The phenomena involved in the reflection of radio waves by ionosphere are similar to

Radiowaves are reflected by a layer of atmosphere called the lonosphere, so they can reach distant parts of the Earth. The reflection of radiowaves by ionosphere is due to total internal reflection. It is the same as total internal reflection of light in air during a mirage, that is, angle of incidence is greater than critical angle.
Ionosphere is transparent optical medium and radiowave is reflected back.
Reflection through transparent surface is total internal reflection so that internal reflection of radio wave takes place.