# Raindrop Elevation & Colour

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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.

• Follow the links embedded in the text for definitions of all the key terms.
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## Description

#### Raindrop Elevation & Colour

###### TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
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.
The wavelength of incident light decreases as it travels from air into a raindrop because water is an optically slower medium.
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.
Yes! Light travels faster in air than in water.
Yes! If droplets are large, 1 millimetre or more in diameter, red, green, and violet are bright but blue is hardly visible.

• This diagram deals with how a single raindrop can contribute to the formation of a primary rainbow.
• The diagram shows that a single falling raindrop appears red then orange, yellow, green, blue and finally violet as it falls towards the ground.
• It is the elevation of a droplet relative to the rainbow axis and observer that determines its colour at any moment as it falls.
• Notice that the diagram shows a ray of white light entering the top half of the raindrop and reflecting once off the interior surface before exiting towards the observer. This is always the case if a raindrop is part of a primary bow.
• So this is the sequence:
• At its largest angular distance from the axis, a raindrop appears red to an observer as it enters into the outer edge of the primary bow.
• Moments later, as that same raindrop falls, and its angular distance decreases, it changes colour, first from red and finally to violet. The diagram shows the moments at which it appears red, yellow and blue.
• As it falls further and its angular distance reduces below 40.70 it exits the inside edge of the bow.
• The droplet is now almost invisible but continues to contribute a little to a scattering of white light that fills this area within the arcs with a light glow.
###### 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.

#### 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.

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.

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.

The perception of colour by an observer results from properties of light that are visible to the human eye. The visual experience of colour is associated with terms like red, blue and yellow.

• The observation of colour depends on:

A human observer is a person who engages in observation by watching things.

• In the presence of visible light, an observer perceives colour because the retina at the back of the human eye is sensitive to wavelengths of light that fall within the visible part of the electromagnetic spectrum.
• The visual experience of colour is associated with words such as red, blue, yellow, etc.
• The retina’s response to visible light can be fully described in terms of wavelength, frequency and brightness.
• Other properties of the world around us must be inferred from patterns of light.

White light is the name given to visible light that contains all wavelengths of the visible spectrum at equal intensities.

• As light travels through a vacuum or a medium it is described as white light if it contains all the wavelengths of visible light.
• As light travels through the air it is invisible to our eyes.
• When we look around we see through the air because it is very transparent and light passes through it.
• The term white light doesn’t mean light is white as it travels through the air.
• One situation in which light becomes visible is when it reflects off the surface of an object.
• When white light strikes a neutral coloured object and all wavelengths are reflected then it appears white to an observer.

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 the 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 becomes visible to an observer.

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