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## Homework Statement

A bead of radius R(=5 μm) is trapped by an optical beam and moved through a

viscous fluid at a speed v

_{d}of 20 μms

^{-1}. If the viscous drag is given by Stokes

law:

[tex]F_{d}=6\pi \eta Rv_{d}[/tex]

obtain an expression for the laser power (intensity). If the process only has an efficiency of 25% what laser power

is required to drag the bead?

(Assume that the viscosity of the medium is η=10

^{-3}Pa s, and its refractive index, n=1.3)

2. Homework Equations

2. Homework Equations

To keep the particle still, the scattering force from the laser must be equal to the viscous drag from the fluid:

F

_{s}=F

_{d}

## The Attempt at a Solution

I can obtain an expression for keeping the particle still, as described in the Relevant equations above. However if we want to move the particle it must (?) involve the gradient force. The force that when the laser is moved will shift the particle towards it's centre, hence the particle will move. But we are not given required info for this derivation, such as the refractive index of the bead.

I'm really lost with this question, has anyone any experience with optics type questions such as these? I've looked online and cant find a similar question anywhere.

Any point in the right direction would really be appreciated.