Deflection & Dispersion in Raindrops

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This is one of a set of almost 40 diagrams exploring Rainbows.

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Description

Deflection & Dispersion in Raindrops

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
When is the best time to see a rainbow?
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.
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.
What does the angle of deflection measure when a ray of light strikes a raindrop?
The angle of deflection measures the difference between the original path of a ray of incident light before striking a raindrop and the degree to which it must bend to be seen by an observer.
Does chromatic dispersion take place as white light travels from air into a raindrop?
Yes! Every wavelength of light is affected to a different degree by the refractive index of a transparent medium and as a result, changes direction by a different amount when passing from air to water or water to air.
Does light travel faster in air than in raindrops?
Yes! Light travels faster in air than in water.

About the diagram

An overview of raindrops

An idealized raindrop forms a sphere. These are the ones that are favoured when drawing diagrams of both raindrops and rainbows because they suggest that when light, air and water droplets interact they produce predictable and replicable outcomes.

  • In real-life, full-size raindrops don’t form perfect spheres because they are composed of water which is fluid and held together solely by surface tension.
  • In normal atmospheric conditions, the air a raindrop moves through is itself in constant motion, and, even at a cubic metre scale or smaller, is composed of areas at slightly different temperatures and pressure.
  • As a result of turbulence, a raindrop is rarely in free-fall because it is buffeted by the air around it, accelerating or slowing as conditions change from moment to moment.
  • The more spherical raindrops are, the better defined is the rainbow they produce because each droplet affects incoming sunlight in a consistent way. The result is stronger colours and more defined arcs.
Real-life raindrops
  • Raindrops start to form high in the atmosphere around tiny particles called condensation nuclei — these can be composed of particles of dust and smoke or fragments of airborne salt left over when seawater evaporates.
  • Raindrops form around condensation nuclei as water vapour cools producing clouds of microscopic droplets each of which is held together by surface tension and starts off roughly spherical.
  • Surface tension is the tendency of liquids to shrink to the minimum surface area possible as their molecules cohere to one another.
  • At water-air interfaces, the surface tension that holds water molecules together results from the fact that they are attracted to one another rather than to the nitrogen, oxygen, argon or carbon dioxide molecules also present in the atmosphere.
  • As clouds of water droplets begin to form, they are between 0.0001 and 0.005 centimetres in diameter.
  • As soon as droplets form they start to collide with one another. As larger droplets bump into other smaller droplets they increase in size — this is called coalescence.
  • Once droplets are big and heavy enough they begin to fall and continue to grow. Droplets can be thought to be raindrops once they reach 0.5mm in diameter.
  • Sometimes, gusts of wind (updraughts) force raindrops back into the clouds and coalescence starts over.
  • As full-size raindrops fall they lose some of their roundness, the bottom flattens out because of wind resistance whilst the top remains rounded.
  • Large raindrops are the least stable, so once a raindrop is over 4 millimetres it may break apart to form smaller more regularly shaped drops.
  • In general terms, raindrops are different sizes for two primary reasons,  initial differences in particle (condensation nuclei) size and different rates of coalescence.
  • As raindrops near the ground, the biggest are the ones that bump into and coalesce with the most neighbours.
Overview of diagram
  • Rainbows form when sunlight encounters a curtain of rain.
  • The sunlight enters raindrops at one point and then emerges at another.
  • Each raindrop is made of liquid water and acts as a tiny prism.
  • Between the point of entry and the point of exit, light undergoes refraction, reflection and dispersion.
  • The angles of refraction and reflection are the main determinants of the angle of deflection.
  • Refraction also causes dispersion, separating sunlight into rainbow (spectral) colours.
  • The visible spectrum is composed of wavelengths between approximately 380 and 740 nanometres and each corresponds with a different colour.
  • Although we recognise the rainbow colours ROYGBV (red, orange, yellow, green, blue and violet) each and every wavelength produces a slightly different colour.
  • Each droplet of rain can only direct one colour towards an observer’s eyes at one time. The apparent colour changes from red through to violet as it falls towards the ground.
  • Only rays that strike a raindrop at a tangent to the arcs of a rainbow and exactly intersect it are reflected towards an observer. Rays that strike to the left or right-hand side miss the observer.
About the diagram
  • This diagram shows an observer looking up towards droplets of rain as parallel rays of white light from the Sun are deflected back towards them.
  • The diagram is in cross-section so the Sun, the eye of an observer, the anti-solar point ( the centre of the rainbow) are all shown along their shared axis.
  • The observer sees coloured droplets at different elevations with red at the top and violet at the bottom.
  • Raindrops that are at an angular distance of a little more than 42.40 deflect infra-red light which is invisible to an observer.
  • As raindrops pass an elevation of 42.40 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 40.70 to violet.
  • At an angular distance of a little less than 40.70 raindrops deflect ultra-violet light which is invisible to an observer.
  • Each colour of visible light corresponds with a different wavelength but instead of seeing a smooth and continuous range of colours an observer sees distinct bands of colour.
  • The fact that we see a few distinct bands of colour in a rainbow, rather than a smooth and continuous gradient of hues, is sometimes described as an artefact of human colour vision.
Rainbows are reflections of the Sun
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Some key terms

Anti-solar point

On a sunny day, if you stand with the Sun at your back and look at the ground, the shadow of your head will align with the antisolar point.

  • The antisolar point is the position directly opposite the Sun, 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 antisolar point, which is the geometric centre of a rainbow.
  • This concept corresponds with what an observer sees in real life: the idea that a rainbow has a center. From a side view, the centre of a rainbow is called the antisolar point, so named because it is opposite the Sun relative to the observer’s position.
  • Unless observed from the air, the antisolar point is always below the horizon. Both primary and secondary rainbows share the same antisolar point, as do higher-order bows, such as fifth and sixth-order rainbows.
Angle of incidence

The angle of incidence measures the angle at which incoming light strikes a surface.

  • The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
  • See this diagram for an explanation: Reflection of a ray of light
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • If the boundary between the media is curved, then the normal is drawn at a tangent to the boundary.
Dispersion
  • 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 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 become visible to an observer.
Angle of reflection

The angle of reflection measures the angle at which reflected light bounces off a surface.

  • The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
  • See this diagram for an explanation: Reflection of a ray of light
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.
Angle of refraction

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.

  • The angle of refraction is measured between a ray of light and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • See this diagram for an explanation: Refraction of a ray of light
  • If the boundary between the media is curved, the normal is drawn perpendicular to the boundary.

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