First slide

Quantum Theory of Light

Question

Light with an energy flux of $16 W / c m^{2}$ falls on a non reflecting surface at normal incidence. If the surface has an area of $20 c m^{2}$ , find the average force exerted on the surface during a 30 minute time span.

Easy

A

$1.2 \times 10^{- 2} N$
B

$5.6 \times 10^{- 6} N$
C

$1.06 \times 10^{- 6} N$
D

$1.06 \times 10^{- 3} N$

Solution

The total energy falling on the surface is
$U = 16 \times 20 \times 30 \times 60$
$5.76 \times 10^{5} J$
The total momentum delivered (for complete absorption) is
$p = \frac{u}{c} = \frac{5.76 \times 10^{5}}{3 \times 10^{8}}$
$\frac{5.76}{3} \times 10^{- 3}$
$= 1.92 \times 10^{- 3}$
The average force exerted $= \frac{p}{t} = \frac{1.92 \times 10^{- 3}}{0.18 \times 10^{4}} = 10.66 \times 10^{- 7}$
$= 1.06 \times 10^{- 6}$

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