Dictionary tag: R

The term rainbow angle is often paired with rainbow ray to measure the angle at which light is deflected back towards an observer as it passes through a raindrop.

• At lightcolourvision.org the term rainbow angle is avoided but is treated as being synonymous with the angle of deflection.
• The angle of deflection (rainbow angle) is measured at the point where the path of an incidence ray and the path of the same ray after it exits a raindrop towards the observer can be shown to intersect.
• To make the incident and exiting ray intersect in a ray-tracing diagram the incident ray is extended forwards in a straight line beyond the raindrop. The ray exiting the droplet towards the observer is then extended backwards until both intersect. The angle of deflection (rainbow angle) lies between the two.
• The angle of deflection (rainbow angle), for any ray that is contributing directly to the arcs of a primary rainbow, is always between approx. 40.7⁰ and 42.4⁰.

Viewing angle, angular distance and angle of deflection

• The term viewing angle refers to the number of degrees through which an observer must move their eyes or turn their head to see a specific colour within the arcs of a rainbow.
• The term angular distance refers to the same measurement when shown in side elevation on a diagram.
• The angle of deflection measures the degree to which a ray striking a raindrop is bent back on itself in the process of refraction and reflection towards an observer.
• The term rainbow rays refers to the path taken by the deflected ray that produces the most intense colour experience for any particular wavelength of light passing through a raindrop.
• The term angle of deviation measures the degree to which the path of a light ray is bent back by a raindrop in the course of refraction and reflection towards an observer.
  • In any particular example of a ray of light passing through a raindrop, the angle of deviation and the angle of deflection are directly related to one another and together add up to 180⁰.
  • The angle of deviation is always equal to 180⁰ minus the angle of deflection. So clearly the angle of deflection is always equal to 180⁰ minus the angle of deviation.
  • In any particular example, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow are all approaching on a trajectory running parallel with the rainbow axis.

Rainbow colour refers to the colours seen in rainbows and other situations where visible light separates into its component wavelengths and the corresponding hues become visible to the human eye.

• Rainbow colour (also called spectral colour) is a colour model.
• A colour model is a theory of colour that establishes terms, definitions, rules and conventions for understanding and describing colours and their relationships with one another.
• A spectral colour is a colour evoked in normal human vision by a single wavelength of visible light (or by a narrow spread of adjacent wavelengths).
• When all the spectral colours are mixed together in equal amounts and at equal intensities, they produce white light.
• In order of wavelength, the rainbow colours (ROYGBV) are red (longest visible wavelength), orange, yellow, green, blue and violet (shortest visible wavelength).
• It is the sensitivity of the human eye to this small part of the electromagnetic spectrum that results in our perception of colour.
• Whilst the visible spectrum and its spectral colours are determined by wavelength (and corresponding frequency), it is our eyes and brains that interpret these differences in electromagnetic radiation and produce colour perceptions.
• Naming rainbow colours is a matter more closely related to the relationship between perception and language than anything to do with physics or optics.
• Even commonplace colour names associated with rainbows such as yellow or blue defy easy definition. These names are concepts related to subjective impressions.
• Modern portrayals of rainbows show six colours – ROYGBV. This leaves out other colours such as cyan and indigo.
• Atmospheric rainbows actually contain millions of spectral colours. Measured in nanometres there are around 400 colours between red and violet, measured in picometres there are 400,000.

• Rainbows are composed of rainbow rays.
• Rainbow rays are responsible for an observer’s perception of a rainbow.
• Rainbow rays are rays of light of a single wavelength that have their origin in individual raindrops. They can be explained in terms of their angular distance from the rainbow axis at the moment they contribute to an observer’s view of a rainbow.
• Rainbow rays are ephemeral. They are not individually observable but more a way of conceptualizing the fact that at a specific moment and in a specific position a raindrop will transmit one spectral colour towards an observer before falling further, perhaps to reappear in a different position and another colour.
• Individual rainbow rays produce the intense appearance of each of the different spectral colours that together constitute the phenomenon of rainbows.
• Rainbows are composed of millions of rainbow rays and each one has its origin within a single raindrop.
• A rainbow ray is a ray of a single wavelength that for a second is responsible for a bright flash of its corresponding colour as a result of being in exactly the right place at the right time.
• Rainbow rays are always located amongst the rays that deviate the least as they pass through a raindrop and bunch together around the minimum angle of deviation.
• The millions of microscopic images of the Sun that produce the impression of a rainbow function in a similar way to the pixels that produce the images we see on digital displays.
• Rainbow rays tend to out-shine all other sources of light in the sky (other than the Sun) and account for the brilliance and imposing appearance of rainbows.
• Because raindrops polarize light at a tangent to the circumference of a rainbow, the path of rainbow rays dissects raindrops exactly in half.
• So:
  • Individual rainbow rays account for the appearance of spectral colours of a single wavelength within the arcs of a rainbow.
  • Bands of colour within a rainbow are composed of rainbow rays that together transmit narrow spreads of wavelengths towards an observer.
  • The overall appearance of a rainbow as a singular phenomenon can be accounted for by optical and geometric rules that determine the passage of light through raindrops and in the process account for rainbow rays.
• Remember: the notion of light rays and rainbow rays are useful when considering the path of light through different media in a simple and easily understandable way. But in the real world, light is not really made up of rays. More accurate descriptions use terms such as photons or electromagnetic waves.

Rainbows result from light encountering raindrops in the presence of an observer. The phenomenon of rainbows offers many clues as to the nature of light.

• Light is a form of radiation, a type of energy that travels in the form of electromagnetic waves and can also be described as a flow of particle-like ‘wave-packets’, called photons.
• Radiation, electromagnetic waves and photons are all concepts that are interchangeable with the more general concept of light.

Theories of light

There are four principal theories that underpin our understanding of the physical properties of light as it relates to rainbows:

• Wave theory – the idea that light is transmitted from luminous bodies in an undulatory wave-like motion.
• Particle theory – the idea that the constitution and properties of light can be described in terms of the interactions of elementary particles.
• Electromagnetic theory – the classical theory of electromagnetism that describes light as coupled electric and magnetic fields, transporting energy as it propagates through space as a wave. The energy is stored in its electric and magnetic fields and can be measured in terms of its intensity.
• Quantum theory – explains the interactions of light with matter (atoms, molecules etc.) and describes light as consisting of discrete packets of energy,  photons. Quantum physics suggests that electromagnetic radiation behaves more like a classical wave at lower frequencies and more like a classical particle at higher frequencies, but never completely loses all the qualities of one or the other.

These theories tell us things about the properties of light

• Light is electromagnetic radiation, the force carrier of radiant energy.
• Whilst it carries energy and has momentum, light has no mass and so is not matter.
• Light is the result of the interaction and oscillation of electric and magnetic fields.
• Light is a microscopic phenomenon that needs macroscopic metaphors such as waves and particles to describe it.
• Once emitted at its source, light can propagate indefinitely through a vacuum in a straight line at the speed of light (299,792,458 metres a second) but can be deflected by gravity.
• In any specific instance, light can be described in terms of the inter-relationship of its wavelength, frequency and energy.
• Light slows down and is deflected as it propagates through air, water, glass and other transparent media as photons interact with matter.

Phenomena associated with light include:

• Absorption
• Diffraction
• Dispersion
• Interference
• Photoelectric effect
• Polarization
• Reflection
• Refraction
• Scattering
• Transmission

Some facts about electromagnetic waves

• An electromagnetic wave carries electromagnetic radiation.
• Electromagnetic radiation is measured in terms of the amount of electromagnetic energy carried by an electromagnetic wave.
• Electromagnetic waves can be imagined as synchronised oscillations of electric and magnetic fields propagating at the speed of light in a vacuum.
• The kinetic energy carried by electromagnetic waves is often simply called radiant energy or light.
• Electromagnetic waves are similar to other types of waves in so far as they can be measured in terms of wavelength, frequency and amplitude.
• Other terms for the amplitude of light are intensity and brightness.
• Another term for the speed at which light travels is its velocity.
• We can feel electromagnetic waves release energy when sunlight warms our skin.
• The position of an electromagnetic wave within the electromagnetic spectrum can be identified by its frequency, wavelength or energy.

Some facts about photons

• Photons are the elementary building blocks and so the smallest unit used to describe light.
• Photons are the carriers of electromagnetic force and travel in harmonic waves.
• Photons are zero mass bosons.
• Photons have no electric charge.
• The amount of energy a photon carries can make it behave like a wave or a particle. This is called the “wave-particle duality” of light.

A ray of light (light ray or just ray) is a common term when talking about how and why rainbows appear.

• 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.
• Modelling light as rays is a way to discuss and represent the path of light through different media in a simple and easily understandable way.
• When light rays are drawn in a ray-tracing diagram they are represented as straight lines connected at angles to illustrate how light moves and what happens when it encounters different situations and conditions.
• More accurate descriptions of light use terms such as photons or electromagnetic waves.
• Don’t forget that:
  • The incident rays of light that contribute to a rainbow seen by an observer are those that approach raindrops parallel with the rainbow axis.
  • To understand why incident rays are always parallel with the rainbow axis we need to think in terms of what the observer sees. See: 2.7 Observer’s point of view.

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.

Rainbows can be formed by droplets of liquids other than water, or even by a cloud of solid transparent microspheres. The table below shows the viewing angles for primary rainbows produced by a number of different media.
 

Substance	Refractive index	Viewing angle
Water	1.33	42.5
Kerosene	1.39	34.5
Carbon tetrachloride	1.46	26.7
Benzene	1.50	22.8
Plate glass	1.52	21.1
Other glass	1.47 to 1.61	25.7 to 14.2

Primary rainbow viewing angles for various media

• Materials with an index of refraction of 2.00 or more do not produce primary rainbows.
• Diamonds, for example, do not produce primary rainbows because their index of refraction is 2.42. However, if a diamond is ground into microspheres, it can produce secondary and higher-order rainbows.

Data from https://www.basic-physics.com/rainbows-figuring-their-angles/

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.

Raindrops, incident light and primary rainbows

Let’s look at the rays of incident light that contribute to a primary rainbow.

• All rays of light that contribute to a primary rainbow strike the surface of each raindrop three times. Once as they enter a droplet and undergo refraction, again as they reflect off the rear interior surface and once more as they undergo refraction for the second time and exit in the direction of the observer.
• Whilst some photons are following paths that will produce a primary rainbow there are many other possibilities for every photon and the vast majority go off in other directions.
• Incident rays of light that form the curved apex of a primary rainbow strike the upper half of raindrops in line with their vertical axis. These rays initially deviate downwards during refraction and internal reflection towards an observer.
  • Rays bend downwards (and slow down) as they enter a droplet and are refracted towards the normal.
  • Rays then reflect off the interior surface on the far side of a droplet and are directed downwards again.
  • When they strike the surface a third time, they are refracted away from the normal (and speed up) as they exit in the direction of the observer.
  • In some cases, this final step is an upward bend and so reduces the overall angle of deviation relative to their source.
• Incident rays of light that form the curved sides of a primary rainbow strike the side of a raindrop in line with their horizontal axis. These rays initially deviate inwards during refraction and internal reflection towards an observer.
• Incident rays of light striking the lower half of raindrops are initially directed upwards and away from the observer.

Raindrops, incident light and secondary rainbows

Now let’s look at the rays of incident light that contribute to a secondary rainbow.

• All rays of light that contribute to a secondary rainbow strike the surface of each raindrop four times. Once as they enter a droplet and undergo refraction, twice as they reflect off the interior surface and once more as they undergo refraction for the second time and exit in the direction of the observer.
• Incident rays of light that form the curved apex of a secondary rainbow strike the lower half of raindrops in line with their vertical axis. These rays initially deviate vertically upwards during refraction and internal reflection.
  • Rays bend upwards (and slow down) as they enter each droplet and are refracted towards the normal.
  • Rays then reflect twice off the interior surface on the far side of the droplet. After the second strike, they are directed downwards towards the observer.
  • Finally, at the fourth strike, they refract away from the normal (and speed up) as they exit.
• Incident rays of light that form the curved sides of a secondary rainbow strike the side of a raindrop in line with their horizontal axis. These rays deviate inwards during refraction and internal reflection towards an observer.
• Incident rays of light striking the upper half of raindrops at the apex of a rainbow during the formation of a secondary rainbow are initially directed downward and away from the observer.

Alexander’s band

• The fact that light deviates downwards when it strikes the upper half of droplets that contribute to a primary rainbow and deviates upwards when it strikes the lower half of droplets that contribute to secondary bows accounts for the darker area between the two known as Alexander’s band.

Polarization of electromagnetic waves refers to a situation in which the rotation of all the coupled electric/magnetic fields is restricted to a single plane from the point of view of an observer.

• It is the electric field that aligns with the plane.
• This phenomenon is known as plane polarization.

• Plane polarization filters out all the waves where the electric field is not orientated with the plane from the point of view of an observer.
• To visualize plane polarization, imagine trying to push a large sheet of card through a window fitted with close-fitting vertical bars.
• Only by aligning the card with the slots between the bars can it pass through. Align the card at any other angle and its path is blocked.
• Now substitute the alignment of the electric field of an electromagnetic wave for the sheet of card, and plane polarization for the bars on the window.
  • Polarizing lenses used in sunglasses rely on plane polarization.
  • The polarizing plane is orientated horizontally and cuts out glare by blocking vertically aligned waves.
  • In the case of a rainbow, it is the position of each raindrop on the arc of the bow, with respect to the observer, that determines the angle of the polarizing plane.
• Rainbows are typically 96% polarized.

Let’s take this one step at a time

• Rainbows form in the presence of sunlight, raindrops and an observer, and involve a combination of refraction, reflection and chromatic dispersion.
• It is during reflection off the back of a droplet that light becomes polarized with respect to an observer.
• The rear hemisphere of a raindrop forms a concave mirror in which an observer sees a tiny reflection of the Sun.
• As a rainbow forms, an image of the Sun forms in each and every raindrop and the ones in exactly the right place at the right time become visible to the observer.
• The light reflected towards an observer is polarized on a plane bisecting each droplet and at a tangent to the arc of the rainbow.
• The rear hemisphere of a raindrop is best thought of as the half of the raindrop opposite the observer and with the Sun at its centre.
• Now recall that to see yourself in a normal flat mirrored surface it has to be aligned perpendicular to your eyes. Get it right and you see yourself right in the middle. If it’s not perpendicular, then you see your image off-centre because the mirror is not aligned with your eyes on either the horizontal or vertical planes.
• The Sun appears right in the centre of every raindrop from the point of view of an observer only if it is in exactly the right position in the sky at the right time. In all other cases, the light is scattered in other directions.
• Only rays that strike at the point where the horizontal and vertical planes intersect are reflected towards the observer. Rays that strike to the left or right or above/below the centre-point miss the observer.
• The correct alignment of a raindrop involves the vertical axis of the rear hemisphere being at exactly 90⁰ with respect to the observer. In the case of a primary rainbow, the horizontal axis is titled downwards by approx. 20.5⁰.

In real-life, full-size raindrops don’t form perfect spheres because they are composed of water which is fluid and are only held together 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, it is composed of areas at different airflows, 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.
• Raindrops start to form high in the atmosphere around tiny particles called condensation nuclei — these can be composed of little pieces of salt left over after seawater evaporates, or particles of dust or smoke.
• Raindrops form around condensation nuclei as water vapour cools producing clouds of tiny droplets that start off roughly spherical.
• Surface tension is the tendency of liquids to shrink to the minimum possible surface area.
• At water-air interfaces, the surface tension that holds water molecules together results from them being attracted to one another more than to the nitrogen, oxygen, argon or carbon dioxide molecules that make up our 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 encounter more vapour and collide with one another. As larger droplets bump into other smaller droplets they increase in size — this is called coalescence.
• Once they 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 (updraught) force raindrops back into the clouds and coalescence starts over.
• As full-size raindrops fall they lose some of their rounded shape. The bottom becomes flattened due to 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 bumped into and coalesced with the most droplets.