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height and width of background picture adapt to each screen size

I've been working for some time on my first website. I have the CSS working but I still need to fix some simple, but no so simply issues. In the index.html file I have a background picture attached to the html. So I have a fullscreen background picture attached via CSS to the html tag. This is the CSS code:

html{   background: no-repeat center center fixed; 
-webkit-background-size: cover;     -moz-background-size: cover;
-o-background-size: cover;  -ms-background-size: cover;
background-size: cover; }

But I'm loading the pictures via Javascript. My objective is to have an array of pictures and each time a user loads the website or triggers it a random picture will be displayed. So I have this code in Javascript which is working:

$(document).ready(function()  {
  var randomImages = ['img1','img2','img3','img4','img5'];
   var rndNum = Math.floor(Math.random() * randomImages.length);
   $("html").css({
      background: "url(_img/bg/index_rnd/" + randomImages[rndNum] + ".jpg)
      no-repeat"
    });
});

All these codes are working. The pictures are selected from an array and displayed randomly once they are loaded. But I have a great problem which I cannot find a clear answer and I'm stuck. I would like that the width and the height are rezised , so the whole picture is displayed in the screen. Of course each screen is different... I read something about innerhieght and innerwidth properties, but I do not know how to proceed. What should I do so the pictures resize to each different screen?

In this moment the pictures are with a resolution of 1024x683. I have a computer with a screen of 15"" and a resolution of 1440x900. My pictures get always a bit more pixelated and to long in height to display, so a part of the picture is cut.

Questions:

What should I do so the pictures resize to each different screen resolution?

A recommended picture resolution so the picture is displayed correctly?

Is there a way to display the picture into the exact size of a screen? Even if its original format gets a bit modified?

REPLY AFTER RECIEVING ANSWER ------------------------------------------------------------- NEW QUESTION -----------------------------------------------------------------------------

Hello, at last I had time to use the code... It does work properly. I only needed to add the url to my image folder and magic!!! So my code is actually like this:

$(window).load(function() {
    var randomImages = ['img1','img2','img3','img4','img5'];
    var rndNum = Math.floor(Math.random() * randomImages.length);

     var $win = $(this);
     var $img = $('#background').attr('src', '_img/bg/index_rnd/' + randomImages[rndNum] + '.jpg').css({'position':'fixed','top':0,'left':0});
        function resize() {
            if (($win.width() / $win.height()) < ($img.width() / $img.height())) {
              $img.css({'height':'100%','width':'auto'});
            } else {
              $img.css({'width':'100%','height':'auto'});
            }
        }
        $win.resize(function() { resize(); }).trigger('resize');
    });

Regarding my html I have for now an image with id background. I want to center the image as told. So my question is if I should put this image in a div. If so, how can I make this image center itself in the center of the screen???

Another question, before I had my image attachted to the html and now to an image. Therefore the image is influencing other elements I have in my body. How can I make that this image be displayed behind all the other elements of my body?!?! For example my logo and header_bg are transformed when my img id="background" is loaded.

Can you help???

This is my html for any doubts...

<body>
        <img id="background" src="" alt="" />
        <div id="header_img">
            <nav>
                <div id="header-bg-left">
                    <div id="nav-content">
                        <div id="logo">
                                <a href="index.html"><img alt="./_img/nav/logo.rosa.png" src="">logo</a>
                        </div>
                        <div id="categories">       
                                <ul>
                                    <li id="nav-quien"><a href="#">quien es</a>
                                        <ul>
                                            <li id="nav-biografia" class="drop1"><a href="biografia.html">biografia</a></li>
                                            <li id="nav-curriculum" class="drop2"><a href="curriculum.html">curriculum</a></li>
                                        </ul>
                                    </li>
                                    <li id="nav-galeria" class="marginli"><a href="gallery.html">galeria</a>
                                        <ul>
                                            <li id="nav-gal-nat" class="drop3"><a href="gallery.html">paisaje natural</a></li>
                                            <li id="nav-gal-urb" class="drop4"><a href="gallery.html">paisaje urbano</a></li>
                                        </ul>
                                    </li>
                                    <li id="nav-prensa" class="marginli"><a href="prensa.html">prensa</a></li>
                                    <li id="nav-links" class="marginli"><a href="links.html">links</a></li>
                                    <li id="nav-contacto" class="marginli"><a href="contacto.html">contacto</a></li>
                                </ul>
                        </div>
                    </div>
                </div>
            </nav>
        </div>
        <footer>    
            <div id="footer-bg-left">
                <div id="foot-content">
                    <p>Diseñado por <a href="mailto:daniramirezescudero@gmail.com">Daniel. R-Escudero</a> <span>|</span> Todos los derechos reservados <span>|</span> <a href="mailto:info@scalesplanet.com">info@rosasusaeta.com</a> <span>|</span><a href="http://www.linkedin.com/"><img src="./_img/footer/logo.linked.png"></a> <a href="http://www.facebook.com/"><img src="./_img/footer/logo.facebook.png"></a></p>
                </div>
            </div>  
        </footer>
    </body>

UPDATED 29 Nov 2012

        $(window).resize(function() {
            resize();
        });
        $(function() {
            $('#background').attr('src', 'http://cdn.com/bg.png').css({
                'position' : 'fixed',
                'top' : 0,
                'left' : 0
            });
            resize();             
        });
        function resize() {
            var $img = $('#background');
            if (($(window).width() / $(window).height()) < ($img.width() / $img.height())) {
                $img.css({
                    'height' : '100%',
                    'width' : 'auto'
                });
            } else {
                $img.css({
                    'width' : 'auto',
                    'height' : $(window).height() + 'px'
                });
            }
        }

<body>
  <img id="background" src="" alt=""/>
</body>

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