How can PHP be used to authenticate and authorize access to a password-protected website within an iframe?

To authenticate and authorize access to a password-protected website within an iframe using PHP, you can create a PHP script that checks the user's credentials and sets a session variable upon successful login. Then, in the iframe source file, you can check if the session variable is set to grant access to the content.

```php
// authentication.php

session_start();

// Check if the user is logged in
if (!isset($_SESSION['logged_in'])) {
    // Check user's credentials (e.g. username and password)
    if ($_POST['username'] == 'admin' && $_POST['password'] == 'password') {
        $_SESSION['logged_in'] = true;
    } else {
        // Redirect to login page
        header('Location: login.php');
        exit();
    }
}

// iframe-source.php

session_start();

// Check if the user is logged in
if (!isset($_SESSION['logged_in'])) {
    // Redirect to login page
    header('Location: login.php');
    exit();
}
```

In this code snippet, the authentication.php script checks the user's credentials and sets a session variable upon successful login. The iframe-source.php script checks if the user is logged in by verifying the session variable, redirecting to the login page if not authenticated.