Ajax POST to PHP - how do I reply?

I have posted an email address from javascript to php via ajax. Then I searched the database in php to find out if the email exists in the database. How can I then send a message back to javascript/html saying that the value exists?

Here is what I am using to send the request:

 function postEmail(){

      var checkEmail = "[email protected]";

      var dataString = 'checkEmail1='+ checkEmail;

      // AJAX Code To Submit Form.
      $.ajax({
      type: "POST",
      url: "myfile.php",
      data: dataString,
      cache: false,
      success: function(result){

      alert("Sent successfully");
      } 
      });
 }

Then in PHP:

 $checkEmail2=$_POST['checkEmail1'];

 $results = mysql_query("select id from myTable where emailaddress='$checkEmail2' ");
 $row = mysql_num_rows($results);

 if ($row > 0 ) {
 echo "email already exists";
 } else {

 if ($row == 0 ) {
 echo "email doesnt exist";
 }

 }

Not sure if I should get the request? Or if you return a value or something. thanks.

(ps, I'm developing a hybrid app, so need to send/retrieve from PHP using JSON)