Raindrop Geometry

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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.
  • For quick reference don’t miss the summaries of key terms further down each page.

Description

Raindrop Geometry

TRY SOME QUICK QUESTIONS AND ANSWERS TO GET STARTED
Rainbow colours are spectral colours. Every rainbow colour is produced by a single wavelength of light.
Red is always on the outside edge of a primary rainbow.
No! The outermost colour on a secondary rainbow is violet because the colours of a secondary rainbow are reversed.
Yes! Each colour in a rainbow between red and violet is a spectral colour.

About the diagram

About the diagram
  • This diagram shows some of the geometry that determines the path of light through a raindrop.
  • This is a measured diagram and the angles shown are indicative of the path of a single yellow ray with a wavelength of 589.29nm travelling through water at 200C.
  • The table below provides a key to the notation used on the diagram.
  • The aim of the diagram is to:
    • highlight the geometric points used to explain changes in the direction and speed of light when it strikes the surface of a raindrop.
    • Show where and how angles are measured.
    • Show connections between angles
  • Note that:
    • The notation used in the diagram is not associated with any other system of identification.
    • Standard mathematical symbols have not been used for this diagram.
LabelDescription
AirEarth's atmosphere is generally considered to be composed of nitrogen, oxygen, argon with trace amounts of carbon dioxide, hydrogen, methane and neon.
Average humidity, pressure and a temperature of 20C produce a refractive index of 1.000293.
RaindropAn 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.
Impact parameter scaleAn impact parameter scale is used on a ray-tracing diagram to measure the point at which incident rays strike the surface of a raindrop. Rays are given a value between 0.0 and 1.0 depending upon their point of impact.
AThe point at which an incident ray strikes a raindrop,
BThe point at which the refracted ray reflects off the inside of a raindrop.
CThe point at which the reflected ray strikes the inside of a raindrop undergoes refraction and exits towards an observer.
DThe point on the rainbow axis at which the angular distance of the deflected ray is measured.
EThe point of intersection between the original path of the incident rays prior to striking the raindrop and deflected ray.
FThe centre of the raindrop.
aEqual angles
a1Angle of incidence at point of impact of incident ray.
b1Angle of refraction at point of impact of incident ray.
bEqual angles
dAngle of deviation
y1 + y2 + y3Equal to angle of deviation (d)
zAngle of deflection
z + dEqual to 180 degrees
>>The symbol used to mark parallel lines.

Key to Rainbow geometry diagram

About raindrop geometry

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.

Don’t forget that the idea of light rays is also a way to simplify the behaviour of light:

  • 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

When discussing the formation of rainbows, the angle of deflection measures the angle between the initial path of a light ray before it hits a raindrop, and the angle of deviation, which measures how much the ray bends back on itself in the course of refraction and reflection towards an observer.

  • See this diagram for an explanation: Rainbow anatomy
  • The angle of deflection and the angle of deviation are always directly related to one another and together add up to 180 degrees.
  • The angle of deflection equals 180 degrees minus the angle of deviation. So, it’s clear the angle of deviation is always equal to 180 degrees minus the angle of deflection.
  • In any particular case, the angle of deflection is always the same as the viewing angle because the incident rays of light that form a rainbow all follow paths that run parallel with the rainbow axis.

Rainbow colours are the colours seen in rainbows and in other situations where visible light separates into its different wavelengths and the spectral colours corresponding with each wavelength become visible to the human eye.

  • The rainbow colours (ROYGBV) in order of wavelength are red (longest wavelength), orange, yellow, green, blue and violet (shortest wavelength).
  •  It is the sensitivity of the human eye to this small part of the electromagnetic spectrum that results in our perception of colour.
  • The names of rainbow colours are a matter more closely related to the relationship between perception and language than anything to do with physics or scientific accuracy. While the spectrum of light and the colours we see are both determined by wavelength, it’s our eyes and brains that turn these differences in light into the colours we experience.
  • In the past, rainbows were sometimes portrayed as having seven colours: red, orange, yellow, green, blue, indigo and violet.
  • Modern portrayals of rainbows reduce the number of colours to six spectral colours, ROYGBV.
  • In reality, the colours of a rainbow form a continuous spectrum and there are no clear boundaries between one colour and the next.

 

 

The angle of refraction measures the angle to which light bends as it passes across the boundary between different media.

  • The angle of refraction is measured between a ray of light and an imaginary line called the normal.
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • See this diagram for an explanation: Refraction of a ray of light
  • If the boundary between the media is curved, the normal is drawn perpendicular to the boundary.

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°.

The angle of incidence measures the angle at which incoming light strikes a surface.

  • The angle of incidence is measured between a ray of incoming light and an imaginary line called the normal.
  • See this diagram for an explanation: Reflection of a ray of light
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • If the boundary between the media is curved, then the normal is drawn at a tangent to the boundary.

A rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflection, refraction (bending) and dispersion (spreading out) of light in individual droplets and result in the appearance of an arc of spectral colours.

  • Atmospheric rainbows only appear when weather conditions are ideal and an observer is in the right place at the right time.
  • Waterfalls, lawn sprinklers and other things that produce air-borne water droplets can produce a rainbow.
  • An atmospheric rainbow is formed from countless individual droplets each of which reflects and refracts a tiny coloured image of the Sun towards the observer.
  • As white light passes through water droplets, refraction causes the light to disperse and separate into the different colours seen by an observer.
  • If the sun is behind an observer then the rainbow will appear in front of them.
  • When a rainbow is produced by sunlight, the angles between the sun, each droplet and the observer determine which ones will form part of the rainbow, the colour each droplet will produce and the sequence in which they appear.

An artificial light source is any source of light created by humans, as opposed to natural light sources like the sun or stars. Artificial light sources are generated by converting different forms of energy into light.

  • There are several major categories of artificial light sources such as:
    • Incandescent: These work by heating a filament until it glows, emitting light (traditional light bulbs).
    • Fluorescent: Electric current triggers gas inside the bulb to produce ultraviolet light, which a phosphor coating converts into visible light.
    • LED (Light-Emitting Diode): Electricity excites semiconductors, causing them to emit light.
    • Gas-discharge lamps: Electric current passes through a gas, producing bright light (e.g., neon signs, street lamps).

The angle of reflection measures the angle at which reflected light bounces off a surface.

  • The angle of reflection is measured between a ray of light which has been reflected off a surface and an imaginary line called the normal.
  • See this diagram for an explanation: Reflection of a ray of light
  • In optics, the normal is a line drawn on a ray diagram perpendicular to, so at a right angle to (900), the boundary between two media.
  • If the boundary between the media is curved then the normal is drawn perpendicular to the boundary.

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