Scattering of light: blue sky, white clouds and red sunsets
Tiny particles scatter light with intensity ∝ 1/λ⁴ (Rayleigh's law). Blue is scattered most, so the sky looks blue and the low Sun looks red.
What scattering is
Sunlight entering a dark room through a gap shows a bright beam, because dust in the air sends light sideways. Scattering is a two-step process. A tiny particle absorbs light and at once sends it out again in all directions. It is not reflection, since scattered light does not obey the laws of reflection. Scattering by air and dust is why light reaches corners that the Sun cannot reach directly. When the particles are smaller than the wavelength of light, as air molecules are, Rayleigh's law holds: the intensity of scattered light is I ∝ 1/λ⁴. So short wavelengths (violet and blue) are scattered far more than long ones (red). Particles bigger than the wavelength scatter all colours almost equally.
Activity: scattering of light in milky water
- 1Fill a clear glass jar with water and stir in a few drops of milk.
- 2In a dark room, shine a narrow beam from a torch or a white bulb through the jar.
- 3Look at the beam from the side, at 90° to it. Observation: the beam looks bluish.
- 4Hold a white card beyond the jar to catch the light that comes straight through. Observation: it looks yellowish to reddish, more so as you add more milk.
- 5Result: the tiny milk particles scatter blue sideways most strongly, so the straight beam loses its blue. This copies the blue sky and the red setting Sun.
Everyday effects of scattering
| What we see | Why |
|---|---|
| Blue sky | Air molecules scatter blue much more than red (I ∝ 1/λ⁴). This blue reaches us from every part of the sky. Violet is scattered even more, but the eye is less sensitive to violet. |
| White clouds | Cloud droplets are larger than the wavelength of light, so they scatter all colours almost equally. |
| Dark rain clouds | Thick clouds absorb and scatter away most of the sunlight before it gets through. |
| Red Sun at sunrise and sunset | Light from the low Sun crosses a much longer path of air. Most of the blue is scattered away on the way, leaving red and orange. |
| White Sun at noon | The path through the air is short, so little blue is lost. |
| Black sky in space | High above the Earth there is almost no air or dust to scatter light. |
| Deep blue sky after rain | Rain washes out dust and large droplets, so scattering by air molecules follows Rayleigh's law closely. |
Worked example: how much more is blue scattered?
Compare the intensity of light scattered by air molecules for blue light of wavelength 450 nm and red light of wavelength 700 nm.
- Rayleigh's law: I ∝ 1/λ⁴, so I(blue)/I(red) = (λred/λblue)⁴.
- λred/λblue = 700 nm ÷ 450 nm ≈ 1.556.
- (1.556)² ≈ 2.42, and (2.42)² ≈ 5.86.
Blue light is scattered about 5.9 times (roughly six times) more strongly than red light.
How to draw the red Sun at sunset
- Draw a large arc for the Earth's surface and a thin shell around it for the atmosphere.
- Mark an observer O on the surface.
- Draw the Sun directly above O, with a short ray through the atmosphere; label it short path: Sun looks white.
- Draw the Sun near the horizon, with a long slanting ray through the atmosphere to O; label it long path: blue scattered away, Sun looks red.
- Draw small arrows leaving the long ray sideways and label them blue light scattered.
The orange glow of the Sun setting over the sea at Kanyakumari is Rayleigh scattering at work. Danger signals and brake lights are red because red is scattered least, so it can be seen farthest through fog and dust.
2 marks: “Why does the sky appear blue on a clear day?” Air molecules are smaller than the wavelength of light. By Rayleigh's law, I ∝ 1/λ⁴, so blue is scattered much more than red. This scattered blue light reaches our eyes from all directions, so the sky looks blue.
2 marks: “Why does the Sun look red at sunrise and sunset but white at noon?” Near the horizon, sunlight travels a long path through the air, and blue and violet are scattered away, so mainly red reaches us. At noon the path is short, little blue is lost, and the Sun looks white.
1 marks: “What colour would the sky look to an astronaut in space? Give a reason.” Black, because there is almost no air or dust to scatter sunlight.
Short waves scatter most: blue bounces around, red runs straight through. I ∝ 1/λ⁴.