Redirecting PHP Login page

I am trying to redirect my php login page so that if user is authorised, it goes to a page (r_index.php) and if the user isn't authorised they go back to the login page (login.html).

This is my code:

    <?php  
if ("password"=="$password") { // Start the condition  ?>  
<a href="r_index.php">Manage classes</a>  
<?php     } // End the condition ?>     
<?php if ("password"=="") { ?>     
<a href="login.html">Login</a>     
<?php } 
?>. 

What am I doing wrong? How should I resolve it?