Q: Connecting my MacBook Air to my Mid 210 iMac

Hi

I want to connect my 2013 MacBook Air to my mid 2010 iMac, so I can run the Air through my iMac. 

I have a  thunderbolt port on my Air and my iMac I have a firewire port and a mini dvi, I think (see pic attached).

Can I buy a single lead (thunderbolt - mini dvi) or do I need a connector of some kind?

Hope this makes sense?

Minchroadster