Question

The low-frequency relative permittivity of water is 88.00 at 0°C. At the same temperature, the index of refraction (at 589.3 nm) is roughly 1.33.

a.Which mechanisms contribute to the refractive index and to the relative permittivity?

b.Why is the refractive index so much smaller than the relative permittivity at low frequencies?

Answer 1

a) Relation between the index of refraction to the relative permittivity (dielectric constant/function) is known that n = √ ϵ r n=ϵr for optical frequencies (i.e. μ r = 1).

n=ϵr−−√n=ϵr works. 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.We know that the relative permittivity of water as 80.4 i.e. ϵ r = 80.4 ϵr=80.4 but we also know that the index of refraction of water is 1.33. so it should be n = √ ϵ r = √ 80.4 = 8.9666
We want to use the relative permittivity in an equation to calculate the electrostatic approximation of the scattering/absorption efficiencies of small spherical particles. should i be solving for relative permittivity from the index of refraction? i.e. n 2 = ( √ ϵ r ) 2 ⇒ ϵ r = 1.33 2 = 1.7689
Permittivity is a function of wavelength (frequency). 80.4 value is valid for microwave diapason, not for optical one. For optical frequencies you should calculate permittivity from refractive index, i.e. ϵ r = n 2

b) 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.

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