Refractive index and Maxwell theory

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The refractive index of water is commonly cited as n=1.33, but using Maxwell's theory with ε_r=81 and μ_r=1 suggests it should be n=9. This discrepancy arises because both the refractive index and reduced electric permittivity are frequency-dependent, not constants. The value of 81 is applicable at low frequencies, which does not accurately reflect optical frequencies where the refractive index is measured. Consequently, at very low frequencies, the refractive index may indeed approach 9, explaining why radio waves have limited penetration in water compared to visible light.
Petar Mali
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Maxwell theory

n=\sqrt{\epsilon_r \mu_r

Refractive index for water is n=1,33. For water \epsilon_r=81, \mu_r=1 so it should be

n=9

Why we have so big anomaly for water?
 
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Petar Mali said:
Maxwell theory

n=\sqrt{\epsilon_r \mu_r

Refractive index for water is n=1,33. For water \epsilon_r=81, \mu_r=1 so it should be

n=9

Why we have so big anomaly for water?

The index of refraction and the reduced electric permittivity are both frequency dependent quantities, they are not constants. The constant value of 81 you refer to is the reduced electric permittivity of room temperature water in the limit that the frequency goes to zero. A frequency of zero is clearly a bad approximation for the optical frequencies where index of refraction is typically measured.

My guess is that the index of refraction of water for very low frequency radiation probably *is* around 9 ... that is probably part of the reason why radio waves cannot penetrate the water very effectively, whereas shorter wavelength visible light penetrates much further.
 
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