Grad School: Portfolio for an IxD master program

I hope I’m not repeating this topic.

I’m an Industrial Designer and I’m interested in pursuing a career in Interaction Design. I want to apply to grad school soon because, in my country, I am not likely to be hire in jobs related to the area if I don’t have specialized studies. My problem is that my portfolio consists mostly of furniture, some graphic design and other misc. projects. This is what my circumstances have allowed me to work on. So, my question is:

What should my portfolio look like when applying to a master program?
How can I convinced them that I can thrive in that field when I haven’t had the opportunity to do a related project yet?

Your answer are appreciated.