Printing images from private destination folder.

hi, i want to display an image into image tag from private folder destination. how do i do that?

i changed these things in my media/file-system.

1 . Public file system path : sites/default/files

2 . Private file system path : sites/default/files/private/my_privatefolder

3 . Default download method : Public local files served by the webserver.

below is my codes.

function my_module_permission(){
	return array(
		'my permission' => array(
			'title' => 'permission for image',
			'description' => 'permission image',
			'restrict access' => TRUE,
		),
	);
}

function my_module_menu(){
	$items['print_image'] = array(
		'title' => 'some title',
		'page callback' => 'my_module_page',
		'access arguments' => array('my permission'),
		'type' => MENU_CALLBACK,
	);
	return $items;
}
function my_module_page(){
             $output  = '';
             $private_img = 'sites/default/files/private/my_privatefolder/images/20140723072203.jpg';
             $private_image = theme('image', array('path' => $private_img, ' width'=>'100','height' => '100','alt' => 'image', 'title' => 'My image', ));
             $output  = $private_image;
return $output;
}