  For a family of self-adjoint Dirac operators $-i c (\alpha \cdot \nabla) +
\frac{c^2}{2}$ subject to generalized MIT bag boundary conditions on domains in
$\mathbb R^3$ it is shown that the nonrelativistic limit in the norm resolvent
sense is the Dirichlet Laplacian. This allows to transfer spectral geometry
results for Dirichlet Laplacians to Dirac operators for large $c$.
