Question

why refractive index of atmosphere is different at different altitudes

Answer 1

This is because at different altitudes the atmosphere has different densities of air. Since refractive index depends on density of the medium, refractive index of atmosphere is different at different altitudes.

Answer 2

refractive index of a medium is the ratio of velocity of light in vacuum to velocity of light in that medium .
as you know, atmosphere is the mixture of many medium because many gases contain in atmosphere which densities are different and velocity of light in that gases are different .
so, when light passes through atmosphere velocity is different at different layers ( altitudes).

hence, refractive index of atmosphere is different at different altitudes