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## QuestionPhysicsClass 12

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

$$\text{Energy}=18\ \text{W/cm}^2$$
$$\text{Area}=20\;\text c\text m^2$$
$$\text{Time}=30$$ minutes
$$\text{c}=$$ Speed of light $$=3\times 10^8\ \text{m/s}$$
$$\text{Power}=\frac{\text{Energy}}{\text{time}}$$
As we have given power/area
The total energy $$=$$  energy $$\times$$  area $$\times$$  time
Total energy
$$\text{U}=18\times 20\times 30\times 60$$
$$\text{U}=6.48\times 10^5\text J$$
The momentum transferred when they strike the surface will be $$\text{U/c}$$
$$p=\frac{\text{U}}{\text{c}}$$
$$p=\frac{6.48\times 10^5}{3\times 10^8}$$
$$p=2.16\times 10^{-3}\;\text{kg/m}$$
Therefore the average force exerted will be
$$F=\frac p t$$
Here $$t$$  is the time period $$30\text{ min}=1800\text{ sec}$$
$$F=\frac{2.16\times 10^{-3}}{1800}$$
$$F=1.2\times 10^{-6}\;\text{N}$$