Chapter 4.5, Problem 55E

(a)

To determine

To show: Two poles of heights $m$ and $n$ separated by the horizontal distance $d$ and a rope is stretched from top of one pole to the ground and then to the top of the other pole, the given configuration requires the least amount of rope occurs when ${\theta }_1={\theta }_2$ (see figure).

(b)

To determine

To show: The light from a source $A$ reflects off a surface and receives at point $B$, the angle of incidence equals the angle of reflection or ${\theta }_1={\theta }_2$ (see figure), where the Fermat`s Principle states that when light travels between two points in the same medium (at a constant speed), it travels on the path that minimizes the travel time.