Refractive index of light from permittivity

• Taylor_1989
In summary: I get 1.056. In summary, the conversation discusses how to calculate 6 parameters related to the properties of water, including the index of refraction, speed of electromagnetic waves, permittivity, permeability, electrical susceptibility, and magnetic susceptibility. The equations ##c^2=\frac{c_0^2}{\epsilon _r\:\mu _r}## and ##n=\frac{c}{v}=\frac{c_0}{c}=\sqrt{\mu _r\epsilon _r}## were suggested as possible starting points, but the values used for ##\mu _r## and ##\epsilon _r## resulted in a value of 1.056 for ##n##,
Taylor_1989

Homework Statement

Given that the relative magnetic permeability and relative electric permeability of water are respectively, ##\mu_{rel}=1## and ##\epsilon=1.769## calculate the following 6 parameters.

1. Index of refraction of water ## n ##

2. speed of electromagnetic waves in water ## c ##

3. Value of permittivity of water ##\epsilon##

4. Value of permeability of water ##\mu##

5. electrical susceptibility of water ## X_{e} ##

6. magnetic susceptibility of water ## X_{m}##

Homework Equations

##c^2=\frac{c_0^2}{\epsilon _r\:\mu _r},\:where\:c_0^2=\frac{1}{\epsilon _0\:\mu _0}##

The Attempt at a Solution

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Normall I would put my working up but I have been looking at this question for well over an hour and can't really make a start, I originally through that looking at Maxwell equation for a light wave would help but that just showed me the equations above. I then throught well ##n=\frac{c}{v}=\frac{c_0}{c}=\sqrt{\mu _r\epsilon _r}## but this gave me 1.1 so that was a no go, at that all I have, I just done know how to start this type of question off can some give a nudge in the right direction please. I am quite new to all this so, is it possible not to go too deep straight away, thanks in advance.

Taylor_1989 said:
I then throught well ##n=\frac{c}{v}=\frac{c_0}{c}=\sqrt{\mu _r\epsilon _r}## but this gave me 1.1 so that was a no go
How did you get 1.1? What values did you use for ##\mu _r## and ##\epsilon _r##?

The values I used 1 and 1.769 as shown in the question

Taylor_1989 said:
The values I used 1 and 1.769 as shown in the question
When I use these values, I don't get 1.1 for ##n##.

1. What is the definition of refractive index?

The refractive index is a measure of how much a material can bend light as it passes through it. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.

2. How is the refractive index related to the permittivity of a material?

The refractive index is directly proportional to the square root of the permittivity of a material. This means that as the permittivity increases, the refractive index also increases.

3. What factors affect the refractive index of a material?

The refractive index of a material is affected by its physical properties, such as density and temperature. It is also influenced by the wavelength and frequency of light passing through it.

4. How is the refractive index of a material measured?

The refractive index of a material can be measured using a variety of techniques, such as using a refractometer or performing a measurement of the angle of refraction. It can also be calculated using the material's permittivity and the speed of light in a vacuum.

5. What are some practical applications of knowing the refractive index of a material?

Knowledge of the refractive index of a material is important in many fields, such as optics, materials science, and engineering. It is used in the design of lenses, prisms, and other optical devices, as well as in the development of new materials for various applications.

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