  Using Fermat's least optical path principle the family of ray-trajectories
through a special but common type of a gradient refractive index lens,
n(r)=n_0+\Delta n R/r, is solved analytically. The solution, i.e. the
ray-equation r(phi), is shown to be closely related to the famous Rutherford
scattering and therefore termed photonic Rutherford scattering. It is shown
that not only do these classical limits correspond, but also the
wave-mechanical pictures coincide: The time-independent Schr\"odingier equation
and the inhomogeneous Helmholz equation permit the same mapping between massive
particle scattering and diffracted optical scalar waves. Scattering of narrow
wave-packets finally recovers the classical trajectories. The analysis suggests
that photothermal single particle microscopy infact measures photonic
Rutherford scattering in specific limits.
