var ajaxurl = '/ajax.php';

function password(email) {
  if (email == "") {
    alert('Írd be az e-mail címet a mezőbe!');
    return;
  }
  var pars = 'email='+email;
  var myAjax = new Ajax.Request(ajaxurl, { method: 'get', parameters: pars, onComplete: passwordshowResponse});
}

function passwordshowResponse(originalRequest) {
  eval(originalRequest.responseText);
}