Fresnel Formulas-interesting

  • Thread starter Stalker
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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]
 
112
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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.
 

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