Editing Ionosphere (section)

====Mechanism of refraction====
When a radio wave reaches the ionosphere, the [[electric field]] in the wave forces the electrons in the ionosphere into [[oscillation]] at the same frequency as the radio wave. Some of the radio-frequency energy is given up to this resonant oscillation. The oscillating electrons will then either be lost to recombination or will re-radiate the original wave energy. Total refraction can occur when the collision frequency of the ionosphere is less than the radio frequency, and if the electron density in the ionosphere is great enough.

A qualitative understanding of how an electromagnetic wave propagates through the ionosphere can be obtained by recalling [[geometric optics]]. Since the ionosphere is a plasma, it can be shown that the [[refractive index]] is less than unity. Hence, the electromagnetic "ray" is bent away from the normal rather than toward the normal as would be indicated when the refractive index is greater than unity. It can also be shown that the refractive index of a plasma, and hence the ionosphere, is frequency-dependent, see [[Dispersion (optics)]].<ref>{{cite book|last1=Lied|first1=Finn|title=High Frequency Radio Communications with Emphasis on Polar Problems|date=1967|publisher=Advisory Group for Aerospace Research and Development|pages=1–6}}</ref>

The [[critical frequency]] is the limiting frequency at or below which a radio wave is reflected by an ionospheric layer at vertical [[angle of incidence (optics)|incidence]]. If the transmitted frequency is higher than the [[plasma frequency]] of the ionosphere, then the electrons cannot respond fast enough, and they are not able to re-radiate the signal. It is calculated as shown below:

: <math>f_{\text{critical}} = 9 \times\sqrt{N}</math>

where N = electron density per m<sup>3</sup> and f<sub>critical</sub> is in Hz.

The Maximum Usable Frequency (MUF) is defined as the upper frequency limit that can be used for transmission between two points at a specified time.

: <math>f_\text{muf} = \frac{f_\text{critical}}{ \sin \alpha} </math>

where <math>\alpha</math> = [[angle of arrival]], the angle of the wave relative to the [[horizon]], and sin is the [[sine]] function.

The [[cutoff frequency]] is the frequency below which a radio wave fails to penetrate a layer of the ionosphere at the incidence angle required for transmission between two specified points by refraction from the layer.