Q: can i connect my mac book to my TV

Is this any use to you?

http://store.apple.com/uk/product/H7129ZM/A/mini-displayport-to-hdmi-adapter

Read this before purchasing

http://support.apple.com/kb/HT4241?viewlocale=en_US

Also setup the sound as per instructions to allow sound through the minidisplay port, I think the Mid 2010 Macbook Pro supports this option but check with the above web page

I have the cable but when I connect it to the TV it only shows the background of the desktop and nothing else.

Have you enabled the mirroring option? I think it is System Preferences/Display.

Other wise I would start a new thread for this problem

I have same problem. I do not have "Mirror" option in my preferences.