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I've been searching for the refraction index in the upper atmosphere such as Stratosphere and Thermosphere but I can't find it, all that I've seen is all equation without any number that I can use it. I really want help here, if there's any way that will calculate this in simple terms without any complex numbers and figures.

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I suppose this isn't the most "technical" answer in the sense that I don't much of a concrete dataset or table to show you, but I can provide some insight.

Here at the surface, the vacuum permittivity is a good approximation for air. In fact, the relative permittivity of air at the surface

$$ \kappa = \frac{\epsilon}{\epsilon_0},$$

only takes on a value of 1.000536, according to Engineering Toolbox. According to Wikipedia,

"The mass of the thermosphere above about 85 km is only 0.002% of the total mass. Therefore, no significant energetic feedback from the thermosphere to the lower atmospheric regions can be expected."

Since the density of the thermosphere is so much lower than that of the surface, I would expect $\kappa \sim 1$ to be a much better approximation of the relative permittivity there. I figure that would work for a lot of calculative purposes.

As can be shown using simple algebra with the definition of the speed of light, the real-component of the index of refraction is given by $n = \sqrt{\kappa}$, so I expect $n\sim 1$ in the thermosphere.

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From the formula

$$n\simeq 1 + \frac{\omega_p^2}{2} \dfrac{1}{\omega_0^2-\omega^2 +i\gamma\omega} $$

with $\omega_p=\sqrt{\dfrac{Nq^2}{m_e \epsilon_0 c^2}}$

we can deduce that $n-1$ is roughly proportional to $N$, the number of atoms per unit volume. So you can forget about all the rest and use $$n-1\propto \frac{moles}{V} $$

So knowing the densities upside and on Earth, you can approximate the value of $n$ for the upper atmosphere.


In short

$$ \dfrac{ n_{up}-1}{n_{down}-1} \approx \frac{mol_{up}}{mol_{down}} $$

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    $\begingroup$ Near 1, the index of refraction is often quoted as $\eta \equiv (n-1)\times\,10^6$, e.g., $\eta = 273 $ for nitrogen at STP. $\endgroup$ – JEB Jul 29 '18 at 0:35

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