A3 - atmospheric optics

refraction

the refractive index: $n = c / v$
$n_{w a t e r} > n_{a i r}$ and $n_{b l u e} > n_{r e d}$ in water
Snell's law:

\frac{\sin θ_{a}}{\sin θ_{w}} = \frac{n_{w}}{n_{a}}

*image: Arizona University

*image: Arizona University

blue appears at the bottom (contrary to the refraction from a single droplet) as observer receives light from different droplets

*image: Arizona University

secondary rainbows can be observed if multiple reflections occur in the raindrop

scattering

when light passes through a medium, it can absorb and reemit light in random directions, called scattering
Rayliegh scattering (molecular scattering) involves particles smaller than the wavelength of light, $λ$ , with $n \approx 1$

S \propto \frac{1}{λ^{4}}

shorter/bluer wavelengths are scattered preferentially, with blue scattered about 15 times more than red
this results in the blue colour of the sky
it filters out the blue light, leaving other colours behind
Mie scattering (non-molecular/aerosol scattering) occurs from water droplets in clouds/aerosols (suspension of fine liquid/solid particles in a gas)
it is not wavelength-dependent