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Perfectly reflecting mirror of mass M mo...

Perfectly reflecting mirror of mass M mounted on a spring consitute a spring mass system of angular frequency `Omega` such that `(4piM Omega)/h=10^(24) m^(-2)` where h is plank constant. N photons of wavelength `lambda=8pixx10^(-6)m ` strikes the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 `mum`. if the value of N is `x xx 10^(12)`, then find value of x.

Text Solution

Verified by Experts

The correct Answer is:
1
Momentum transferred on mirror `=(2Nh)/(lambda)`
`(2Nh)/(lambda) =MV_("(mean position)")`
`V_("(mean position)")=Omega A " " ("Where" A=1 mu M)`
`(2Nh)/(lambda) =M omegaA " " ("Where" lambda=8pixx10^(-6))`
`N=(Momega(10^(-6)) lambda)/(2h)=(MOmega8pixx10^(-6)xx10^(-6))/(2h)`
`N=(4piM Omega)/hxx10^(-12)`
`=10^(24)xx10^(-12)`
`N=1xx10^(12)`
x=1
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