= 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 is
$$
\mathbf F_r\sim\frac{n_mP_r}{c}
(\hat{\mathbf s}_{\mathrm{in}}-\hat{\mathbf s}_{\mathrm{out}}),
$$
with 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.
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