Snell's Law

Snell’s Law Simulation

$\frac{\sin {\theta }_T}{\sin {\theta }_I}=\frac{n_1}{n_2}$

• ${\theta }_T$ is the angle between the boundary normal and the transmitted wave propagation vector
• ${\theta }_I$ is the angle between the boundary normal and the incident wave propagation vector
• $n_1$ is the refractive index for the medium the incident wave travels through
• $n_2$ is the refractive index for the medium the transmitted wave travels through

$\frac{\sin ({\theta }_a)}{\sin ({\theta }_b)}=\frac{v_a}{v_b}=\frac{n_b}{n_a}$

• $\lambda =\frac{{\lambda }_0}{n},k=n{k}_0$
• $\lambda$ 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