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

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In summary, the Fresnel formulas are derived when the magnetic permeability is not equal to 1. In most cases, the Snell's formula is used to simplify the Fresnel formulas. However, when the magnetic permeability is not equal to 1, the formulas become more complex. The perpendicular reflection coefficient and the transmission coefficient are calculated using the equations provided on page 114 of Hecht-Optics.
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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?
 
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[tex]
r_{\bot} \equiv \left( \frac {E_{0r}}{E_{0i}} \right) =
\frac {\frac {n_i}{\mu_i} Cos \theta_i - \frac {n_t}{\mu_t} Cos \theta_t}
{\frac {n_i}{\mu_i} Cos \theta_i + \frac {n_t}{\mu_t} Cos \theta_t}
[/tex]
 
  • #3
perpendicular reflection coefficient:
[tex]
r_{\bot} \equiv \left( \frac {E_{0r}}{E_{0i}} \right)_{\bot} =
\frac {\frac {n_i}{\mu_i} Cos \theta_i - \frac {n_t}{\mu_t} Cos \theta_t}
{\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} =
\frac {2 \frac {n_i}{\mu_i} Cos \theta_i}
{\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.
 

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

1. What are the Fresnel equations and what do they describe?

The Fresnel equations are a set of equations that describe the reflection and transmission of polarized light at the interface between two materials with different indices of refraction.

2. What is the main application of the Fresnel equations?

The Fresnel equations are commonly used in optics and photonics to calculate the behavior of light at the interface between materials, such as in the design of optical coatings and lenses.

3. How do the Fresnel equations differ from other equations in optics?

The Fresnel equations take into account the polarization of light, whereas other equations in optics may only consider unpolarized light. Additionally, the Fresnel equations are specific to the interface between two materials with different indices of refraction, while other equations may describe other optical phenomena.

4. What are some real-world examples of the Fresnel equations in action?

The Fresnel equations are used in a variety of applications, including the design of anti-reflective coatings on camera lenses, the calculation of reflectivity in thin film coatings on solar panels, and the design of optical filters in spectrophotometry.

5. Are there any limitations or assumptions of the Fresnel equations?

Yes, the Fresnel equations assume that the materials at the interface are flat and smooth, and that there is no absorption of light at the interface. They also do not take into account the effects of multiple reflections or scattering of light at the interface.

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