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.