Why might the path of longer wavelength light (red light) be mostly unaffected by Earth's atmosphere?

When light passes through the atmosphere, it undergoes refraction: the ray of light is deviated and changes speed.

The amount of the deviation is given by Snell's Law:

(1)

where

are the index of refraction of the first (vacuum, in the space) and second (air, in the atmosphere) medium

are the angle that the incident and refracted ray of light make with the normal to the interface between the two mediums

The index of refraction is related to the wavelength of the light, according to:

where

is the wavelength in a vacuum

is the wavelength in the medium

This means that the refractive index is higher for a shorter wavelength (blue light), while it is smaller for a longer wavelength (red light).

From eq.(1),

However, the first medium is vacuum, so its index of refraction is 1. So we can write:

We said that the index of refraction in air is smaller for red light: since is a number slightly larger than 1, this means that for red light is closer to 1, and so the difference between and is smaller compared to other colors: and this means that red light is deviated less by the Earth's atmosphere, compared to other colors.