  We present exact results for magnetic impurities in nanoscopic systems with
focusing properties. We analyze the spectroscopic and magnetic properties of
Kondo, intermediate valence and magnetic impurities on a sphere with a metallic
surface. Exact calculations show the occurrence of spectroscopic and magnetic
mirages at the antipodes of the impurity location. Comparison with calculations
performed using effective models validates previous calculations of
spectroscopic mirages. Our results can be extended to other systems with
focusing properties like quantum corrals.
