  Dark matter is a major constituent of our universe and the axion is a prime
candidate. In this article, it is shown that by exploiting the axion induced
magnetization in a magnetic rod and the Faraday effect, axions in the mass
range $500$ to $5000~\mu$eV, a part of which ($> 3500~\mu$eV) is currently
inaccessible to experiments, can be searched for using the same experimental
setup in a year using the existing technologies. The magnetic rod is placed
inside a high finesse optical cavity, which by confining the probe light inside
it increases the interaction time and thus enhances the Faraday effect. This
rotates the plane of polarization of the probe light sufficiently and produces
a robust signal. Axions of different mass are selected using a dc magnetic
field. Detection is carried out by counting photons in the optical domain using
a readily available and high quantum efficiency ($\approx 1$) photon counter in
a noise-free environment. An optical interferometric scheme that could provide
spectroscopic information about the axion to be searched is also proposed.
