5. Dispersion, Scattering, and Colour Phenomena

5.1 Dispersion of Light by a Prism

When a narrow beam of white sunlight is passed through a triangular glass prism, it splits into a band of seven colours — violet, indigo, blue, green, yellow, orange, and red (remembered by the mnemonic VIBGYOR) — arranged in order from the most bent to the least bent. This splitting of white light into its constituent colours is called dispersion, and the resulting band of colours is called a spectrum.

Dispersion happens because white light is actually a mixture of many colours of different wavelengths, and the refractive index of glass (or any transparent medium) is slightly different for each wavelength. Violet light, having the shortest wavelength among the visible colours, is refracted (bent) the most, while red light, having the longest wavelength, is refracted the least. Consequently, as white light passes through a prism, each colour is bent by a slightly different amount and the colours separate out into a fan-shaped band, with violet at one end and red at the other.

Recombination: If the dispersed spectrum from one prism is passed through a second, identically oriented, inverted prism, the colours recombine to give back white light — proving that white light is indeed a mixture of these seven colours and not a single 'pure' colour, as Isaac Newton famously demonstrated in his classic prism experiments.

5.2 Formation of a Rainbow

A rainbow is a natural example of dispersion, combined with refraction and internal reflection, that occurs when sunlight interacts with tiny suspended water droplets in the atmosphere, typically after rainfall and when the observer stands with the Sun behind them. Sunlight entering a spherical raindrop is first refracted (and dispersed into its constituent colours) as it enters the drop, then undergoes total internal reflection off the back inner surface of the drop, and is refracted a second time as it exits the drop towards the observer's eye. Because different colours are bent by different amounts at each refraction, the colours emerge from the raindrop at slightly different angles, and the overall effect — seen across countless raindrops — is the familiar arc of colours, with red on the outer edge of the arc and violet on the inner edge (for a primary rainbow). Occasionally a fainter secondary rainbow is visible outside the primary one, formed by light that undergoes two internal reflections inside the raindrop; in the secondary bow the colour order is reversed, with violet outermost and red innermost.

5.3 Scattering of Light

Scattering of light occurs when light travelling through a medium encounters small particles (much smaller than or comparable to the wavelength of light) and is redirected (scattered) in various directions. The amount of scattering depends strongly on the wavelength of light: shorter wavelengths are scattered much more than longer wavelengths. This wavelength-dependence, described mathematically by Lord Rayleigh (Rayleigh scattering, where the scattering intensity is inversely proportional to the fourth power of the wavelength), explains several everyday colour phenomena.

The Tyndall Effect

The Tyndall effect refers to the scattering of a beam of light by the colloidal particles suspended in its path, making the path of the beam visible from the side (as a bright cone or streak), even though the medium itself may look clear. It is named after the physicist John Tyndall. Everyday examples include the visible shaft of sunlight passing through dust particles in a darkened room, headlight beams becoming visible in foggy or dusty conditions, and the blue colour seen when a beam of light is passed through a colloidal solution or a fine milk-water mixture.

Why the sky is blue

Sunlight, though it appears white, is actually a mixture of all the colours of the visible spectrum. As sunlight passes through Earth's atmosphere, it collides with the tiny gas molecules (mainly nitrogen and oxygen) that make up the air. Because of Rayleigh scattering, blue and violet light, having the shortest wavelengths among visible colours, are scattered far more strongly by these gas molecules than the longer-wavelength colours like red and orange. Although violet is scattered even more than blue, our eyes are more sensitive to blue light and less sensitive to violet, and some violet light is also absorbed in the upper atmosphere, so the sky we see overhead appears predominantly blue rather than violet.

Why sunrise and sunset appear red/orange

At sunrise and sunset, the Sun is close to the horizon, and its light must therefore travel through a much greater thickness of the atmosphere to reach an observer's eyes than it does at noon. Over this long path, almost all the blue and violet light is scattered away out of the direct line of sight by the many gas molecules encountered along the way, leaving mainly the longer-wavelength colours — red, orange, and yellow, which are scattered the least — to reach the observer directly from the Sun's disc. This is why the Sun and the sky around it take on a reddish-orange hue at sunrise and sunset, while at midday, when sunlight travels through much less atmosphere, the Sun appears nearly white or pale yellow.

Why the sea appears blue, and why clouds appear white

The blue colour of large water bodies such as the sea is partly a reflection of the blue sky above (water reflects the colour of the sky that falls on it), and partly because water itself very weakly absorbs red light more than blue light as light travels through it, so light that has travelled any appreciable depth in water and scattered back to the surface tends to be bluer. Clouds, on the other hand, appear white (not blue) because the water droplets that make up a cloud are considerably larger than the gas molecules in clear air — comparable to or larger than the wavelength of visible light — and such larger particles scatter all wavelengths of visible light roughly equally (a phenomenon called Mie scattering, as opposed to the strongly wavelength-dependent Rayleigh scattering caused by much smaller gas molecules). Since all colours are scattered equally by cloud droplets, the scattered light recombines to appear white, the same colour as the sunlight that entered the cloud.

A related fact often tested: in outer space, where there is no atmosphere to scatter light, the sky appears black even during 'daytime', which is why astronauts see a black sky with visible stars even when the Sun is shining.