1 According to the law of refraction, light from source, S, travels to detection point, D, via interface point, I, via two segments or two lights paths given by SI and ID. The shortest path from S to D is a straight line segment SD shown as a dashed line. Indeed, light does not take this shortest-path length in refraction and takes the longer path that is sum of segments SI and ID. Hence, Hero’s shortest-path principle violates the law of refraction. (See Figure PS.1.)
FIGURE PS.1 Possible paths of light travel in refraction. As an example, shown for Medium 1 refractive index lower than Medium 2 refractive index.