# Optical Tweezers in the Ray Optics Regime

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1. Mar 28, 2017

### JamesB

1. The problem statement, all variables and given/known data
Consider an optical tweezer operated in the ray optics regime as shown in Figure. Net reflection angle of the ray shown in Figure is θ = 10◦ (See Figure). Since more photons take the thick ray than the thin ray, a net force of F = 1 pN is exerted on the sphere toward the left. The wavelength of the photon is λ = 1000 nm. Let Nthick and Nthin be the number of photons per second in the thick and thin ray, respectively. Find ∆N = Nthick − Nthin.

2. Relevant equations
p = h/λ
E = hf
f = c/λ
F = dp/dt

3. The attempt at a solution
I feel like there is not enough information given in this problem to solve for the total number of photons.
I know in the Ray Optics Regime:

Fscat = (nm*P)/c(1+Rcos(2ΘR)-TF2(cos(2ΘR-2ΘT)+Rcos(2ΘR)/1 + R2 + 2Rcos(2ΘT))

Fgrad = (nm*P)/c(1+Rsin(2ΘR)-TF2(sin(2ΘR-2ΘT)+Rcos(2ΘR)/1 + R2 + 2Rcos(2ΘT))

I am not sure with the given information how to manipulate these equations to determine the solution or if I am overthinking. Please Help!!!!!

2. Apr 2, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.