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Question

Perfectly reflecting mirror of mass M mounted on a spring constitutes a spring mass system of angular frequency Ω, such that 4π MΩh=1034m3, where h is planck constant, N photons of wavelength λ=8π×106 m strikes the mirror simultaneously at normal incidence such that the mirror gets displaced by 1μ m. If the value of N is x×102, then the value of x is

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Solution

Momentum transferred on mirror =2Nhλ
2Nhλ=MVmean position
For SHM
Vmean position=Ω A(where,A=1μ M)

2Nhλ=MΩ A(where, λ=8π ×108)
N=MΩ (106)λ2h=MΩ 8π×106×1062hN=4π MΩh×1012=1024×1012
N=1×1012
x=1

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