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Our lives will be less interesting without the display of wonderful ever-changing panoramic colours in the environment - the sky is blue during the day but at sunrise and sunset it turns red/orange; clouds are white and grey but take some striking hues; oceans are blue or deep green, and may even look red sometimes. Ice is considered white - then why a glacier, a big chunk of ice, deep blue? We have all experienced the surprise and delight when the majestic rainbow suddenly appears -- a double rainbow is just awesome.
Some fascinating physics is in play to enrich our lives with these (and many other) wonderful displays. The physics is about the way sunlight interacts with particulate matter and gas molecules (mostly oxygen and nitrogen) in the atmosphere. Light interaction with water molecules in liquid (swimming pools/ocean) and solid state (glaciers) is completely different. The physics of rainbows is different still and has already been discussed in detail here.
In the atmosphere, how the particles and gas molecules scatter sunlight depends on their size, number density and on the colour (wavelength) of light. In liquid water and ice, the internal structure of water molecules determines how longer wavelengths (yellow and red colours) are removed more efficiently than shorter 'blue' wavelengths.
In this article, I shall delve into the science of colours in the environment with the aim to convey a greater understanding of how light and matter interact. In Part 1, I shall discuss the colours of the sky and clouds, and deal with the case of bulk water and ice in Part 2.
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To maintain continuity of presentation, some background information will be included in the Appendix.
PART 1: Why is the sky blue during the day but at sunset it turns red?
Slide 1
Slide 2
Slide 5
I have added a brief description of the physics of how light interacts with matter particles in the Appendix.
It is convenient to identify three scattering regimes (see last column of slide 5). The important number is the scattering parameter (x = 2 𝜋 r/𝜆) which tells us how big or small a particle of radius r is relative to the wavelength of visible light (𝜆); in our case, 𝜆 covers the range from 450 nm to 700 nm. For gas molecules (oxygen and nitrogen), the radius is equal to 0.15 nm and x is of the order of 0.0015 - much smaller than 1; and only Rayleigh scattering needs to be considered. Mie scattering is important when x is of the order of 0.1 to 1.0. For larger values of x, the scattering is called geometrical (aka optical). Slides 6,7, 8 & 9 explain the situation. Only Rayleigh scattering is strongly wavelength sensitive (1/𝜆⁴ dependence) with blue light at 450 nm scattered almost five times more strongly than red light at 650 nm.
Slide 6
Slide 7
Slide 8
The probability of light scattering from a particle increases as particle size gets bigger. Very roughly, Mie scattering can be >10000 stronger than Rayleigh scattering (see slide A2) while optical scattering increases as the square of the particle radius (click here for quantitative details). However, note that the number density of molecules that cause Rayleigh scattering is extremely large (see slide 5), and at higher altitudes the contribution of Rayleigh scattering is the most important. Even with the large number of gas molecules (of the order of 10²⁵ per m³), a light photon only experiences a single scattering event in passing through the Earth's atmosphere.
The density of aerosols at high altitudes is very low, and only at altitudes less than 5 km Mie scattering by aerosols in the troposphere becomes significant. At even lower altitudes, geometric scattering by clouds and pollution particulates may dominate - depending on the weather and contaminants generated by natural and/or human activities.
Another interesting feature to note is the angular distribution of scattered light - Rayleigh scattering shows a modest forward and backward peaking with only half as much light scattered along perpendicular directions (scattering is peanut shaped - see slide 6). Mie scattering is forward peaking and becomes more so for bigger particles. In optical scattering, due to multiple scattering effects, all wavelengths are scattered more or less uniformly in all directions; for bigger particles like raindrops or ice crystals, light can enter into the particle body and produce phenomena like the rainbows.
Slide 10 is best viewed by clicking on it for a full page image. The blueness of the sky at various points is well reproduced by mixing different amounts of MO to RC. In fact a full spectrum of blue hues from quite sharp to very soft may be obtained this way. This is explained in slide 11.
Slide 11
It is not advised to look directly at the Sun which is more or less white with some yellowish hue. The sky near the Sun is less blue than the sky at angles further away from it. In regions close to the Sun, some blue light is indeed scattered out from the white sunlight by Rayleigh scattering but the overall light is still nearly white. Slide 12 explains the colour of the sky near the Sun.
Remember that when you look at any part of the sky you are observing its features in a very small angular range (much less than a degree) and the light from the Sun can only reach you if it is scattered out of sunrays by some object. For example, the line of sight along the direction YA shows how the scattering by aerosols (Mie and Optical scattering), redirects white light from sunrays towards the observer and dilutes the blueness of the sky due to RC. In the absence of any atmosphere, the Sun will appear as a white disc surrounded by black sky (Slide 3).
Slide 12
The contribution from Mie scattering decreases as one looks away from the Sun and the sky becomes progressively deeper blue. Along the horizon away from the Sun, the path length of sunrays in the lower atmosphere is rather large and while Mie scattering contributes little, optical scattering by larger aerosol particles becomes important and the sky colour has much more whiteness (see slide 1).
An interesting observation of the scattering of light from the atmosphere is made by high flying U2 planes. They fly at about 20 km altitude - above the troposphere - and can receive Rayleigh scattered blue light from gas molecules in the atmosphere. Also note that the outer space looks pitch dark - there are no molecules or aerosols there to scatter sunlight back towards the Earth.
Slide 12a
Clouds consist of water droplets and/or ice crystals. Majority of the clouds are in the troposphere and come in many shapes and sizes. Clouds form by water molecules condensing on an aerosol particle (dust, sea-salt, soot etc. typically of size around 0.0002 mm or 0.2 micron). Cloud droplets may vary in size from about 20 to 3000 microns. Low clouds are found at altitudes below about 2 km, but high clouds can form at heights from 5 to 20 km or even higher - they are generally thin and are not associated with weather.
Cloud thickness is an important parameter for our discussion; it varies enormously depending on the cloud type. Clouds can be quite thin - a few hundred meters (e.g. cirrus) to > 10 km in thickness (e.g. cumulonimbus).
Sunlight is efficiently reflected by water droplets and ice crystals - more or less isotropically (equally in all directions) - very little light is actually absorbed by the clouds (slide 13).
Slide 13
Path Length at Sunset in Atmosphere:
Slide A3 (appendix) gives a simple derivation of the path length D through the troposphere (of height 10 km) for various elevations of the Sun. D increases to over 500 km when the Sun elevation is 1⁰. At this elevation, to reach the observer, light will travel 2500 km in the stratosphere. Actually, at sunset refraction in the atmospheric layers increases the path length even more. For such long path lengths, light scatters many times from gas molecules (Rayleigh scattering); on each scattering, five times more blue light is scattered out of the sunrays (and hence lost) than red light. By the time light reaches the observer, it is highly deficient in blue and green, and consists mainly of longer reddish wavelengths.
Secondly, the lower atmosphere consists of aerosols particles of larger sizes which efficiently scatter light in all directions - this further reduces the amount of blue light (as well as longer wavelengths). The result is an overall attenuation of light in the lower atmosphere, making sunsets less bright. The light, rich in yellow to red colours, reflects from the bottom of surrounding clouds and makes them appear bright yellow, orange, pink or red.
Another interesting feature to note (slide 15) is that the sky at larger elevations of greater than a few degrees still appears blue - although not as bright as it is during the day. This happens because light from the setting Sun still reaches upper layers of troposphere and stratosphere where it is Rayleigh scattered by gas molecules towards the observer - scattered light received by the observer is rich in blue colour. Density of molecules in the upper atmosphere is not large and the overall the sky is not as bright as it is during the day.
Refraction of Light in the Earth's atmosphere - Total Lunar Eclipse:
At sunset, sunrays pass close to the Earth's surface where the pressure and hence the gas density changes rapidly with altitude. Sharp density gradients cause light path to bend (see slide 17) and the Sun to appear higher in the sky than it really is. The change in elevation depends on atmospheric conditions but is of the order of 0.5 degrees. Light from the lower parts of the sun's disc is refracted by a greater amount and the apparent position of the bottom of the Sun is shifted more than the top of the Sun - giving the Sun a squeezed appearance (oblate disc shape).
Slide 17
Colour of the Moon at Total Lunar Eclipse: An interesting consequence of refraction of light in the Earth's atmosphere is during a total lunar eclipse when the Moon is seen to acquire a reddish brown colour at the time of total occlusion. This happens when the Earth is directly in the path between the Sun and the Moon and casts a shadow big enough to totally block any sunlight from reaching the Moon. Normally this would imply that the Moon disappears from our view. However, rays from the Sun still pass through the Earth's atmosphere and refraction causes their paths to bend in such a way that Moon is illuminated by the refracted sunlight. Because the light has passed through a big length of Earth's atmosphere, Rayleigh scattering causes blue (shorter) wavelengths to preferentially scatter out of the sunrays leaving the transmitted light rich in longer red wavelengths. The intensity of such light that reaches the Moon and is then reflected back to the observers on Earth is rather weak and the Moon, at the time of total eclipse appears muddy red.
Slide 18
Earth's Shadow, Sunset, Twilight Zones and Dusk:
It is not widely appreciated that even though the troposphere has about 80% of the atmosphere mass, the stratosphere and mesosphere (slide 4) hold appreciable amount of gas molecules. Besides the ozone layer at about 25 km altitude, there are aerosol particles which may stay in the stratosphere for long periods of time - such aerosols reach the stratosphere from volcanic eruptions, high flying aeroplanes etc. Dust from meteorites in the mesosphere and beyond consists of very fine nanometer sized particles that act as water condensation centres and form clouds.
During the day, scattered light from the constituents of the stratosphere and mesosphere is indeed present but is masked completely by the much more intense scattered light by gas molecules in the troposphere. In the evening around sunset through twilight zones (our discussion is equally valid for sunrise) Earth's shadow blocks sun rays from illuminating the troposphere, but sunlight can still reach higher altitudes of the atmosphere (slides 19, 20 and 21).
Slide 19
Slide 20
Slide 21
Rare 'mother-of-pearl' cloud spotted in Scotland
APPENDIX
Slide A1
Scattering of Light by Particles: Light is an electromagnetic (EM) wave - a manifestation of oscillating electric and magnetic fields. All matter consists of atoms which have a cloud of negative electrons located around a massive (about 2000 times heavier than the total mass of the electrons) positively charged nucleus. The electric field of the incident light causes the electrons to oscillate - an oscillating dipole forms which itself radiates EM waves. Waves from the oscillating dipole combine with incident light to cause modification in the way the incident light propagates - its direction may be affected - this is the process of scattering. In a single scattering event, most of the light remains unaffected and only a very small portion suffers a change of direction.
The detailed theory is the Mie theory. In the limits of very small particle size, Mie theory may be simplified to give Rayleigh Approximation. Similarly, for large particles, Mie theory converges to the simpler Optical scattering. This is explained in slide A2.
Slide A2
Slide A5 shows the stages as the sun sets below the horizon.
Slide A5
