<form method="post" id="height_form" action="#">
 <input class="opts_headlines" type="text"  id="height_opt" name="length" value="15">
</form>

$( document ).ready(function() {
      $("#btn_refresh").click(function(){
          $.ajax({
            url: 'generator/generator.php',
            type: "POST",
            data: $("#height_form").serialize(),
            success: function(data) {
              console.log(data);
            }
          });
          return false;
      });
    });

$data = $_POST['length'];
    $length =$data;
    $log = $length === null;
    if ($log) {
        $length = 15;
    }

<?php
$example_checked = isset($_POST['example-checked']);