Refraction in a raindrop

An important optical effect that explains how raindrops produce rainbows is refraction.

Refraction

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 slower medium such as water to a faster medium such as air it bends away from the normal and speeds up.
  • In a diagram illustrating optical phenomena like refraction or reflection in a raindrop, the normal is a line drawn from the surface of a raindrop to its centre.
  • The speed at which light travels through a given medium is expressed by its refractive index (also called the 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 the smaller refractive index.
    • Which is the slower, more optically dense medium with the higher refractive index.
  • The degree to which refraction causes light to change direction 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.
More about refraction in a raindrop
  • Light rays (streams of photons) undergo refraction twice when they encounter a raindrop, once as they enter, then again as they leave.
  • Once inside a raindrop, a given photon may reflect off the inside surface of a raindrop several times, but on each refraction, some light crosses the boundary back and undergoes refraction as it escapes into the surrounding air.
  • Some photons never escape, instead, they are absorbed when they strike electrons within a raindrop, releasing heat that can causes evaporation.

Saturation

Saturation refers to the perceived difference between one colour and another in terms of vividness. The hue of a vivid colour appears to be at full strength rather than insipid or washed out.

Associating saturation with a colour model

To avoid confusion about the term saturation, it is best to associate it with a colour model, a practical application and a family of related terms.

  • Examples of colour models include spectral colour, RGB colour, CMYK colour and HSB colour.
  • Examples of practical applications include digital design, stage lighting, mixing of oil or water-based paints, inks and dyes.
Colour in general terms
  • When an observer asks themselves what colour something is, they might refer to spectral colours and use names associated with rainbows (ROYGBV), to a set of colours (a palette of colours) they are working with or to a family of colours such as warm or cool colours.
  • A broader vocabulary of names can be used to describe colours such as dark red, vermilion, golden yellow, lemon yellow, pale yellow, greenish-yellow, chartreuse, leaf green or light green.
  • A colour model derived from a theory of colour allows for a more exact and reproducible approach to colour.
Colour models
  • Colour models are the how-to part of colour theory. Together they establish terms and definitions, rules or conventions and a system of notation for encoding colours and their relationships with one another.
  • These days, the most practical colour models are built into applications such as Adobe Creative Cloud which allow easy digital output to TV’s, computers and phones or printing onto paper and other surfaces.
  • Widely used colour models include:
    • Spectral colour
    • RGB colour
    • HSB colour
    • CMYK colour
Using the term saturation
  • At lightcolourvision.org we use saturation in relation to the colour models it belongs to. One of our favourites is the HSB colour model.
  • Colour models describe the attributes of colour in different ways.
  • The HSB colour model refers to saturation alongside hue and brightness.
  • The HSB colour model is extensively used for digital design and can be used to describe any colour on a TV, computer or mobile phone.
  • The CMYK colour model uses a different set of attributes because one of its main concerns is how coloured inks appear on paper. Because saturation isn’t part of the vocabulary used in that field the term is best avoided.
Saturation and wavelength
  • A colour appears saturated when it contains a narrow range of wavelengths.
  • Unsaturated colours appear washed out because they contain a broader range of wavelengths.
  • Saturation is related to light complexity. Complexity refers to the range or spread of wavelengths of light used to produce a colour.
  • A colour produced by a single wavelength of light is often referred to as pure spectral colour.
  • In real-life, colour is usually produced by a mixture of different wavelengths. The greater number of spectral colours in a light, the lower the saturation.
HSB colour model
  • The HSB colour model provides an intuitive way to select and adjust colours in software applications used for graphic design, web development and photography.
  • HSB describes the fundamental characteristics of how colours appear when reflected by or transmitted through an object towards an observer as:
    • Hue refers to the perceived difference between one colour and another by using names such as red, yellow, green or blue. Hue can be measured as a location on the standard colour wheel and expressed as a degree between 0 and 360.
    • Saturation refers to the perceived difference between one colour and another in terms of vividness. Saturation is measured between a fully saturated colour (100%) and an unsaturated colour that appear dull and washed out until all colour disappears leaving only a monochromatic grey tone (0%). On many colour wheels, saturation increases from the centre to the edge.
    • Brightness refers to the perceived difference between a colour observed in ideal sunlit conditions compared with conditions where the vitality of the hue is lost because the lighting is poor. Brightness can be measured as a percentage from 100% to 0%. As the brightness of a fully saturated hue decreases it appears progressively darker.
References
  • https://en.wikipedia.org/wiki/Colorfulness#Saturation

Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.  In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.

Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.
In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.
 

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.
Scattering in physics

Rayleigh scattering refers to the scattering of visible light or other electromagnetic radiation by particles smaller than the wavelength of the radiation. Rayleigh scattering is wavelength dependent.

Mie scattering refers to the scattering of visible light or other electromagnetic radiation by particles larger than the wavelength of the radiation. Mie scattering is wavelength dependent. Mie scattering is responsible for the white appearance of the clouds.

Non-selective scattering is similar to Mie scattering and takes place when the particles are much larger than the incident radiation. This type of scattering is not wavelength dependent and is the primary cause of atmospheric haze.

References
  • https://en.wikipedia.org/wiki/Scattering
  • https://www.google.com/search?client=firefox-b-d&q=Rayleigh+scattering
  • https://en.wikipedia.org/wiki/Mie_scattering

Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.  In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.

Scotopic curve

A scotopic curve is a diagram showing that, at low levels of light, where determining colour differences is difficult, the strongest response of the human eye moves towards blue and violet end of the visible spectrum with less sensitivity towards the red when compared with a photopic curve.

  • Whilst a  scotopic curve describes the response of the human eye to low levels of light a photopic curve is a diagram showing that, in bright light, the strongest response of the human eye is to the colour green with less sensitivity towards the spectral extremes of red and violet.

Secondary colour

secondary colour is a colour made by mixing two primary colours in a given colour space. The colour space may be produced by an additive colour model that involves mixing different wavelengths of light or by a subtractive colour model that involves mixing pigments or dyes.

  • Secondary colours produced by an additive colour model are quite different from the spectral colours seen in a rainbow.
  • A spectral colour is produced by a single wavelength, or a narrow band of wavelengths, within the visible spectrum.
  • A secondary colour produced by an additive colour model results from superimposing wavelengths of light from different areas of the visible spectrum.
  • For the human eye, the best additive primary colours of light are red, green, and blue.
  • RGB colour can be used to produce an extremely wide range of colour.
  • Because RGB colour involves adding different wavelengths of light together (thus the term “additive colour”), the resulting combinations always appear lighter to an observer.
  • When all three primaries (or for that matter all three secondaries) are combined in equal amounts, the result is white.
  • The RGB secondary colours produced by the addition of light turn out to be the best primary colours for pigments, the mixing of which subtracts light.

Secondary colour

secondary colour is a colour made by mixing two primary colours in a given colour space. The colour space may be produced by an additive colour model that involves mixing different wavelengths of light or by a subtractive colour model that involves mixing pigments or dyes.

Secondary rainbow

A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.

  • A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
  • A secondary rainbow has violet on the outside and red on the inside of the bow.
  • When both primary and secondary bows are visible they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.
  • A secondary bow is never as bright as a primary bow because:
    • Light is lost during the second reflection as a proportion escapes through the surface back into the air.
    • A secondary bow is broader than a primary bow because the second reflection allows dispersing wavelengths to spread more widely.
Remember that:
  • The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
  • The space between a primary and secondary rainbow is called Alexander’s band.

Sine

In mathematics, the sine is a trigonometric function of an angle.

  • The sine of an acute angle is defined in the context of a right-angle triangle.
  • For any specified angle, it’s sine is the ratio of the length of the side opposite that angle, to the length of the longest side of the triangle (the hypotenuse).
  • The mathematical notation for sine is sin.

Sine

In mathematics, the sine is a trigonometric function of an angle.

  • The sine of an acute angle is defined in the context of a right-angle triangle.
  • For any specified angle, it’s sine is the ratio of the length of the side opposite that angle, to the length of the longest side of the triangle (the hypotenuse).
  • The mathematical notation for sine is sin.

Slow medium

Light travels through different media such as air, glass or water at different speeds. A slow medium is one through which it passes more slowly.

  • Light travels through a vacuum at 299,792 kilometres per second.
  • Light travels through other media at lower speeds. In some media, it travels at a speed which is nearer the speed of light as it passes through a vacuum and in others it travels much more slowly.
  • It is useful to know whether a medium is fast or slow to predict what will happen when light crosses the boundary between one medium and another.
  • so:
    • If light crosses the boundary from a medium in which it travels fast into a material in which it travels more slowly, then it will bend towards the normal.
    • If light crosses the boundary from a medium in which it travels slowly into a material in which it travels more quickly, then the light ray will bend away from the normal.

https://en.wikipedia.org/wiki/Refraction

Snell’s law calculator

To calculate the angle of refraction of an incident ray entering a raindrop enter:

  1. The refractive index of air for a ray with wavelength 589.29 nm. n1) = 1.000293
  2. The refractive index of water for ray with wavelength 589.29 nm, (n2) = 1.3333
  3. The Angle of incidence of your ray as it strikes the surface. (θi) = angle between the ray and the normal

The angle of refraction2) will appear in the final box.

https://www.omnicalculator.com/physics/snells-law

Snell’s Law Calculator

To calculate the angle of refraction of an incident ray entering a raindrop enter:

  1. The refractive index of air for a ray with wavelength 589.29 nm. n1) = 1.000293
  2. The refractive index of water for ray with wavelength 589.29 nm, (n2) = 1.3333
  3. The Angle of incidence of your ray as it strikes the surface. (θi) = angle between the ray and the normal

The angle of refraction2) will appear in the final box.

https://www.omnicalculator.com/physics/snells-law

So you want a photo of a rainbow

Make sure you are always carrying your camera or phone with you. Natural rainbows are rarer than you might think? You may get your photo on the first day, or it may be weeks before the conditions are right.

  • If you can’t wait for nature to make you a rainbow, then there are other options. Rainbows can be produced by waterfalls, water fountains, lawn sprinklers and other things that create a spray of water.
  • Once you find your rainbow then ideally, place your camera on something solid or use a tripod.
  • If you are using a phone then set it to maximum resolution (the largest file size).
  • If you are using a camera, have the option, and plan to edit your shots, then select camera raw. This is a file format that gathers as much detail as possible without worrying about file size.
  • Take plenty of photos. It’s best to take a whole series. Zoom in, zoom out change the framing.
  • If you have the option, then use a range of exposure settings. This is sometimes called exposure bracketing. The rainbow will show up best if a photo is a bit darker so that there is more detail in the sky.
  • If your camera has the option, select HDR (high dynamic range) for some shots. This mode allows your device to take three (or more) shots at different exposures and then blends them together to create a better overall result.
  • Once you have the photos, the next option is Adobe Photoshop or similar. With the right set of skills, you can make endless edits and adjustments until your rainbow looks just right.

Solar radiation

Solar radiation is the electromagnetic radiation emitted by the sun.

  • Electromagnetic radiation is a type of energy that is commonly known as light. Detached from its source, it is transported by electromagnetic waves (or by their quanta, particles called photons) and propagates through space.
  • Electromagnetic radiation includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.
  • Electromagnetic radiation is sometimes called EM radiation or electromagnetic radiant energy (EMR).
  • All forms of electromagnetic radiation can be described in terms of both waves or particles.
  • All forms of electromagnetic radiation travel at 299,792 kilometres per second in a vacuum.

Spectral colour

A spectral colour is a colour evoked in normal human vision by a single wavelength of visible light, or by a narrow band of adjacent wavelengths.

About spectral colours
    • A spectral colour is a hue evoked in normal (trichromatic) human vision by a single wavelength of visible light, or by a narrow band of adjacent wavelengths.
    • Sunshine contains nearly all spectral colours.
    • Spectral colourss are commonly associated with rainbows, prisms and diagrams showing the colours of the visible spectrum (red to violet). But any medium that reflects or transmits a single wavelength of light produces a spectral colour.
    • Rainbow colours include red, orange, yellow, green, blue and violet but the human eye can distinguish many thousands of other spectral colours between each of these.
    • In a continuous spectrum of wavelengths, separate hues are indistinguishable to the human eye.
    • The brightness of a spectral hue viewed by an observer may alter considerably depending on the situation. For example, a low-intensity orange-yellow may appear brown, and a low-intensity yellow-green may appear olive-green.
    • Spectral colours can be mimicked by RGB colour. This involves mixing coloured lights tuned to the three spectral primaries, red, green and blue. The resulting colours are not spectral colours because of the resulting mix of wavelengths.
    • Spectral colours are sometimes called spectral hues, pure hues or monochromatic hues.
    • The fact that we see the distinct bands of colour in a rainbow is an artefact of human colour vision.

Spectral colour model

A spectral colour is a colour evoked in normal human vision by a single wavelength of visible light, or by a narrow band of adjacent wavelengths.

About spectral colour
    • A spectral colour is a hue evoked in normal (trichromatic) human vision by a single wavelength of visible light, or by a narrow band of adjacent wavelengths. This is how we see colour in normal viewing conditions such as sunlight or artificial light.
    • Sunshine is a typical case in so far as it contains nearly all spectral hues.
    • Sunshine has a very broad spectral power distribution and as light strikes surfaces, some wavelengths are absorbed, and others are reflected. The mix of reflected wavelengths results in the non-spectral colours we see.
Non-spectral colour
    • A non-spectral colour is any hue that cannot be produced by light of a single wavelength or that does not occur in the visible spectrum (e.g. Magenta).
    • Spectral hues are commonly associated with rainbows, prisms and diagrams showing the colours of the visible spectrum (red to violet). But any medium that reflects or transmits a single wavelength of light produces a spectral colour.
    • Spectral colours can be mimicked by RGB colour. This involves mixing coloured lights tuned to the three spectral primaries, red, green and blue. The resulting colours are not spectral colours because of the resulting mix of wavelengths.
    • The intensity, which is to say, the brightness, of a spectral hue viewed by an observer may alter considerably depending on the situation. For example, a low-intensity orange-yellow may appear brown, and a low-intensity yellow-green may appear olive-green.
The human eye and spectral colour
    • The human eye, and so human perception, is tuned to the visible spectrum and so to all wavelengths that correspond with spectral colours between red and violet.
    • The visible spectrum is the range of wavelengths of the electromagnetic spectrum that correspond with all the different colours we see in the world. We do not see colour when exposed to wavelengths of infrared or ultraviolet light.
    • A spectral colour is a hue corresponding with a single wavelength of visible light, or with a narrow band of adjacent wavelengths.
    • In other situations, spectral hues are called pure hues or monochromatic hues.
    • Spectral colours include all the pure hues associated with a rainbow so are sometimes called rainbow colours.
Rainbow colours
  • Rainbow colours include red, orange, yellow, green, blue and violet but the human eye can distinguish many thousands of other spectral colours between each of these.
  • In a continuous spectrum of wavelengths, separate hues are indistinguishable to the human eye.
  • The fact that we see the distinct bands of colour in a rainbow is an artefact of human colour vision.
  • Spectral colours can be mimicked by RGB colour. This involves mixing coloured lights tuned to the three spectral primaries, red, green and blue.

https://en.wikipedia.org/wiki/Spectral_color

Spectral power distribution

The spectral power distribution (spectral distribution) of a light or colour stimulus refers to the range, mixture and intensity of wavelengths of light that it produces.

  • A diagram showing the accurate measurement of the spectral power distribution of the light given off (emitted, transmitted, or reflected) by a light source or by a surface provides complete information about that stimulus.
  • The human eye contains three colour receptors (cones), which means that every spectral power distribution is reduced to three sensory quantities that can be described by tristimulus values.
  • Different stimuli can in some cases produce the same colour sensation for an observer. This effect (called metamerism) occurs because each type of cone responds to the distribution of energy across the entire spectral power distribution of a light source.