  In the context of the quantum mechanical modelling of a measurement process
using the Stern-Gerlach setup, we critically examine the relationship between
the notion of `distinguishability' of apparatus states defined in terms of the
inner product and spatial separation among the emerging wave packets. We show
that, in general, the mutual orthogonality of these wave packets does not
necessarily imply their unambiguous spatial separation even in the asymptotic
limit. A testable scheme is formulated to quantify such departures from
`idealness' for a range of relevant parameters.
