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(C) The force exerted by the laser beam on the foil is given by the radiation pressure formula. For a surface with reflection coefficient $\rho$,the f

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$< 39 \, mg$

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(C) The force exerted by the laser beam on the foil is given by the radiation pressure formula. For a surface with reflection coefficient $ho$,the force $F$ is given by:$F = \frac{P}{c} (1 + ho)$where $P$ is the power of the laser beam and $c$ is the speed of light $(3 	imes 10^8 \, m/s)$.The power $P$ is the energy $E$ divided by the pulse duration $\Delta t$:$P = \frac{E}{\Delta t} = \frac{10 \, J}{0.13 	imes 10^{-3} \, s} \approx 7.69 	imes 10^4 \, W$.For the foil to be supported,the radiation force must balance the gravitational force $(F = mg)$:$mg = \frac{E}{\Delta t \cdot c} (1 + ho)$$m = \frac{E (1 + ho)}{g \cdot \Delta t \cdot c}$Substituting the given values:$m = \frac{10 	imes (1 + 0.50)}{10 	imes 0.13 	imes 10^{-3} 	imes 3 	imes 10^8}$$m = \frac{15}{3.9 	imes 10^5} \approx 3.846 	imes 10^{-5} \, kg = 38.46 \, mg$.Rounding to the nearest appropriate value,the mass is approximately $39 \, mg$.

Similar Questions

$A$ laser beam with wavelength $\lambda = 633 \ nm$ has a power of $3 \ mW$. If the cross-sectional area of the beam is $3 \ mm^2$,what is the pressure exerted by the beam on a surface? (Assume the surface is a perfect reflector and the light is incident normally.)

Light with an energy flux of $9 \ Wcm^{-2}$ falls on a non-reflecting surface at normal incidence. If the surface has an area of $20 \ cm^2$, the total momentum delivered for complete absorption in one hour is:

Light falls on a non-reflecting surface normally. If the average force exerted on a surface with area $15 \text{ cm}^2$ during a $20 \text{ minute}$ time interval is $10^{-6} \text{ N}$,then the energy flux (intensity) of light is (Velocity of light $= 3 \times 10^8 \text{ ms}^{-1}$)

$A$ radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is ($C =$ velocity of light).

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