Refractive index and Maxwell theory

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SUMMARY

The discussion centers on the refractive index of water and its relationship with Maxwell's theory. The calculated refractive index using the formula n=sqrt(ε_rμ_r) suggests a value of 9 for water, given ε_r=81 and μ_r=1. However, the actual refractive index of water is 1.33 due to the frequency-dependent nature of both the index of refraction and reduced electric permittivity. The constant value of 81 applies only at zero frequency, which is not applicable for optical frequencies where the refractive index is measured.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Knowledge of refractive index and its calculation
  • Familiarity with electric permittivity and magnetic permeability
  • Concept of frequency dependence in optical materials
NEXT STEPS
  • Research the frequency dependence of electric permittivity in materials
  • Study the implications of Maxwell's equations on optical properties
  • Explore the behavior of electromagnetic waves in different media
  • Learn about the refractive index measurements at various frequencies
USEFUL FOR

Physicists, optical engineers, and students studying electromagnetism and optics will benefit from this discussion, particularly those interested in the properties of materials and their interaction with electromagnetic radiation.

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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