Dictionary tag: R

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 the geometrical orientation of their oscillations.

Polarization restricts the orientation of the oscillations of the electric field of electromagnetic waves to a single plane from the point of view of an observer. 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.
• Plane polarization is one of the optical effects that account for the appearance of rainbows.
• It is the position of each raindrop on the arc of a rainbow, 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.

Not all incident light striking a raindrop crosses the boundary into the watery interior of a droplet. Some of the incident light is reflected off the surface and a small proportion of that travels towards the observer.

• Incident light reflected off the surface facing an observer undergoes neither refraction nor dispersion.
• Because the outside surface of a raindrop forms a shiny convex mirror, reflected light diverges in every possible direction depending on its initial point of impact.
• Just as raindrops form the coloured arc of a primary rainbow, they can also reflect white light towards an observer.
• White light reflected towards an observer off the outside of raindrops helps to account for why the sky on the inside of a rainbow (between its centre and coloured arcs) appears brighter and lighter than the area of sky outside.