Refractive index of light from permittivity

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The discussion focuses on calculating various parameters related to the refractive index of water, given its relative magnetic permeability and electric permittivity. The key parameters to be calculated include the index of refraction, speed of electromagnetic waves, permittivity, permeability, and electrical and magnetic susceptibilities. A participant expresses difficulty in starting the calculations and mentions an incorrect value of 1.1 for the index of refraction. Clarification is sought regarding the values used for relative permeability and permittivity, indicating a need for accurate application of the relevant equations. The conversation highlights the challenges faced by those new to the topic while seeking guidance on the calculations.
Taylor_1989
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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.
 
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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##.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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