Definition (Law of Reflection).
- Reflected rays lie in the plane of incidence
- The angle of reflection $\theta’$ equals the angle of incidence $\theta$
Proof. We will show that $\overline{AB} + \overline{BC}$ is the shortest possible path by Hero’s Principle.
Observe that $\overline{BC} = \overline{BC’}$; therefore, $\overline{AB} + \overline{BC’}$ must also be the shortest length. By coinciding $B$ with $B’$, we can see a straight line $\overline{AB’C’}$ connecting $A$ to $C’$.
Thus, $\overline{AB} + \overline{BC}$ is the shortest path and $\theta = \theta’$.
