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.
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 $T$.
