Scattering & Tyndall Effect
Look up on a clear day and you see a vivid blue sky. Look at the horizon near sunset and that same sky burns orange and red. Neither colour comes from the atmosphere glowing or being coloured itself — instead, both effects arise from the scattering of sunlight by tiny particles far smaller than the wavelength of visible light. Scattering is the process by which a particle absorbs a photon and almost instantaneously re-emits it in a different direction. The crucial insight is that the efficiency of this process depends strongly on the wavelength of the incoming light. The Tyndall effect is a closely related phenomenon observed in colloids — mixtures where fine particles (roughly 1–1000 nm across) are suspended in a medium, such as milk, fog, or smoke in air. When a beam of light passes through a colloid, the beam becomes visible from the side because the suspended particles scatter light towards the observer. This is why a torch beam is visible in a dusty or misty room but invisible in perfectly clear air. The Tyndall effect is both a beautiful everyday phenomenon and a useful laboratory test for distinguishing colloids from true solutions. Both the blue sky and the Tyndall effect are explained by the same underlying physics, formalised in Rayleigh scattering theory. The key result is that scattering intensity is inversely proportional to the fourth power of wavelength, meaning short (blue) wavelengths scatter enormously more than long (red) wavelengths. This single mathematical relationship explains why the sky is blue, why sunsets are red, and why colloids glow when illuminated.
- What is scattering?
- The wavelength dependence — the 1/λ⁴ law
- Why the sky is blue and not violet
- Why sunsets are red and orange
- The Tyndall effect in colloids
- Particle size and Mie scattering
What is scattering?
When an electromagnetic wave encounters a particle much smaller than its wavelength, the oscillating electric field of the wave forces the electrons in the particle to oscillate. These accelerating charges act like tiny antennae, re-radiating energy in many directions. This re-radiation is scattering. Crucially, the re-emitted light has the same frequency as the incoming light (elastic scattering), but travels in a new direction.
The wavelength dependence — the 1/λ⁴ law
Lord Rayleigh showed that for particles much smaller than the wavelength of light (diameter d ≪ λ), the intensity of scattered light is proportional to 1/λ⁴. Violet light (λ ≈ 400 nm) scatters roughly (700/400)⁴ ≈ 9.4 times more intensely than red light (λ ≈ 700 nm). Blue (λ ≈ 450 nm) scatters about (700/450)⁴ ≈ 5.9 times more than red. This enormous difference is what gives the sky its colour.
Why the sky is blue and not violet
If violet scatters even more than blue, why isn't the sky violet? Two reasons: firstly, the Sun emits less violet light than blue light to begin with; secondly, the human eye is far more sensitive to blue than to violet. The combined effect of solar spectrum and eye sensitivity means the scattered light reaching us looks blue rather than violet.
Why sunsets are red and orange
At sunset or sunrise, sunlight must travel through a much greater thickness of atmosphere — sometimes 40 times more than at noon. Over this long path, almost all the blue and violet light has been scattered away in other directions. Only the longer wavelengths — red, orange, and yellow — survive to reach your eyes directly, painting the horizon in warm colours. The same logic explains why the Moon appears orange when it is low on the horizon.
The Tyndall effect in colloids
In a colloid, the suspended particles are larger than individual molecules but still small enough to scatter light strongly. When a narrow beam of light passes through a colloid (e.g. dilute milk, fog, or a blue-tinted gemstone), the scattered light is visible from the side, making the beam appear as a glowing cone — the Tyndall cone. In a true solution (e.g. salt dissolved in water), the solute particles are too small (sub-nanometre) to scatter visible light significantly, so no cone is visible. This makes the Tyndall effect a simple diagnostic test: colloid vs. true solution.
Particle size and Mie scattering
Rayleigh scattering applies only when the scattering particle is much smaller than λ (typically d < λ/10). When particles are comparable in size to wavelengths of light — such as water droplets in clouds — a more complex theory called Mie scattering applies. Mie scattering is much less wavelength-dependent, which is why clouds appear white: all visible wavelengths are scattered roughly equally by the larger water droplets.
The Key Equation
- I — Scattered intensity (W m⁻²): Power of scattered light per unit area reaching the observer.
- I_0 — Incident intensity (W m⁻²): Power per unit area of the incoming beam before scattering.
- \lambda — Wavelength (m (or nm)): Wavelength of the incident light. The 1/λ⁴ dependence causes short wavelengths to scatter far more strongly.
- \theta — Scattering angle (degrees or radians): Angle between the incident beam direction and the direction of observation. Scattering is strongest in the forward and backward directions.
Worked Example
Problem. Blue light has a wavelength of 450 nm and red light has a wavelength of 700 nm. How many times more intensely is blue light scattered than red light by air molecules (Rayleigh scattering)?
Answer. Blue light is scattered approximately 5.9 times more intensely than red light by air molecules.
Origins · 1 minJohn William Strutt, 3rd Baron Rayleigh and how this was discovered
Rayleigh derived the mathematical theory of light scattering by particles much smaller than the wavelength of light, publishing his landmark explanation of the blue sky in 1871. His 1/λ⁴ scattering law, now called Rayleigh scattering, quantitatively explained why short wavelengths scatter far more efficiently than long ones. He also contributed foundational work in acoustics, wave theory, and the discovery of argon, for which he won the 1904 Nobel Prize in Physics. Rayleigh was so meticulous that when he first noticed the density of nitrogen extracted from the air differed slightly from chemically produced nitrogen, he published a letter asking if anyone could explain the discrepancy — which ultimately led to the discovery of argon, a brand new element hiding in every breath.
Related Concepts
- Wave Properties of Light — Rayleigh scattering depends fundamentally on the wave nature of light — specifically its wavelength — so understanding light as a wave is essential background.
- Reflection and Refraction — Reflection, refraction, and scattering are all mechanisms by which light changes direction when interacting with matter, and they are often contrasted in optics.
- Dispersion and Rainbows — Rainbows arise from a combination of refraction, dispersion, and internal reflection in water droplets — another spectacular example of atmospheric optics closely linked to scattering.
- Polarisation of Light — Rayleigh-scattered sunlight is partially polarised; polarising sunglasses exploit this fact, and studying polarisation reveals more detail about the scattering geometry.