 Solution

Refraction changes the propagation direction, and hence the momentum, of transmitted light. The particle receives the opposite momentum change by conservation of momentum. For a ray carrying power $P_r$, a useful force scale iswith corrections for reflected rays and their momentum fluxes. Here $n_m$ is the surrounding refractive index; this is a ray-force scaling rather than a complete electromagnetic stress calculation.

For fixed geometry and refractive indices, $P_r=I\delta A$, so the force contribution is proportional to the local intensity $I$. Refraction toward the normal on entry and away from the normal on exit must both be included: a force inferred from only the first interface can have the wrong direction.

The specified size is larger than the wavelength, so a geometrical optics treatment is appropriate despite the generic “nanoparticle” label. A dipole/Rayleigh-particle formula would use the opposite size limit.