Optical Tweezers in the Ray Optics Regime

[JamesB]

Homework Statement

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 = N_thick − N_thin.

Homework Equations

p = h/λ
E = hf
f = c/λ
F = dp/dt

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:

F_scat = (n_m*P)/c(1+Rcos(2Θ_R)-T_F²(cos(2Θ_R-2Θ_T)+Rcos(2Θ_R)/1 + R² + 2Rcos(2Θ_T))

F_grad = (n_m*P)/c(1+Rsin(2Θ_R)-T_F²(sin(2Θ_R-2Θ_T)+Rcos(2Θ_R)/1 + R² + 2Rcos(2Θ_T))

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

 

[BigJDubs]

A:The number of photons is determined by the power incident on the sphere, which is not given. You can try to calculate it, but without knowing the source intensity and distance from the sphere, it's impossible to do.