Q: Can I add an external monitor to my 21.5" iMac?

Yes, all you need a Mini Display adapter or if you have a 2011 iMac and you want the 27" Thunderbolt display you can get a Thunderbolt adapter and connect to the Thunderbolt Display. If you have a 2009 or 2010 machine with Mini Display port only the you need MDP to:

VGA or DVI or HDMI depending on the external display you get. Read your owners manual for the specificatios and instructions.

You can only attach a TB device (e.g., a TB monitor) to a TB source (e.g., a TB iMac).  No adapters are available.

Confusing Mini DisplayPort with Thunderbolt

Note, apple still sells the mini-displyport version of their 27" display.

If you have most any other kind of monitor (single or dual link dvi, hdmi, vga, mini-displayport)  then  you can connect it to your iMac, possibly with a suitable adapter.  For mini-displayport displays no adapter is necessary.  For dvi displays single link mini-displayport to dvi adapters are required if the display resolution is less than 1920 x 1200 otherwise a dual link mini-displayport to dvi adapter is required.  For vga you need a mini-displayport to vga adapter, and so on.

I've just hooked up my early 2010 iMac to my flat screen tv, using a Mini DisplayPort adapter and a latest-version HDMI cable. These are transferring audio & video to the tv perfectly.

My only issue so far is that I can't find a setting to turn off the computer display, so that stuff is only displayed on the television. It's distracting and seems very wasteful to have them both going.

Also, even when I go to settings and drag the menu bar over to the TV display, it doesn't show up. I've even tried all the different resolutions, in case it was being pushed off the page by its size. No luck.

Otherwise: Great!

P.S. I was very careful to buy cables and adapters capable of carrying audio and video because I didn't want to have to run a separate digital audio cable. READ BEFORE YOU BUY.

I've just hooked up my early 2010 iMac to my flat screen tv, using a Mini DisplayPort adapter and a latest-version HDMI cable. These are transferring audio & video to the tv perfectly.

 

My only issue so far is that I can't find a setting to turn off the computer display, so that stuff is only displayed on the television. It's distracting and seems very wasteful to have them both going.

 

Also, even when I go to settings and drag the menu bar over to the TV display, it doesn't show up. I've even tried all the different resolutions, in case it was being pushed off the page by its size. No luck.

Distracting?  Wasteful?  To each his own I guess.  Personally I like the main monitor to be separate from my TV and play.  It leaves me to do other things on the computer or keep the video controller there on a screen where I can see it as opposed to a TV 6 or 7 feet away which make pretty bad computer monitors in the first place.  Videos and pictures, fine.  Anything else, forget it.

If you find the main screen "distracting" then dim it.  There's even an app to click in the menu bar to do it (Isolator, and many others).

And there are no setting to disable monitors which is why you cannot find any.  If you really want to disable a monitor then use SwitchResX.

As for why you can't see the menu bar even when you make your TV the main monitor is because (a) you didn't set the TV up correctly, (b) you didn't set the Displays preferences correctly, or (c) there's something "deficient" with your TV.

(a)  You didn't set the TV up correctly.  TV's can have underscan or overscan.  Underscan is when the picture doesn't fill the screen and you see black bands all around.  Overscan is the opposite, i.e., the edge of the picture is outside the screen boundaries.  Most TV have underscan/overscan settings but they generally use different terminology.  You should go through your TV's manual to see if you can find any settings addressing these two problems.  It sounds like you are suffering from overscan if the menu bar is off the top of the picture.

(b) You didn't set the Displays preferences correctly.  The TV's Displays preferences should generally be set with a the resolutions 720p, 1080i, 1080p.  There may also be a seperate refresh rate setting.  And there may also be a underscan/overscan slider to adjust the picture size on the TV.

(c) There's something "deficient" with your TV.  If the Displays doesn't present the proper resolutions and there is no underscan/overscan setting then the TV is not sending the correct EDID info to the computer.  If the TV doesn't have settings of its own to address overscan/underscan then that is another problem with the TV model.