Can refractive index be used interchangeably with wave impedance? Everything I've been taught so far for EMR and waves at an incidence has been using the refractive index.
for example, the reflection coefficient for a wave normal to an incident  is 
$$R = ((n1-n2)/(n1+n2))^2$$
but I'm looking at examples online and they're all using wave impedance instead of refractive index. 
 A: The wave impedance of a plane electromagnetic electromagnetic wave in a nonconductive medium is given by $$Z=\sqrt{\frac {\mu}{\epsilon}}= \sqrt{\frac {\mu_r \mu_0}{\epsilon_r \epsilon_0}}=\sqrt{\frac {\mu_0}{\epsilon_0}}\sqrt{\frac {\mu_r}{\epsilon_r}}=Z_0\sqrt{\frac {\mu_r}{\epsilon_r}}=Z_0\frac {\mu_r}{n} \tag 1$$ where $Z_0$ is the vacuum wave impedance, $\mu$ and $\epsilon$ are the absolute permeability and permittivity of the medium, and the refractive index is given by  $$n=\frac {c_0}{c}=\sqrt{\mu_r\epsilon_r} \tag 2$$  Equation (1) shows that the wave impedance $Z$ is inversely proportional to the refractive index $n$. 
In nonmagnetic media with $\mu_r=1$,which are mostly used, the wave impedance is just the vacuum wave impedance $Z_0$ divided by $n$ $$Z=\frac {Z_0}{n} \tag 3$$ Thus the larger the refractive index $n$, the smaller the wave impedance $Z$. The reflection coefficient $r$ between two media can thus be expressed both by the wave impedances and the refractive indices:$$r= \frac {Z_2-Z_1}{Z_2+Z_1}=\frac {n_1-n_2}{n_1+n_2} \tag 4$$ The reflectance $R$ is given by $$R=|r|^2 \tag 5$$ Analogous formula hold for the transmission coefficient $t$ and transmittance $T$.
