Question

Light with an energy flux of $18 \,W \,cm^{-2}$ falls on a non-reflecting surface at normal incidence. If the surface has an area of $20 \,cm^2$, the average force exerted on the surface during a $30$ minute time span is

• A. $2.1 \times 10^{-6}\, N$
• B. $1.2 \times 10^{-6}\, N$
• C. $1.2 \times 10^{6}\, N$
• D. $2.1 \times 10^{6}\, N$

Answer 1

Answer: (B)

$1.2 \times 10^{-6}\, N$

Answer 2

The total energy falling on the surface is $U= 18 \times 20 \times (30 \times 60) = 6.48 \times 10^5\, J$ Therefore, the total momentum delivered (for complete absorption is) $P = \frac{U}{c} = \frac{6.48 \times 10^{5}}{3 \times 10^{8}}$ $= 2.16 \times 10^{-3}\,kg\,m\,s^{-1}$ The average force exerted on the surface is $F = \frac{p}{t} = \frac{2.16 \times 10^{-3} }{0.18 \times 10^{4}}$ $= 1.2 \times 10^{-6}\,N$