Do the Relative Permittivity and Refractive Index of Water Match Up?

In summary, the conversation discusses the different values for the relative permittivity and refractive index of water and how they can affect the calculation of the speed of light in water. It is noted that both these values are dependent on frequency and should be measured at the same frequency for accurate calculations.
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DaMasta345
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Many textbooks and online sources give the relative permittivity of water as about 80 and the refractive index as 1.33. If you use the definition of refractive index to find the speed of light in water, you will find v = c/n ~ 2.56e8 m/s. However, if you use the equation to find the speed of light in a medium, c = 1/sqrt(permittivity*permeability), you will find c ~ 0.335e8 m/s, which is off from the former calculation by a factor of 10. I tried to find the complex permittivity of water, but because the conductivity of water is relatively low, the imaginary portion of the permittivity will be small, and thus I am lost. Did I do something wrong or is there another explanation to this discrepancy?
 
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  • #2
Both permitivity and index of refraction are functions of frequency.
The refractive index of 1.33 is measured at frequencies corresponding to visible light range.
The value of 80 for permitivity is measured in DC regime or very low frequency.
You need to use the values measured at the same frequency for that formula to hold.
 
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1. What is relative permittivity of water and how does it differ from refractive index?

The relative permittivity, also known as the dielectric constant, of water is a measure of how much the electric field inside water is affected by the presence of water molecules. On the other hand, the refractive index of water is a measure of how much light bends when passing through water. While both properties are related to the interaction of water with electric fields, they are not the same and have different physical meanings.

2. What is the value of the relative permittivity and refractive index of water?

The relative permittivity of water varies slightly with temperature and frequency, but at 20°C and 1 kHz it has a value of approximately 80. The refractive index of water also varies with temperature and wavelength, but at 20°C and visible light wavelengths it has a value of approximately 1.33.

3. Why is it important to know the relative permittivity and refractive index of water?

Knowing the relative permittivity and refractive index of water is important for understanding its interaction with electric fields and light, respectively. These properties also play a crucial role in many scientific and technological applications, such as in optics, electronics, and materials science.

4. How are the relative permittivity and refractive index of water measured?

The relative permittivity of water can be measured using a dielectric constant meter, which applies an electric field to a sample of water and measures how much it is affected. The refractive index of water can be measured using a refractometer, which measures the angle at which light is bent when passing through water.

5. Do the relative permittivity and refractive index of water always match up?

No, the relative permittivity and refractive index of water do not always match up. This is because they are influenced by different factors and can vary independently. For example, the relative permittivity of water can be affected by the concentration of dissolved ions, while the refractive index can be influenced by temperature and wavelength.

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