  • The size of the longest wavelengths is unknown but the shortest is believed to be in the vicinity of the Planck length (approximately 1.6 x 1035 meters).
About raindrops and the polarization of light

Polarization of electromagnetic waves refers to the geometrical orientation of their oscillations.

Polarization restricts the orientation of the oscillations of the electric field of electromagnetic waves to a single plane from the point of view of an observer. This phenomenon is known as plane polarization.

  • Plane polarization filters out all the waves where the electric field is not orientated with the plane from the point of view of an observer.
  • To visualize plane polarization, imagine trying to push a large sheet of card through a window fitted with close-fitting vertical bars.
  • Only by aligning the card with the slots between the bars can it pass through. Align the card at any other angle and its path is blocked.
  • Now substitute the alignment of the electric field of an electromagnetic wave for the sheet of card, and plane polarization for the bars on the window.
  • Polarizing lenses used in sunglasses rely on plane polarization. The polarizing plane is orientated horizontally and cuts out glare by blocking vertically aligned waves.
  • Plane polarization is one of the optical effects that account for the appearance of rainbows.
  • It is the position of each raindrop on the arc of a rainbow, with respect to the observer, that determines the angle of the polarizing plane.
  • Rainbows are typically 96% polarized.
Let’s take this one step at a time
  • Rainbows form in the presence of sunlight, raindrops and an observer, and involve a combination of refraction, reflection and chromatic dispersion.
  • It is during reflection off the back of a droplet that light becomes polarized with respect to an observer.
  • The rear hemisphere of a raindrop forms a concave mirror in which an observer sees a tiny reflection of the Sun.
  • As a rainbow forms, an image of the Sun forms in each and every raindrop and the ones in exactly the right place at the right time become visible to the observer.
  • The light reflected towards an observer is polarized on a plane bisecting each droplet and at a tangent to the arc of the rainbow.
  • The rear hemisphere of a raindrop is best thought of as the half of the raindrop opposite the observer and with the Sun at its centre.
  • Now recall that to see yourself in a normal flat mirrored surface it has to be aligned perpendicular to your eyes. Get it right and you see yourself right in the middle. If it’s not perpendicular, then you see your image off-centre because the mirror is not aligned with your eyes on either the horizontal or vertical planes.
  • The Sun appears right in the centre of every raindrop from the point of view of an observer only if it is in exactly the right position in the sky at the right time. In all other cases, the light is scattered in other directions.
  • Only rays that strike at the point where the horizontal and vertical planes intersect are reflected towards the observer. Rays that strike to the left or right or above/below the centre-point miss the observer.
  • The correct alignment of a raindrop involves the vertical axis of the rear hemisphere being at exactly 900 with respect to the observer. In the case of a primary rainbow, the horizontal axis is titled downwards by approx. 20.50.

Some key terms

Rainbow colours

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.

 

 

Bands of colour

An observer perceives bands of colour when visible light separates into its component wavelengths and the human eye distinguishes between different colours.

  • The human eye and brain together translate light into colour.
  • When sunlight is dispersed by rain and forms a rainbow, an observer will typically distinguish red, orange, yellow, green, blue and violet bands of colour.
  • Although a rainbow contains electromagnetic waves with all possible wavelengths between red and violet, some ranges of wavelengths appear more intense to a human observer than others.

 

Polarization

Polarization of electromagnetic waves refers to the direction in which they oscillate, perpendicular to the direction of the wave’s propagation.

  • Polarization can be induced in light waves by various means, such as reflection, refraction, and scattering.
  • There are several types of polarization, including circular, elliptical and plane polarization.
    • Circular polarization refers to waves that rotate in circles as they propagate, with the electric and magnetic fields perpendicular to each other.
    • Elliptical polarization combines linear and circular polarization, in which the wave oscillates in an elliptical pattern.
    • Plane polarization (sometimes called linear polarization) refers to waves that oscillate in a single plane, such as waves that are vertically or horizontally polarized.
Spectral colour model

The spectral colour model represents the range of pure colours that correspond to specific wavelengths of visible light. These colours are called spectral colours because they are not created by mixing other colours but are produced by a single wavelength of light. This model is important because it directly reflects how human vision perceives light that comes from natural sources, like sunlight, which contains a range of wavelengths.

  • The spectral colour model is typically represented as a continuous strip, with red at one end (longest wavelength) and violet at the other (shortest wavelength).
  • Wavelengths and Colour Perception: In the spectral colour model, each wavelength corresponds to a distinct colour, ranging from red (with the longest wavelength, around 700 nanometres) to violet (with the shortest wavelength, around 400 nanometres). The human eye perceives these colours as pure because they are not the result of mixing other wavelengths.
  • Pure Colours: Spectral colours are considered “pure” because they are made up of only one wavelength. This is in contrast to colours produced by mixing light (like in the RGB colour model) or pigments (in the CMY model), where a combination of wavelengths leads to different colours.
  • Applications: The spectral colour model is useful in understanding natural light phenomena like rainbows, where each visible colour represents a different part of the light spectrum. It is also applied in fields like optics to describe how the eye responds to light in a precise, measurable way.

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