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

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Fresnel formulas can be derived for cases where magnetic permeability (μ) is not equal to 1, affecting the reflection and transmission coefficients. The perpendicular reflection coefficient (r⊥) is expressed as the difference between the indices of refraction adjusted for permeability, divided by their sum. Similarly, the transmission coefficient (t⊥) is calculated using the same adjusted indices, emphasizing the role of μ in wave behavior at interfaces. These formulas highlight the complexity introduced by varying magnetic properties in optical materials. Understanding these variations is crucial for applications in optics and materials science.
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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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<br /> 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}<br />
 
perpendicular reflection coefficient:
<br /> 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}<br />
transmission coefficient:
<br /> 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}<br />

I copy these from Hecht-Optics page 114.
 
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