Polarization of Light in a Raindrop

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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.

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  • For quick reference don’t miss the summaries of key terms further down each page.

Description

POLARIZATION OF LIGHT IN A RAINDROP

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
Yes! Chromatic dispersion takes place as light crosses the boundary between one transparent medium and another if it has a different refractive index.
Yes! Sunlight undergoes plane polarization when it strikes a raindrop. The planes in all cases are oriented radially so each plane passes through both the centre of each raindrop and the centre of the rainbow.

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.

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 energyphotons. 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
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 rainbows 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

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.

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.

Rainbows are at their best early morning and late afternoon when a shower has just passed over and the Sun is illuminating the curtain of raindrops formed on the trailing edge of the falling rain.

A rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflection, refraction and dispersion of light in individual droplets and results in the appearance of an arc of spectral colours.

  • Rainbows only appear when weather conditions are ideal and an observer is in the right place at the right time.
  • Waterfalls, lawn sprinklers and other things that produce water droplets can produce a rainbow.
  • A rainbow is formed from millions of individual droplets each of which reflects and refracts a tiny coloured image of the sun towards the observer.
  • It is the dispersion of light as refraction takes place that produces the rainbow colours seen by an observer.
  • When the sun is behind an observer then the rainbow will appear in front of them.

The visible part of the electromagnetic spectrum is called the visible spectrum.

  • The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world.
  • As light travels through the air it is invisible to our eyes.
  • Human beings don’t see wavelengths of light, but they do see the spectral colours that correspond with each wavelength and colours produced when different wavelengths are combined.
  • The visible spectrum includes all the spectral colours between red and violet and each is produced by a single wavelength.
  • The visible spectrum is often divided into named colours, though any division of this kind is somewhat arbitrary.
  • Traditional colours referred to in English include red, orange, yellow, green, blue, and violet.

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.

ROYGBV is an acronym for the sequence of hues (colours) commonly described as making up a rainbow: red, orange, yellow, green, blue, and violet.

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