  The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of
the electronic Hamiltonian confined to a specific Landau level, and its
interplay with the formation of composite fermions has attracted much attention
of late. This article investigates an emergent symmetry in the fractional
quantum Hall effect, namely the PH symmetry of {\em composite fermions}, which
relates states at composite fermion filling factors $\nu^*=n+\bar{\nu}$ and
$\nu^*=n+1-\bar{\nu}$, where the integer $n$ is the $\Lambda$ level index and
$0\leq \bar{\nu}\leq 1$. Detailed calculations using the microscopic theory of
composite fermions demonstrate that for low lying $\Lambda$ levels (small $n$):
(i) the 2-body interaction between composite-fermion particles is very similar,
apart from a constant additive term and an overall scale factor, to that
between composite-fermion holes in the same $\Lambda$ level; and (ii) the
3-body interaction for composite fermions is an order of magnitude smaller than
the 2-body interaction. Taken together, these results imply an approximate PH
symmetry for composite fermions in low $\Lambda$ levels, which is also
supported by exact diagonalization studies and available experiments. This
symmetry, which relates states at electron filling factors
$\nu={n+\bar{\nu}\over 2(n+\bar{\nu})\pm 1}$ and $\nu={n+1-\bar{\nu}\over
2(n+1-\bar{\nu})\pm 1}$, is not present in the original Hamiltonian and owes
its existence entirely to the formation of composite fermions. With increasing
$\Lambda$ level index, the 2-body and 3-body pseudopotentials become
comparable, but at the same time they both diminish in magnitude, indicating
that the interaction between composite fermions becomes weak as we approach
$\nu=1/2$.
