how to display new iMac to 1920x1080 on my HDTV

I got a new Imac and a new Sony HDTV,Both with higher resolution of 1920x1080,when i go to display and I tried to put the higher resolution wont let me on VGAdisplay only works with 1600x1200,60Hz...The iMac is correctly displayed in 1200x1080
Why doesnt let me put my VGA cable to the maximum resolution in my HDTV..Any way to fix that or i need a new cable
Also the iMac dont turn off completly when im playing videos,macbooks do it but not iMac... Is annoying

If you want to use VGA to any manufacturers HDTV, you need to open the user manual and check the capability of it's VGA port. The better manufacturers (and Sony is one of those) will have a listing of the resolutions the TV is capable of accepting over VGA.

(The correct resolution on the new 21.5" iMac is 1920X1080.)

And remember that your HDTV screen is NOT measured in pixels, but in lines. TV screens and computer monitor are NOT the same resolution ever, produce images very differently, etc. Your TV is interlaced, your computer monitor is progressive. Even if your TV can do progressive, it's doing lines, not pixels. Pixels have nothing to do with video. I'd strongly recommend in intermediary box that turns the signal into HDMI to get true HD to your TV without the headaches.

what box is that to get it

Disagree that there is any reason to pay $100-$250 for a convertor box. Don't even believe there is a box made for conversion from the current iMac's displayport to HDMI. You would have to use a mini displayport to VGA and then a convertor to HDMI. Essentially going from digital to analog and back to digital again.

If you have the current model iMac with mini displayport, there are a whole lot of happy folks using a mini displayport to HDMI cable ($10-$13).

edit:

Before you consider moving to HDMI, I still suggest opening up the Sony manual and verify what resolutions and frequencies your TV supports through VGA. If you don't have it, you can find your Sony manual online at Sony.

Some older TV sets specifically state not to connect a PC via HDMI. None of the new sets have this limitation. Need to check this out.

Also, if you are looking to get the sound output through the TV rather than a separate surround system, you will need to read the manual and verify that your TV will allow for a separate input to be matched to your HDMI port. There are many TV's that do not as they are expecting the sound to be carried over the HDMI cable.

VGA resolutions in manual says````````````````640x480,but im using now 1600x1200 60 Hz

If that is an older HDTV, it very well may not accept any but 4:3 resolutions through VGA.

How do I know I'm using 4:3 resolution thru VGA?

1600x1200 is 4:3 - and you'll have black bars on each side of the screen if your HDTV is a widescreen.

Yes I do have black bars,,,Can I use the new HDTV Cable from apple store?

There is no such thing as a specific cable by the name "HDTV cable".

The term "HDTV cable" applies to multiple different types of cables that are capable of carrying a high definition image.

If you want to move from VGA to a different cable and would like someone to recommend a specific adapter/cable or be able to say "yes, that is the one you need", then you will have to provide the info requested in the first post here.

I thought that the new apple hdtv cable for 20$ can be used as they told me at apple store but since they dont know anything im asking her first

You can ask. Until you provide the info requested in the link I provided above, you'll not get an answer that is based on anything other than pure conjecture.