Final answer:
Hero of Alexandria used a minimization principle for the law of reflection, stating that the angle of incidence is equal to the angle of reflection, which can be confirmed through simple experiments involving shining a flashlight at different angles against various surfaces.
Step-by-step explanation:
The minimization principle used by Hero of Alexandria to explain the law of reflection is based on the idea that light travels the path of least time, which corresponds to a path such that the angle of incidence is equal to the angle of reflection. This principle states that when a light ray strikes a surface, the angle at which the light is reflected (θ1) is equal to the angle at which the light arrives, or the angle of incidence (θi). These angles are measured relative to the perpendicular to the surface at the point where the ray strikes.
Hero's principle is an early example of what would later be formalized in Fermat's Principle of Least Time in the 17th century. This principle is demonstrated in a simple Take-Home Experiment, where one can shine a flashlight on a piece of paper or mirror at an angle, and observe that the light reflects at the same angle. To confirm the law of reflection, one can measure these angles, which should correspond according to the figures provided.