What are the Fresnel formulas for magnetic permeability not equal to 1?

  • Context: Graduate 
  • Thread starter Thread starter Stalker
  • Start date Start date
  • Tags Tags
    Fresnel
Click For Summary
SUMMARY

The discussion focuses on deriving the Fresnel formulas for scenarios where magnetic permeability (μ) is not equal to 1. The formulas for the perpendicular reflection coefficient (r⊥) and transmission coefficient (t⊥) are provided, highlighting the dependence on the indices of refraction (n) and the angles of incidence (θ). The formulas are expressed as r⊥ = (n_i/μ_i Cos θ_i - n_t/μ_t Cos θ_t) / (n_i/μ_i Cos θ_i + n_t/μ_t Cos θ_t) and t⊥ = (2 n_i/μ_i Cos θ_i) / (n_i/μ_i Cos θ_i + n_t/μ_t Cos θ_t). These derivations extend the application of Snell's law in optics.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Familiarity with electromagnetic theory and magnetic permeability
  • Knowledge of reflection and transmission coefficients
  • Basic calculus for manipulating trigonometric functions
NEXT STEPS
  • Study the derivation of Fresnel equations in the context of varying magnetic permeability
  • Explore applications of Fresnel formulas in optical systems
  • Learn about the implications of magnetic permeability on light behavior in different media
  • Investigate advanced topics in optics, such as polarization and its relation to Fresnel equations
USEFUL FOR

Physicists, optical engineers, and students studying electromagnetism who are interested in the behavior of light in media with varying magnetic properties.

Stalker
Messages
2
Reaction score
0
Derive Fresnel Formulas for the case when magnetic permeability (myu) is not 1. How will they look like? In most cases myu=1, so the Snells formula becames easy , and after it we get Fresnel Formulas, with the help of Snell Formula.What will be when myu is not 1?
 
Science news on Phys.org
[tex] r_{\bot} \equiv \left( \frac {E_{0r}}{E_{0i}} \right) =<br /> \frac {\frac {n_i}{\mu_i} Cos \theta_i - \frac {n_t}{\mu_t} Cos \theta_t}<br /> {\frac {n_i}{\mu_i} Cos \theta_i + \frac {n_t}{\mu_t} Cos \theta_t}[/tex]
 
perpendicular reflection coefficient:
[tex] r_{\bot} \equiv \left( \frac {E_{0r}}{E_{0i}} \right)_{\bot} =<br /> \frac {\frac {n_i}{\mu_i} Cos \theta_i - \frac {n_t}{\mu_t} Cos \theta_t}<br /> {\frac {n_i}{\mu_i} Cos \theta_i + \frac {n_t}{\mu_t} Cos \theta_t}[/tex]
transmission coefficient:
[tex] t_{\bot} \equiv \left( \frac {E_{0t}}{E_{0i}} \right)_{\bot} =<br /> \frac {2 \frac {n_i}{\mu_i} Cos \theta_i}<br /> {\frac {n_i}{\mu_i} Cos \theta_i + \frac {n_t}{\mu_t} Cos \theta_t}[/tex]

I copy these from Hecht-Optics page 114.
 

Similar threads

Undergrad Fresnel Zone Equation Problem
  • · Replies 8 ·
Replies
8
Views
3K
High School Calculating non-dielectric reflectance without using complex numbers
  • · Replies 6 ·
Replies
6
Views
2K
Graduate What are the key considerations for imaging with a condenser fresnel lens?
  • · Replies 58 ·
2
Replies
58
Views
9K
Undergrad Overview of General Fresnel Equations + Complex IORs
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Finding the Fresnel coefficients from interface conditions
  • · Replies 2 ·
Replies
2
Views
9K
Graduate Understanding a Generalization of Snell's Law
  • · Replies 19 ·
Replies
19
Views
6K
Undergrad How Can One Derive the Diffraction Pattern Formula from a 1D Aperture?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Propagation of Angular Spectrum Code
  • · Replies 1 ·
Replies
1
Views
4K
Graduate CPC and Fresnel Lenses for Solar Cell Power
  • · Replies 5 ·
Replies
5
Views
6K
Graduate How can I show that the amplitude of a reflected wave?
  • · Replies 3 ·
Replies
3
Views
2K