Question

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\omega$ such that $\frac{4\pi M\omega }{h}=10^{24}{m}^{-2}$ with $h$ as Planck's constant. $N$ photons of wavelength $\lambda =8\pi \times 10^{-6}m$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1\mu m$ . If the value of $N$ is $x\times 10^{12}$ . Then the value of $x$ is [Consider the spring as massless]

Answer 1

Answer: 1

$m{V}_{\max }=\left(\frac{2h}{\lambda }\right)N$
$m\cdot \omega A=\frac{2h}{\lambda }N$
$N=\frac{m\omega \lambda A}{2h}$
$N=\frac{10^{24}}{4\pi }\times \frac{8\pi \times 10^{-6}}{2}\left(10^{-6}\right)$
$N=10^{12}$
$\therefore x=1$