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Question

A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the surface.

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Solution

Power of the incident beam, P = 10 watt
Relation between wavelength λ and momentum (p):
λ=hp,wherehisPlanck'sconstant⇒p=hλOndividingbothsidesbyt,weget:pt=hλt...1
Energy,
E=hcλ⇒Et=hcλt
Let P be the power. Then,
P=Et=hcλtP=pct[Usingequation1]⇒Pc=ptForce,F=pt=PcSinceF=MomentumTimeForce,F=710(absorbed)+2×310(reflected)F=710×Pc+2×310×PcF=710×103×108+2×310×103×108F=133×10-8=4.33×10-8N

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