# What causes the sudden change in atmospheric reflection of long-band radio waves?

This picture shows up a lot. The explanations that tend to accompany it say that the long-band radio waves above ~10m are reflected, whereas other wavelengths are scattered or absorbed or transmitted.

Question: Why the sudden qualitative change around 10m? What process causes 5m waves to pass through and 20m waves to reflect?

The refractive index of a plasma is $$\sqrt{\epsilon_r}$$, where the relative permittivity is given by $$$$\epsilon_r = 1 - \frac{n_e e^2}{\epsilon_0 m_e \omega^2}=1 - \frac{\omega_p^2}{\omega^2}\,,$$$$ where $$\omega_p$$ is known as the plasma frequency.
The refractive index will become imaginary when $$\omega<\omega_p$$ and an EM wave will not propagate.
In the Earth's ionosphere, the electron number density $$n_e\simeq 10^{12}$$ m$$^{-3}$$ and $$\omega_p \simeq 6\times 10^7$$ rad/s, corresponding to a wavelength of $$\simeq 30$$ m.