Rayleigh’s Scattering

1. Rayleigh’s Scattering • In 1871, John Rayleigh quantified the scattering of light by gases • Occurs when the radius of the scattering object is much smaller than the wavelength of light. • r<<λ • The scattering is explained as the oscillation of dipole atoms when excited by an EM wave

2. Mathematical Representation • I = I0 8π4α2N/(λ4 R2)(1 + cos2θ) • Where: • I is the Intensity and I α 1/λ^4 • αis a measurement for the polarizability • λ is the wavelength • N is the number of scattering molecules • R is the distance to the particle • Also can be represented as a cross section σ. • σs=2π5/3*d6/λ4((n2-1)/(n2+2))2 • d is the diameter of the particle • n is the refractive index

3. Consequences • Remember that, • I α 1/λ4 • The large dependence on the λ4 means that shorter wavelengths scatter with greater intensity. • So at a wavelength of 400 nm (blue) the scattering is 9 times greater than at 700 nm (red) • Therefore, red lights are better used for signaling from large distances.

4. The sky • Gases such as Nitrogen and Oxygen along with water and Argon gas are the most common substances that make up the Earth’s atmosphere. • Rayleigh’s scattering says r<<λ, so water is too big but the gases are small enough to scatter light.

5. What happens • The sun gives off white light. • Once it enters the atmosphere it is absorbed by gas molecules when the two collide. • The light is then radiated in all directions. • The color given off is the color absorbed. • I α 1/λ4 • Blue is absorbed more than other colors. • We see blue because it is the most scattered.

6. Sunsets • The effect on the horizon is actually seen at all times of day. • During midday, the color is more white though. • The horizon marks the furthest point at which the light travels to our eyes. • Shorter wavelength colors are scattered off more. Meaning the longer wavelength colors are the only ones left in the direct beam. • When the sun is on the horizon, this gives us the reds, oranges, and pinks we see.