Is it normal to cry when leaving your baby alone?

My son is 5 weeks old and I've been with him the whole time since birth. I never wanted to leave his side! So earlier my husbands mother came over to watch the baby while I went out to lunch with friends. First time leaving him and I thought it would be just fine. I felt fine when we left but as we got in the restaurant and sat down my mind went to the baby. I was missing him already and was thinking that he was probably home crying for me which made me start to cry. I kept phoning my mother in law but she wouldn't answer which made it worse. One of my friends drove me back home and when I got there he was sleeping soundly and my mother in law had been in the bathroom. Is this normal? How long will this last?