Work Step by Step
Yes, for reflection, a principle of "least distance" would explain the observed paths of light rays just as accurately as a principle of "least time". This is because light stays in one medium, and does not change speed. In that case, the least-distance path always coincides with the least-time path. However, for refraction, a principle of "least distance" does NOT explain the observed paths of light rays as accurately as the correct principle of "least time". In refraction, light does transition between mediums, and changes speed. When this happens, the least-distance path (a straight line) takes more travel time than the least-time path (which isn't a straight line). By traveling for a longer time in the "fast" medium, the light gets to its destination faster, even at the cost of taking a non-straight path. This is explained on page 524, and illustrated in Figures 28.13 and 28.14.