  We study the depletion interaction between spherical particles of radius R
immersed in a dilute solution of rigid rods of length L. The computed
interaction potential is, within numerical accuracy, exact for any value of
L/R. In particular we find that for L of order R, the depth of the depletion
well is smaller than the prediction of the Derjaguin approximation. Our results
bring new light into the discussion on the lack of phase separation in
colloidal mixtures of spheres and rods.
