The Trace Velocity Matching Principle states that the [[Trace Velocity]] $c_{\text{tr}}$ of the incident [[Wave]], [[Refraction|Refracted Wave]], and transmitted wave must be the same.
$\huge \sin \theta_{I} = \frac{c_{1}}{c_{\text{tr}}} $
The incident wave, refracted wave, and incident wave all have the some [[Frequency]] and [[Period]].
$\huge \begin{align}
f_{1} = \frac{c_{1}}{\lambda_{1}}&=f_{2}=\frac{c_{2}}{\lambda_{2}} \\
T_{1} &= T_{2} \\
\sin \theta_{1} &= \frac{c_{1}t}{v_{\text{tr}}t} \\
\sin \theta_{2} &= \frac{c_{2}t}{v_{\text{tr}}t} \\
\frac{\sin\theta_{1}}{\sin \theta_{2}} &= \frac{c_{1}}{c_{2}} \\
\end{align} $
This is a derivation for [[Snell's Law]].
>[!warning] secretly [[Diffraction]]?