Dispersion of White Light in a Raindrop
This is one of a set of almost 40 diagrams exploring Rainbows.
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Dispersion of White Light in a Raindrop
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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.
- 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
- The diagram provides a general picture of the combined effects of refraction and dispersion as white light is transmitted through a raindrop.
- White light refers to light that contains equal proportions of all wavelengths within the visible spectrum.
- The diagram shows the effect of refraction and chromatic dispersion on white light into spectral colours from red to violet.
- It is slight differences in the refractive index of water for different wavelengths of light that result in chromatic dispersion and the scattering of white light into rainbow colours.
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 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.
- 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).
- 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.
About sections (temp)
Some key terms
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).
- Visible light is a form of electromagnetic radiation.
- Other forms of electromagnetic radiation include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays.
- Visible light is perceived by a human observer as all the spectral colours between red and violet plus all other colours that result from combining wavelengths together in different proportions.
- A spectral colour is produced by a single wavelength of light.
- The complete range of colours that can be perceived by a human observer is called the visible spectrum.
- The range of wavelengths that produce visible light is a very small part of the electromagnetic spectrum.
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.
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.
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