  A well known conjecture of Yau states that the first eigenvalue of every
closed minimal hypersurface $M^n$ in the unit sphere $S^{n+1}(1)$ is just its
dimension $n$. The present paper shows that Yau conjecture is true for minimal
isoparametric hypersurfaces. Moreover, the more fascinating result of this
paper is that the first eigenvalues of the focal submanifolds are equal to
their dimensions in the non-stable range.
