Whenever any person required to give proof of financial responsibility under this chapter is or later becomes an operator in the employ of any owner, or is or later becomes a member of the immediate family or household of the owner, the director shall accept proof given by such owner in lieu of proof by such other person to permit such other person to operate a motor vehicle for which the owner has given proof as herein provided. The director shall designate the restrictions imposed by this section on the face of such person’s license.