Allah impose the veil upon believing women to differentiate them from unbelieving women and believing slaves, see Ibn Kathir's tafsir (
33:59,
24:31,
24:30), the verse was revealed after Umar recognized Sauda when she was going to the toilet (Buk
146), The ladies cut their waist sheets and covered their heads and faces (Buk
4759), A woman who reach puberty can displays only her face and hands (Daw
4104 ), Omar hit a believing slave women's head until she removed her veil (Sha
6295)