using HD large screen as additional monitor

Sorry about that...
ok: os is version: 10.6.5
Imac 24" screen 9 if that matters)
appx 1 yr old.
Bought from Best Buy,..

You say you have an adapter(mini to HDMI and a large HDMI cable. (guess that means a long one?)
You then go on to describe how you connect the TV to the Mac (note the Caps), "I plug the cable into the TV, and into the back of my MAC screen (the dvi via the adapter)."

Where did this second adapter suddenly appear from and what is its purpose?

You are either connecting via the Mini to HDMI or via the mini to DVI connector. You cannot be doing both at once.

Have you been into System Preferences > Displays while you had the TV connected to the Mac? If you have everything connected correctly, you should see the second monitor in that System Preference Pane.

BTW, MAC is an abbreviation for Media Access Control, not Macintosh. Mac is the normally accepted abbreviation for that.

P

Sorry I don't know all the "correct" terms.
Let's try this.
My TV (television) has 3 HDMI inputs, I use one input for cable, one for DVD and the third is open.
On the back of my "Macintosh" desk top computer (see above for OS and computer info) there is a small socket that I understand is for video out.
I bought a HDMI cable with the thoughts I could plug on end into the Television, and the other into the socket on the back of my Macintosh screen, but since it (the socket) is NOT HDMI, I purchased an adapter that does fit the socket on the back of the screen, and the HDMI cable plugs into that adapter..
My intent was/is, to be able to watch Macintosh screen content on my Television, and this is apparently not the way to accomplish that. I understand I will need something different AND I will need something more/different for sound.

Did you go to the System Preferences panel?

What did you find?

Audio is not carried on the video output of the iMac, you will need to take the audio from the audio out port of the iMac and into the Audio input of the TV.

Does your TV have any other input ports, other than the HDMI, like component, VGA or DVI?

P

Sorry about the previous blank reply. Finger check.

I plug an HMDI cable into the DVI out of my 2008 MacBook Pro through a DVI male to HDMI female adapter, then plug the other end of the HDMI cable into one of the HDMI ports on my Sharp HDTV many times. Works like a charm. However, I DO have to go the the VIDEO SELECTION menu on the TV and select the input where the mac signal is coming in. You didn't say you did that. Did you?

Incidentally, back on the Mac, if you go into System Preferences > Display,

you should see both your Mac monitor and your TV, and be able to arrange your TV to be on the left or right extension of your Mac monitor.