Dispersion of White Light in a Raindrop

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


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

Description

Dispersion of White 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! 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.
Every wavelength of light is affected to a different degree by the refractive index of a material and as a result changes direction by a different amount when passing from one medium (such as air) to another (such as glass or water).
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

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.
About the diagram
  • To delve a bit further into the diagram let’s go on to review the three key concepts, refraction, chromatic dispersion and scattering.
Chromatic dispersion

Chromatic dispersion means dispersion according to colour and associated wavelengths of light. Under certain conditions, chromatic dispersion causes light to separate into its component wavelengths producing a rainbow of colours for a human observer.

  • Chromatic dispersion is best demonstrated by passing a beam of light through a glass prism.
  • A familiar example of chromatic dispersion is when white light strikes raindrops and a rainbow of colours becomes visible to an observer.
  • As light first enters and then exits each raindrop, it separates into its component wavelengths which the observer sees as a band of distinct colours.
  • Chromatic dispersion can be explained in terms of the relationship between wavelength and refractive index.
  • When light propagates from one medium (such as air) to another (such as glass or water) every wavelength of light is affected to a different degree according to the refractive index of the media concerned. As a result, each wavelength changes direction by a different degree. In the case of white light, the separate wavelengths fan out with red on one side and violet on the other.
  • Remember that wavelength is a property of electromagnetic radiation, whilst colour is a feature of visual perception.
Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.  In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.

Definition

Explanation

Summary

About sections (temp)

References

Refraction
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Some key terms

Internal reflection takes place when light travelling through a medium such as water fails to cross the boundary into another transparent medium such as air. The light reflects back off the boundary between the two media.

  • Internal reflection is a common phenomenon so far as visible light is concerned but occurs with all types of electromagnetic radiation.
  • For internal refraction to occur, the refractive index of the second medium must be lower than the refractive index of the first medium. So internal reflection takes place when light reaches air from glass or water (at an angle greater than the critical angle), but not when light reaches glass from air.
  • In most everyday situations light is partially refracted and partially reflected at the boundary between water (or glass) and air because of irregularities in the surface.
  • If the angle at which light strikes the boundary between water (or glass) and air is less than a certain critical angle, then the light will be refracted as it crosses the boundary between the two media.
  • When light strikes the boundary between two media precisely at the critical angle, then light is neither refracted or reflected but is instead transmitted along the boundary between the two media.
  • However, if the angle of incidence is greater than the critical angle for all points at which light strikes the boundary then no light will cross the boundary, but will instead undergo total internal reflection.
  • The critical angle is the angle of incidence above which internal reflection occurs. The angle is measured with respect to the normal at the boundary between two media.
  • The angle of refraction is measured between a ray of light and an imaginary line called the normal.
  • In optics, the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
  • If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

As light crosses the boundary between two transparent media, the law of refraction (Snell’s law) states the relationship between the angle of incidence and angle of refraction of the light with reference to the refractive indices of both media as follows:

When electromagnetic radiation (light) of a specific frequency crosses the interface of any given pair of media, the ratio of the sines of the angles of incidence and the sines of the angles of refraction is a constant in every case.

  • Snell’s law deals with the fact that for an incident ray approaching the boundary of two media, the sine of the angle of incidence multiplied by the index of refraction of the first medium is equal to the sine of the angle of refraction multiplied by the index of refraction of the second medium.
  • Snell’s law deals with the fact that the sine of the angle of incidence to the sine of the angle of refraction is constant when a light ray passes across the boundary from one medium to another.
  • Snell’s law can be used to calculate the angle of incidence or refraction associated with the use of lenses, prisms and other everyday materials.
  • When using Snell’s law:
    • The angles of incidence and refraction are measured between the direction of a ray of light and the normal – where the normal is an imaginary line drawn on a ray diagram perpendicular to, so at a right angle to (900), to the boundary between two media.
    • The wavelength of the incident light is accounted for.
    • The refractive indices used are selected for the pair of media concerned.
    • The speed of light is expressed in metres per second (m/s).

The refractive index of a medium is the amount by which the speed (and wavelength) of electromagnetic radiation (light) is reduced compared with the speed of light in a vacuum.

  • Refractive index (or, index of refraction) is a measure of how much slower light travels through any given medium than through a vacuum.
  • The concept of refractive index applies to the full electromagnetic spectrum, from gamma-rays to radio waves.
  • The refractive index of a medium is a numerical value and is represented by the symbol n.
  • Because it is a ratio of the speed of light in a vacuum to the speed of light in a medium there is no unit for refractive index.
  • If the speed of light in a vacuum = 1. Then the ratio is 1:1.
  • The refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. The ratio is therefore 1:1.333.
  • As light undergoes refraction its wavelength changes as its speed changes.
  • As light undergoes refraction its frequency remains the same.
  • The energy transported by light is not affected by refraction or the refractive index of a medium.
  • The colour of refracted light perceived by a human observer does not change during refraction because the frequency of light and the amount of energy transported remain the same.

Visible light is the range of wavelengths of electromagnetic radiation perceived as colour by human observers.

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.

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.

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