Dielectric constant refractive index relationship

[tomas632]

hi, i have seen on another topic here that the refractive index equals the square root of the dielectric constant. from datasheet values we have...

water refractive index = 1.333
dielectric constant = 80.1

Without even doing the calculation its obvious that the square root of 80.1 is not 1.333...im clearly missing something here, can somebody help me with this please?

Thanks

Tom

 

[Simon Bridge]

Look at the definition of the dielectric constant and the definition of the refractive index - find the relationship between these things and the speed of light.
http://en.wikipedia.org/wiki/Refractive_index#Dielectric_constant

 

[nasu]

Both dielectric constant and index of refraction depend on frequency.
When you write the relationship between them the values should be measured at the same frequency.
The value of about 80 is water's dielectric constant in DC regime or at very low frequency.
The 1.33 is the index of refraction at the frequency of visible light (about 10^14 Hz).

 

[drhassan]

in general the refractive index is equal to the sqrt(dielectric constant), but you have to notice the frequency dependence as mentioned by nasu (the previous Post)

 

[sardar]

Hello Tom,

You are correct that the square root of 80.1 is not 1.333. However, the relationship between the dielectric constant and refractive index is not a simple one-to-one correlation. The equation for calculating the refractive index from the dielectric constant is n = √(εr), where n is the refractive index and εr is the dielectric constant.

This relationship is based on the concept of permittivity, which is a measure of how easily a material can be polarized by an electric field. The refractive index is a measure of how much a material bends light, and it is affected by the permittivity of the material. The higher the permittivity, the higher the refractive index will be.

In the case of water, the refractive index is 1.333 and the dielectric constant is 80.1. This means that water has a high permittivity, which causes it to have a higher refractive index compared to other materials with lower permittivity values. The square root relationship between the two values is a result of the way light interacts with the polar molecules in water.

I hope this helps to clarify the relationship between the dielectric constant and refractive index. If you have further questions, please don't hesitate to ask.