  Composite fermions (CFs) are the particles underlying the novel phenomena
observed in partially filled Landau levels. Both microscopic wave functions and
semi-classical dynamics suggest that a CF is a dipole consisting of an electron
and a double $2h/e$ quantum vortex, and its motion is subject to a Berry
curvature that is uniformly distributed in the momentum space. Based on the
picture, we study the electromagnetic response of composite fermions. We find
that the response in the long-wavelength limit has a form identical to that of
the Dirac CF theory. To obtain the result, we show that the Berry curvature
contributes a half-quantized Hall conductance which, notably, is independent of
the filling factor of a Landau level and not altered by the presence of
impurities. The latter is because CFs undergo no side-jumps when scattered by
quenched impurities in a Landau-level with the particle-hole symmetry. The
remainder of the response is from an effective system that has the same Fermi
wavevector, effective density, Berry phase, and therefore long-wavelength
response to electromagnetic fields as a Dirac CF system. By interpreting the
half-quantized Hall conductance as a contribution from a redefined vacuum, we
can explicitly show the emergence of a Dirac CF effective description from the
dipole picture. We further determine corrections due to electric quadrupoles
and magnetic moments of CFs and show deviations from the Dirac CF theory when
moving away from the long wavelength limit.
