Answer to Question #122243 in Field Theory for Dheeraj

Question

The relative dielectric constant ε of water is 80 . This does not justify its refractive
index n = 1.33 violating the expression n^2 = ε. This is because?

Answer 1

It is just that the dielectric “constant” isn’t actually a constant. For under 1kHz, water’s dielectric “constant” is around 86. But for visible light (600THz, 500nm), water has a dielectric “constant” of 1.77, which gives you the refractive index of 1.33.

The reason why the dielectric “constant” isn’t constant is it is a product of the polarization of the material. Polarization is the ability of a material to polarize. Think of a magnet that gets stronger, except instead of a magnet, we’re talking about electrical forces. The more the polarization mechanisms, the higher the dielectric “constant.” There are four major polarization mechanisms. They are electronic polarization, ionic polarization, orientation polarization, and interface polarization.

Each of the polarization mechanisms only works up until a certain frequency, so at higher frequencies, less polarization mechanisms are active in any material. That is what happens in water at light’s frequency. Water losses its orientation polarization mechanism with light. Below is a chart that demonstrates how the polarizability and thereby the dielectric “constant” changes with frequency.