Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)