Editing Critical frequency (section)

== Relationship with index of refraction ==
The [[Refractive index|index of refraction]] has the formula <math>n=\frac{c}{v}</math>which shows dependence in [[wavelength]].<ref>{{Cite web|url=http://scienceline.ucsb.edu/getkey.php?key=3064|title=UCSB Science Line|website=scienceline.ucsb.edu|access-date=2018-09-14}}</ref> The result that the force due to the polarization field in an ionized gas of low concentration is canceled by the effect of collisions between ions and electrons is re‐established in a simple manner that clearly displays the physical basis for the effect. Because of this cancellation the [[Sellmeier equation|Sellmeyer formula]], determines the relation between the electron number density, '''''N''''', and the index of refraction, '''''n''''', in the ionosphere when collisions are neglected.<ref>{{Cite journal|last1=Theimer|first1=Otto|last2=Taylor|first2=Leonard S.|date=October 1961|title=On the index of refraction in the ionosphere|journal=Journal of Geophysical Research|language=en|volume=66|issue=10|pages=3157–3162|doi=10.1029/jz066i010p03157|bibcode=1961JGR....66.3157T |issn=0148-0227}}</ref>

<math>n^2-1=\frac{-Ne^2}{\epsilon_o m \omega^2}</math>.

Using the default values for electron charge <math>e</math>, permittivity of free space and electron mass <math>\epsilon_o</math>, and changing angular velocity <math>\omega</math>with respect to frequency <math>f</math>this yields to

<math>n^2-1=\frac{3182.607N}{(2\pi f)^2}</math>

and solving for the [[Refractive index|refraction index]] '''n,'''

<math>n=\sqrt{1-\frac{80.616N}{f^2}} \approx \sqrt{1-\frac{81N}{f^2}} </math>