Deflection & Dispersion in Raindrops


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

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Deflection & Dispersion in Raindrops

The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
The angle of deflection measures the difference between the original path of a ray of incident light prior to striking a raindrop and the degree to which it must bend to be seen by an observer.
Yes! Chromatic dispersion takes place as light crosses the boundary between one transparent medium and another if it has a different refractive index.

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

Tiny images of the Sun mirrored in millions of individual raindrops create the impression of bands of colour arching across the sky when an observer sees an atmospheric rainbow.

  • Rainbows are formed from tiny indistinguishable dots of light and each one is produced by a water droplet from which an observer manages to catch a glimpse of an image of the Sun.
  • It is the precise position of each individual raindrop in the sky that determines:
    • Whether or not it is in the range of possible positions that will enable it to reflect an image of the Sun towards the observer.
    • The exact spectral colour that it will produce at any moment and over the passage of time as it falls.
  • The precise position of each raindrop changes over time as it falls, causing its colour to change from red through to violet. Prior to reflecting red, each raindrop is invisible to an observer. After reflecting violet the amount of light reflected by each raindrop drops off sharply.
  • Raindrops reflect and refract the greatest concentration of photons towards an observer from the intense bands of colour within the arcs of a rainbow.
  • Raindrops inside the coloured arcs, in the area between the anti-solar point and the inside edge of the violet bow, direct light towards an observer causing this area to appear lighter or brighter than the rest of the sky.  Factors that determine the appearance of this area include:
    • Lower intensity: Each raindrop reflects far fewer photons in the direction of an observer once they have fallen below the violet band of a rainbow.
    • Reduced saturation: The saturation of each rainbow colour reduces sharply as raindrops leave the violet band because they mix with other droplets that are reflecting other colours.
    • Any situation where an observer is exposed to a mixture of a wide range of wavelengths in similar proportions produces the impression of white rather than a specific colour.
    • Scattering: Light reflected by a raindrop in the direction of an observer may encounter a series of other raindrops on its journey causing random scattering of light in other directions.

Some key terms


Dispersion (or chromatic dispersion) refers to the way that light, under certain conditions, separates into its component wavelengths and the ...

Angle of refraction

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

Anti-solar point

On a sunny day, stand with the Sun on your back and look at the ground, the shadow of your ...

Angle of reflection

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

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