The average force ($F$) exerted by a light beam on a perfectly reflecting surface is given by the change in momentum per unit time. For a perfectly reflecting surface, the force is $F = \frac{2P}{c}$, where $P$ is the power of the incident light and $c$ is the speed of light.

First, calculate the Power ($P$): $P = \text{Energy Flux} \times \text{Area}$ Given Energy Flux ($I$) = $25 \times 10^4$ W/m$^2$ Area ($A$) = $15 \text{ cm}^2 = 15 \times 10^{-4} \text{ m}^2$ $P = (25 \times 10^4) \times (15 \times 10^{-4}) = 375$ Watts

Now, calculate the Force ($F$): $F = \frac{2 \times 375}{3 \times 10^8} = \frac{750}{3 \times 10^8} = 250 \times 10^{-8} \text{ N}$ $F = 2.5 \times 10^{-6} \text{ N}$