# Changing electric field and refractive index

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1. Mar 5, 2015

I am learning sky wave propagation and in my book, a relation between refractive index, dielectric constant and electro field strength is given.
$$\mu=\mu_0\sqrt{1-\frac{Ne^2}{\epsilon_0m\omega^2}}$$
Is this a form of Kerr opto-electric effect? How do you get this expression? If you think I cannot understand the derivation, can you explain its meaning?

2. Mar 5, 2015

### blue_leaf77

What is $\mu$ in that expression?

3. Mar 5, 2015

Refractive index

4. Mar 5, 2015

### Vagn

That looks like the refractive index for a plasma, where the plasma frequency is given by $\omega_p^2=\frac{Ne^2}{\epsilon_0 m}$. In the context of the atmosphere, this would be referring to the ionosphere.

5. Mar 5, 2015

### blue_leaf77

Yes it is refractive index of plasma, derived using Drude model for free electrons motion.

6. Mar 5, 2015

Yes. It is for ionosphere. Its about reflection of waves from ionosphere. As N the number density of electrons increase, the value of $\mu$ decreases hence the critical angle increases.
I am studying in 12th standard. I know single variable variable integration and I know how to solve linear first order differential equations. Can you explain the relation between mu and Eletric field?

7. Mar 5, 2015

Drude model explains the drift of electrons in a coductor when an electric field is applied right?

8. Mar 6, 2015

### DelcrossA

There's a few different approaches to the derivation. The most straight-forward, in my opinion, is to start by solving the equation of motion of a free electron under the influence of some incident plane-wave. This will allow you to calculate the polarization of the free electron gas and then find the dielectric function and then the refractive index.

9. Mar 6, 2015

### blue_leaf77

Agree with DelcrossA.

10. Mar 6, 2015