Observed Colour of Raindrops
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.
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Observed Colour of Raindrops
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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 geometric raindrops
An idealised raindrop forms a geometrically perfect sphere. Although such a form is one in a million in real-life, simplified geometrical raindrops help to make sense of rainbows and reveal general rules governing why they appear.
The insights that can be gained from exploring the geometry of raindrops apply to every rainbow, whilst the rainbows we come across in everyday life demonstrate that each individual case is unique.
- The idea that light is made up of rays is so commonplace when describing and explaining rainbows that it is easily taken for granted.
- The idea of light rays is useful when trying to model how light and raindrops produce the rainbow effects seen by an observer.
- Light rays don’t exist in the sense that the term accurately describes a physical property of light. More accurate descriptions use terms like photons or waves.
Basics of raindrop geometry
- A line drawing of a spherical raindrop is the starting point for exploring how raindrops produce rainbows.
- The easiest way to represent a raindrop is as a cross-section that cuts it in half through the middle.
- A dot or small circle can be used to mark the centre whilst the larger circle marks the circumference.
- Marking the centre makes it easy to add lines that show the radius and diameter.
- Marking the centre also makes it easy to add lines that are normal to the circumference.
- A normal (or the normal) refers to a line drawn perpendicular to and intersecting another line, plane or surface.
- A normal is used in a diagram to connect the centre with a point where a ray strikes the circumference.
- The diameter of a circle is a line that passes through its centre and is drawn from the circumference on one side to the other.
- The radius of a circle is a line from the centre to any point on the circumference.
- The horizontal axis of a raindrop is a line drawn through its centre and parallel to incident light. The vertical axis intersects the horizontal at 900 and also passes through the centre point.
- The angle at which incident light strikes the surface of a raindrop can be calculated by drawing a line that shows where an incident ray strikes a droplet and then drawing the normal. The angle of incidence is measured between them.
- The path of light as it strikes the surface and changes direction as it is refracted at the boundary between air and water can be calculated using the Law of Refraction (Snell’s law).
- When light is refracted as it enters a droplet it bends towards the normal.
- The law of reflection can be used to calculate the change of direction each time light reflects off the inside surface of the raindrop.
- When light exits a raindrop the angle of refraction is the same as when it entered but this time bends away from the normal.
Some key terms
- In the field of optics, diffusion refers to situations that cause parallel rays of light to spread out more widely. When light undergoes diffusion it becomes less concentrated.Diffuse reflections occur when light scatters off rough or irregular surfaces.
- When microscopic features on a surface are significantly larger than the individual wavelengths of light within the visible spectrum, each wavelength of light encounters bumps and ridges exceeding their size.
- Instead of reflecting neatly in one direction, the light scatters in different directions.
- In this case, scattering doesn’t happen completely randomly. The surface features influence the direction of the scattered light, depending on the angle of incidence and the specific bumps and ridges it encounters.
- This scattering creates diffuse reflections, responsible for the soft, uniform illumination seen on textured surfaces like matte paint or unpolished wood.
- In the case of a matte phone screen, for example, the light doesn’t form a clear reflection of your face but rather creates a soft, hazy glow due to the diffused light.
- When discussing rainbows, angular distance is the angle between the line from the observer to the centre of the rainbow (rainbow axis) and the line from the observer to a specific colour within the arc of a rainbow.
- See this diagram for an explanation: Angular distance & Raindrop colour
- Angular distance is one of the angles measured on a ray-tracing diagram that illustrates the sun, an observer, and a rainbow from a side view.
- Think of angular distance as the angle between the line to the centre of a rainbow down which an observer looks and the line to a specific colour in its arc. The red light is deviated by about 42.4° and violet light by about 40.7°.
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.
On a sunny day, stand with the Sun on your back and look at the ground, the shadow of your head coincides with the antisolar point.
- The anti-solar point is the position on the rainbow axis 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 anti-solar point – the geometric centre of a rainbow.
- The idea that a rainbow has a centre corresponds with what an observer sees in real-life.
- As seen in side elevation, the centre-point of a rainbow is called the anti-solar point.
- ‘Anti’, because it is opposite the Sun with respect to the location of an observer.
- Unless seen from the air, the anti-solar point is always below the horizon.
- The centre of a secondary rainbow is always on the same axis as the primary bow and shares the same anti-solar point.
- First, second, fifth and sixth-order bows all share the same anti-solar point.
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.
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.
- 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.
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