Snell's Law

#Physics
Snell’s Law Simulation

$\displaystyle \frac{\sin \theta_{T}}{\sin \theta_{I}}=\frac{n_{1}}{n_{2}}$

$\displaystyle \theta_{T}$ is the angle between the boundary normal and the transmitted wave propagation vector
$\displaystyle \theta_{I}$ is the angle between the boundary normal and the incident wave propagation vector
$\displaystyle n_{1}$ is the refractive index for the medium the incident wave travels through
$\displaystyle n_{2}$ is the refractive index for the medium the transmitted wave travels through

$\frac{\sin(\theta_a)}{\sin(\theta_b)}=\frac{v_a}{v_b}=\frac{n_b}{n_a}$

$\lambda=\frac{\lambda_0}{n},\space k=nk_0$
$\lambda$ is the wavelength of light in the medium
$\lambda_0$ is the wavelength of light in a vacuum
$n$ is the index of refraction
$k$ is the wave number of light in the medium
$k_0$ is the wave number of light in the vacuum
$f$ stays constant between mediums, $\lambda$ shortens to compensate for the wave slowing down