Dispersion of Light, Atmospheric Refraction and Scattering

Introduction — Colour, Sky and the Setting Sun

Sunlight looks white, yet a rainbow bursts with seven colours. Stars twinkle but planets do not. The noon sky is blue, and the setting sun glows orange-red. Every one of these beautiful phenomena is explained by three pieces of physics — dispersion, atmospheric refraction and scattering. In this part we study each in turn.

10.10 Dispersion of White Light by a Prism

Sir Isaac Newton (1666) found that when a narrow beam of sunlight is passed through a triangular glass prism, it splits into a band of seven colours — Violet, Indigo, Blue, Green, Yellow, Orange, Red — remembered as VIBGYOR. This band is called a spectrum, and the phenomenon is called dispersion.

10.10.1 Newton's Recombination Experiment

Newton then placed a second prism, inverted, beside the first. The seven colours entered the second prism and recombined into a beam of white light that emerged parallel to the original. This proved that white light is a mixture of the seven colours, not an indivisible entity.

10.11 The Rainbow

A rainbow is a natural spectrum that appears in the sky, usually after a shower, when the Sun is behind the observer. Tiny water droplets suspended in air act like millions of miniature prisms.

• Sunlight enters a droplet and is refracted (dispersion begins here).
• It undergoes total internal reflection from the back wall of the droplet.
• It is refracted again as it exits, separating into colours.

Red appears on the outer (upper) edge of the bow and violet on the inner (lower) edge.

10.12 Atmospheric Refraction

The Earth's atmosphere is not uniform — its temperature, density and hence refractive index vary continuously with height. Light from the Sun or a distant star, passing through such layers, bends. This bending of light by the atmosphere is called atmospheric refraction.

10.12.1 Twinkling of Stars

Light from a distant star, on entering the Earth's atmosphere, keeps bending at the boundaries between layers of different densities. Small air currents continually change these layers, so the apparent position of the star and the amount of light reaching us fluctuates. A star therefore appears to twinkle.

Why do planets not twinkle? Planets are much closer to us than stars and appear as tiny disks rather than point sources. Light comes from many points on a planet's disk; when one point fluctuates another compensates, and the total light we receive averages out — the planet appears steady.

10.12.2 Advance Sunrise and Delayed Sunset

Near the horizon the Sun's light traverses a long, dense column of air. Atmospheric refraction bends the rays downward, so the Sun appears to be at a higher position than it actually is. Because of this:

• We see the Sun about 2 minutes before it is geometrically above the horizon — advance sunrise.
• We continue to see it for about 2 minutes after it has actually set — delayed sunset.

Thus the day is about 4 minutes longer than it would be without an atmosphere. The Sun near the horizon also looks flattened (oval) because rays from its lower edge are refracted more than those from its upper edge.

10.13 Scattering of Light

When a beam of light falls on tiny particles (dust, water droplets, smoke, even molecules of air), each particle re-emits light in all directions. This redirection is called scattering of light.

10.13.1 Tyndall Effect

When a narrow beam of sunlight enters a dusty room through a small opening, the path of the beam becomes visible because dust particles scatter the light. This everyday demonstration is the Tyndall effect. It is seen when light passes through smoke, mist or a colloid.

10.13.2 Rayleigh Scattering

Air molecules (N₂, O₂) are much smaller than the wavelength of visible light. Lord Rayleigh showed that such small particles scatter light in a colour-selective way:

Since blue light has a shorter wavelength than red, blue is scattered much more strongly (by a factor of about \((700/450)^{4}\approx 6\)) than red.

10.13.3 Why is the Sky Blue?

In the absence of an atmosphere the sky would look black. Because air molecules scatter blue far more than red (Rayleigh scattering), whichever direction you look in the daytime sky (other than directly at the Sun), you mainly receive the scattered blue component of sunlight. Hence the sky appears blue.

10.13.4 Reddening of the Sun at Sunrise & Sunset

At sunrise and sunset the Sun is near the horizon, so its light has to travel through a much longer column of the atmosphere than at noon. Blue and other short-wavelength colours are scattered away along this long path. Only the longer-wavelength components — orange and red — reach the observer, and the Sun appears orange-red. At noon the Sun is overhead, its light travels through a smaller thickness of air, so less scattering occurs and the Sun appears white.