We study the depletion interaction between spherical particles of radi
us R immersed in a dilute solution of rigid rods of length L. The comp
uted interaction potential is, within numerical accuracy, exact for an
y value of L/R. In particular we find that for L similar to R, the dep
th of the depletion well is smaller than the prediction of the Derjagu
in approximation. Our results bring new light into the discussion on t
he lack of phase separation in colloidal mixtures of spheres and rods.