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
What is going on is an effect called Rayleigh’s scattering. Quantified by John Rayleigh in 1871, Rayleigh showed that when the radius of the scattering object is much

2. Mathematical Representation
I = I0 8π4α2N/(λ4 R2)(1 + cos2θ)
Where:
I is the Intensity and I α 1/λ^4
α is 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.