Why does dispersion occur

In the atmosphere, some of the light coming from the sun is scattered, i.e. deflected in other directions. The short-wave rays are scattered more strongly than the long-wave rays by the small particles (molecules, tiny water droplets and dust particles). Therefore, the short-wave components predominate in the scattered light, the sky appears blue, while direct sunlight is yellowish, or even reddish when the sun is low. Goethe believed he saw the original phenomenon of color formation in this.

Because the light is scattered by the air particles, you can see the forest in the background as if behind a bluish veil ("air perspective"). A little sky blue very close.

The thicker the penetrated layer, the greater the portion of the light deflected by scattering, so that at sunset almost only the longest wave portion reaches the observer in a straight line and the sun appears red.

Just before sunset on a hazy day. At the time of the picture the sun was still approx. 0.8º above the horizon. Enlarged section on the right.
More pictures of the sunset

Just after sunset on a clear day. In the west the sky is brightest near the horizon (left picture), in the east it is darkest there because the deepest layers of air are already in the earth's shadow (right picture). Above the shadow of the earth as a pale pink hint of the reflection of the red setting sun.

Lunar eclipse

 The play of colors from sunrise and sunset is even transferred to the moon: If the earth's shadow darkens the moon during a lunar eclipse, it is weakly illuminated by the light scattered into the shadow area by the earth's atmosphere. This light is predominantly reddish, as the shorter-wave components are mostly scattered in other directions. From the moon, the earth's atmosphere could be seen as a luminous fringe of light, which is red on the inside where there are no clouds and fades and becomes bluish on the outside.

Partial lunar eclipse of August 16, 2008, photographed at 11:15 p.m. CEST
Lunar eclipse of February 21, 2008


Rayleigh scattering

Let us consider a single "air particle", that is, a nitrogen or oxygen molecule. Fine details do not matter here, so the idea of ​​positive charges (in which almost all of the mass is concentrated) surrounded by a cloud of negative charges is sufficient. The size of the structure is on the order of tenths of a nanometer, i.e. several thousand times smaller than the wavelengths of light.
If the molecule is in an electric force field, then forces act on the negative charge cloud and the electrically positively charged nuclei in opposite directions, the centers of gravity of the charge cloud and the positive charges are pulled apart somewhat, and the molecule becomes a small electric dipole.
Since the electrons have a much smaller mass than the nuclei, we can ignore the movement of the nuclei and assume a negative charge as a molecular model, which is bound to its rest position by a "spring force" (electrical origin). An electric field creates an additional force that deflects the charge from its rest position.
If light of a certain wavelength and thus a fixed frequency is incident, a periodic force acts on the charge and the charge will oscillate around its rest position. This forced oscillation occurs with the frequency of the incident radiation. For our considerations it is important that the frequencies of the visible light are much smaller than the resonance frequencies of the oscillators under consideration. From this one can conclude that the amplitude is in a first approximation independent of the excitation frequency.
The molecule we are considering becomes a dipole that oscillates with the frequency of the incident wave. Becomes the center of gravity of the negative charge -q against that of the positive charge + q by a piece x0 postponed, then the product q.x0, the dipole moment, a measure of the dipole strength (because if twice as much charge is deflected half as much, the resulting field is the same as long as the distance between the two charges can be viewed as small). The dipole moment now depends trivially on the acting electric field strength, therefore polarizability is introduced as a material property - this is the dipole moment divided by the field strength. The polarizability is the molecular size, which is important here, and which in the cases that are of interest here is only slightly dependent on the frequency.
The observed molecule now reverses its polarity periodically, and thus acts like a small transmitter.

The calculation shows that the power emitted by an oscillating dipole is proportional to the square of the dipole moment and the fourth power of the oscillation frequency. This is a consequence of the small size of the dipoles compared to the wavelengths considered. An emitter size comparable to the wavelength would be ideal for radiation. The ratio of dipole size to wavelength is more favorable for short waves, so there is more radiation at the short wavelengths. The short-wave light is more strongly scattered than the long-wave, inversely proportional to the fourth power of the wavelength. Light with a wavelength of 450 nm (blue) is scattered over four times more than red with a wavelength of 650 nm.

That's why the sky is blue.

Sky blue,
of all things

Perhaps the reference to an invoice that has not been presented does not seem particularly convincing - but the result is plausible, as the following example shows:
You can create water waves by hand by periodically moving your hand up and down just below the surface of the water. If you do this quickly enough, you will get clearly visible waves. Waves with a distance of about 20 to 30 cm from wave crest to wave crest are easy to generate. If you want to stimulate longer waves, you have to move your hand more slowly, but then soon you can hardly see anything. The slower the hand is moved up and down, the less energy is carried away by the waves generated, and this is because the hand is small compared to the wavelength. (But if the flank of a larger island moves a little during an earthquake, waves with very long wavelengths can be excited.)

Let us now consider a dilute gas. Light is scattered on every single molecule. In principle, if you want to know how much light arrives at a certain point in the room, you have to add the field strengths of the waves coming from the various scatterers, and the intensity is then proportional to the square of the expression obtained. One obtains interference (i.e. spatially alternating mutual amplification and weakening or cancellation) between the waves from the individual scattering centers. But since these are distributed completely randomly, and also still in motion, the interference terms change extremely quickly and are therefore not observable; we can only determine the mean value over time and space, and notice that under these circumstances the intensities of the light scattered by the individual molecules add up. And so there is again an inverse proportionality to the fourth power of the wavelength (Rayleigh scattering) for the intensity of the scattered light.

This power law applies as long as the scattering of the light that has already been scattered can be neglected. The thicker or denser the scattering layer, the more noticeable multiple scattering becomes noticeable - the short-wave light scattered from a distant point to the observer is also directed most strongly in other directions, whereby the proportion of long-wave scattering increases over a long distance . Therefore, the sky blue near the horizon is whiter than high up.

Next, let's examine a tiny droplet that is still small against the wavelengths of light, and off N Molecules of water. To simplify (and not quite correctly) assume that the electric field felt by each particle is equal to the field of the incident wave, the whole droplet acts like a molecule with a N-fold polarizability, and the scattered wave is of N2-fold intensity. As long as the droplet is small compared to the light wavelengths, the short-wave light is again scattered much more strongly.

Bigger droplets

The picture changes with increasing droplet size: the scattered waves coming from the individual sub-areas begin to cancel each other out through interference; With dimensions of the droplets that are large compared to the wavelengths, the scattered waves from the interior are extensively extinguished, and what remains, we interpret summarily as reflection and refraction. There is practically no more scattering within the volume. If the scattering particles are larger than the wavelength of the light (fog, clouds), then overall more light is scattered and all wavelengths are equally affected - in this case one speaks of Mie scattering. The spectral composition of the scattered light depends on the scattering angle. In dense clouds this angle dependency is averaged out by different droplet sizes and by multiple scattering and the clouds appear white or gray.

For an extended medium in which the density is practically constant, the scattered waves cancel each other out in all directions except the direction of propagation of the light. A homogeneous liquid does not scatter light, the polarizability of the particles only leads to a change in the wavelength of the light in the medium; this is taken into account by introducing a refractive index.



The Tyndall Effect

Scattering occurs again when small particles of differing polarizability are suspended in a transparent medium (in a liquid) (Tyndall effect). Mastic (a resin) dissolved in alcohol, rosin or, for example, spruce resin added to water provide favorable conditions for observing the effect.
In this case, too, the size of the suspended particles is decisive: if the particles are small compared to the wavelengths of light, color phenomena can be observed, if they are larger, the suspension is simply whitish and cloudy.

The picture on the right shows a suspension of spruce resin in water, illuminated from below with a white diode lamp. The transmitted light falls on top of a sheet of white paper held at an angle over the glass.
    
The amorphous opal consists of some water-containing silicon dioxide ("silica"). The cloudiness (opalescence) is caused by the alternation of differently water-containing components, water inclusions between submicroscopic silica spheres, see the SEM images shown on the pages of pinfire.de. Tyndall scattering at the inclusions is the reason why the stone appears bluish in the reflected light and yellowish in the translucent light. Due to the regular arrangement of the scattering centers, colored reflections occur.

On the right an opal from Ethiopia, length 22 mm
Glass becomes cloudy due to finely distributed, submicroscopic crystals with a different refractive index, opalescent or milky depending on the concentration. This is done by adding phosphoric acid lime (bone ash), tin oxide or fluorides (cryolite, Na3Al F6) reached to the glass melt.
Cryolite glass (opal glass, picture on the right) appears sky-blue against a dark background and orange-yellow in the translucent light.
    
Light scattering (the Tyndall effect and the Rayleigh scattering, which is not significantly different from it) can be observed quite frequently.
The blue eye color is probably the best-known color phenomenon due to the Tyndall effect (picture on the right). The iris of the human eye does not contain any blue dye. The optically cloudy front layer of the iris, if it contains little or no pigment (melanin), appears blue in front of the dark rear layer due to the preferred scattering of short-wave light.


Goethe recommends soaking chestnut bark in water to obtain a suitably cloudy liquid that appears blue against a dark background. But horse chestnuts contain aesculin, a blue fluorescent substance that converts radiation from the near ultraviolet into short-wave light (like the optical brighteners in many laundry detergents). The blue fluorescence can easily be misinterpreted as Tyndall scattering.

absorption

We have assumed in our considerations that the scattering particles do not absorb in the visible range of the spectrum. This is equivalent to the assumption that we only need to consider the oscillators outside the resonance ranges. In the case of resonance, energy is absorbed or released, the resonance frequencies of the atoms and molecules are identical to the absorption and emission frequencies.
However, smoke appears bluish against a dark background and yellowish against a light background, although the soot or tar particles are dark. Here the Tyndall effect is superimposed on the absorption without any noticeable changes.
However, if the observed particles absorb light very strongly, the situation is much more complicated: tiny gold spheres distributed in glass ("colloidal gold solution"), for example, cause the ruby ​​glass to turn red. This is often viewed as a variant of the Tyndall Effect. However, gold ruby ​​glass hardly appears cloudy, so the scattering due to the low concentration of gold particles is imperceptible, while the strong absorption of the shorter-wave components of the light results in the red color. You can find more details on this in the section on solids in metals.

Density fluctuations

We got to know Rayleigh scattering for dilute gases because the intensities of the individual scattering waves had to be added. At atmospheric pressure, however, a cube-shaped volume with an edge length of 400 nm (corresponding to the shortest visible wavelengths) contains around 1.7 million molecules. Are the conditions for independent scattering of the individual particles still met or is the situation more that of a uniform density, in which the scattered waves disappear due to interference? This question was investigated at the beginning of the 20th century by Einstein and Smoluchowski, who found that scattering on the density fluctuations of an ideal gas gives exactly the same result as scattering on the individual molecules of this gas, which are regarded as independent of one another.

Of course, the waves scattered by the individual particles always overlap, and constructive and destructive interference occurs. But if the locations of the individual particles are completely independent of each other, then the interference terms average out for a large number of particles, i.e. constructive and destructive interference are balanced, and the intensity of the scattering waves is the sum of the intensities of all scattering ones Particle.

Blue and green in the animal kingdom

In the animal kingdom one can find numerous examples of non-iridescent (i.e. not dependent on the perspective), but not caused by pigments or dyes. The cause is a tissue layer with small-scale density fluctuations (e.g. due to embedded tiny light-scattering particles) in front of a layer that is darkly colored by melanin. This is very similar to the Tyndall effect, but recent studies have shown that the spectrum of the reflected light does not have the well-known Rayleigh-Tyndall shape (inversely proportional to the fourth power of the wavelength) because the scattering centers are not arranged completely irregularly, but are clearly correlated in their intervals (Prum et al., 1999a, 1999b, 2004a, 2004b). The blue is more likely to be attributed to the structural colors.



Feather from a jay. Image width on the left 4 cm. Enlarged section on the right.

In the Tyndall effect, the scattering particles are distributed with a relatively low density in a larger volume. In order to achieve a noticeable scatter in a thin layer, the density must be much higher. With a completely random arrangement, clumps would form, so a certain minimum distance between the particles is aimed for. Although this does not lead to long-range order, it does lead to a more even distribution. The following pictures should illustrate this.

     
Left pair of images: disordered, uncorrelated distribution, right: statistical distribution with a fixed minimum distance. They are stereoscopic image pairs that show the spatial depth when one looks with one eye on one and the other on the other image of the couple.

Attempt a model calculation

A small spherical area with a radius of 4 μm is filled with scattering tiny particles that (a) are statistically distributed or (b) must be at least 200 nm apart. Then only about 16000 particles fit into the sphere, therefore the number of particles is also limited to this value in case (a). In both cases, the coordinates are determined by a random number generator. The intensities calculated by neglecting multiple scattering show strong statistical fluctuations in their dependence on scattering angle and wavelength. In order to reduce this, the mean value is calculated over a larger number of similar systems. The diagrams below show the intensities for a scattering angle of 120 degrees, multiplied by the fourth power of the wavelength and plotted in arbitrary units.

     
(a) Tyndall scattering from a spherical area with a radius of 4 μm, which is randomly filled with approx. 15700 tiny scattering particles. Averaging over 200 systems (b) Scattering by approximately 15,700 particles, but with a minimum distance of 200 nm from one another, averaging over 80 samples.

In the case of Tyndall scattering, the size shown should give a horizontal line for "infinitely many particles". It can be clearly seen that the longer-wave components of the spectrum are suppressed by the selected minimum distance, which deepens the blue color. These results fit the experimental findings of Prum and co-workers.


With structural colors, caused by nanostructures such as multilayers (beetles, hummingbirds, butterflies) or even more complicated spatial grid-like formations (peacocks, pheasants, butterflies), the whole spectrum of bright colors can be found. The irregular distribution of "nano-scattering centers" only ever provides nuances close to sky blue, so the similarity with the Tyndall effect is greater than that with the other structural colors.

Green coloring is achieved by additional yellow coloring agent (usually a carotenoid).


Hyla arborea, tree frog
(Photo: Ineptus)
The green color of amphibians and reptiles comes about in this way. Different colored cells are arranged in several layers on top of each other: yellow xanthophores further out, below them guanophores in which the colorless substance guanine is suspended in tiny crystals in the cell fluid, at the bottom a layer darkly colored by melanophores. (See: "Nature's palette" by Margareta Wallin.)
Due to the Tyndall effect, the guanophores appear blue in front of the black background if the guanine crystals are small; if larger crystals are suspended, the remitted light becomes whiter. (Flat shape of the guanine crystals or stacks of such leads to a silvery appearance or "metallic" luster and interference colors, one then speaks of iridophores.)

Two parrots, Ara militaris, military macaw
(Photo: RoFra, License CC BY 3.0)
Blue and green colors in birds are also caused by the "Tyndall-like" effect, provided they are not iridescent colors, see "The plumage colors of birds". In parrot feathers, the pith, which is colored black by melanin, is surrounded by large giant cells in the branches branching out from the feather shaft, in which melanin granules are distributed in low concentration, which again scatter the short-wave light more strongly than long-wave light and which therefore appear blue before the black pith. The outermost layer of the branches consists of transparent, colorless cells (blue feathers) or cells colored yellow by a carotenoid (green feathers). The rays emanating from the branches are colorless, transparent or darkly colored by melanin.

Ischnura elegans (van der Linden)
Great pitch dragonfly, male
The blue, but not metallic, shiny color of dragonflies is also created in this way.The epidermal cells under the transparent cuticle contain a suspension of the tiniest particles in front of the layer underneath which is colored black by melanin (according to Sternberg & Buchwald (1999): Die Libellen Baden-Württemberg, Volume 1. (© Ulmer Verlag, Stuttgart), see "Body structure of the Dragonflies ").


Appendix: Color fidelity and white balance

Can the color of the sky be documented by photos?
Below you can see three images of the cloudy sky that were taken within a short time and show roughly the same section of the sky (the clouds moved very quickly). The recordings differ in the type of white balance.


Left: "DAYLIGHT" setting
Center: "AUTO" setting (automatic white balance)
Right: "CLOUDY" setting.

The middle picture matches the visual impression quite well, and that is exactly what you want a photo to be. The automatic white balance works very well in most cases. But this does not answer the question of the "real" color of the sky and the clouds. Our sense of sight does not make absolute color measurements either.
Another example:
Autumn-colored leaves of a grapevine in a bush (rock pear) that has already shed its leaves. Sunny weather, cloudless sky, automatic white balance. The direct comparison (alternately looking out of the window and looking at the computer screen) showed that the color reproduction is optimal.
The same motif a day later with an overcast sky and drizzle.
Left: automatic white balance, right: Setting: "CLOUDY".

Here the right picture corresponds better to the visual impression than the left one. Without a direct comparison it would hardly have been possible to decide.
Since the camera does not receive all the information that our sense of sight evaluates for the white balance, and since the lighting conditions are by no means always the same when the sky is overcast, it is sometimes necessary to edit the photos afterwards. In this respect, it seems to me, too much of a good thing is occasionally done.

Back to overview: How does color come about?

Continue to discuss diffraction phenomena (including: iridescent clouds)

Continue to discuss rainbows and other atmospheric color phenomena



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