Question

You are working in a laser laboratory. Your current project involves suspending spherical glass beads in the Earth's gravitational field using a vertically directed laser beam. Today's experiment involves a black bead of radius r and density ρ. Assuming that the radius of the laser beam is the same as that of the bead and that the beam is centered on the bead, determine the minimum laser power required to suspend this bead in equilibrium. (Use any variable or symbol stated above along with the following as necessary: g and c.)

Answer 1

Suppose the power of the laser beam is P

Suppose the beam is completely absorbed by the bead. Then the radiation force on the bead is

where c is the speed of light in vacuum. This radiation force on the bead is acting upwards.

The mass of the bead is density times its volume

The weight of the bead is mass time gravitational acceleration which is

The radiation force counters the weight of the bead for the bead to be in equilibrium

or

or the power of the laser beam is