When light waves traveling in a transparent medium strike the surface of a second transparent medium, they change direction. This change of direction is called refraction and is defined by Snell’s Law of Refraction,
$\frac{\sin \theta_{1}}{v_{1}}=\frac{\sin \theta_{2}}{v_{2}}$
where $\theta_{1}$ and $\theta_{2}$ are the magnitudes of the angles shown in the figure and $v_{1}$ and $v_{2}$ are the velocities of light in the two media. Show that this problem is equivalent to that in Exercise $51,$ and that light waves traveling from $P$ to $Q$ follow the path of minimum time.