Under the attention and scrutiny of the public, as in
The rock star's activities were very much in the public eye. This usage, which is similar to
in the limelight, dates from the late 1800s. It should not be confused with the similar-sounding
in the eyes of the public, which means "in the opinion or views of the general public" (as in
In the eyes of the public the mayor was guilty of perjury). Also see
in the eye of, def. 2.