Fresnel's Equation

${\tilde{E}}_{0_R}=\left(\frac{\alpha -\beta }{\alpha +\beta }\right){\tilde{E}}_{0_I}$

• Reflected wave amplitude for incident wave that hits the boundary at an angle ${\theta }_I$ (angle between the normal to the boundary and the incident wave propagation wave)
• $\alpha \equiv \frac{\cos {\theta }_T}{\cos {\theta }_I}$
  • ${\theta }_T$ is the angle between the normal to the boundary and the transmitted wave propagation vector
• $\beta \equiv \frac{{\mu }_1{v}_1}{{\mu }_2{v}_2}=\frac{{\mu }_1{n}_2}{{\mu }_2{n}_1}$

${\tilde{E}}_{0_T}=\left(\frac{2}{\alpha +\beta }\right){\tilde{E}}_{0_I}$

• Transmitted wave amplitude