Insert after every x img tags in a post

I want to insert <!--nextpage--> after every 10 image tags in a wordpress post (if there are 30 images, I'll get 3 pages), but I can't seem to figure out how to do it. I found a php function that does it for paragraphs, so I tried to rewrite it, but I don't know how to target the img tag, and can't find anything about that either.. I'm stuck.

<?php
$show_after_img = 2;
$content = apply_filters('the_content', $post->post_content);
if(substr_count($content, '<img>') > $show_after_img)
{
    $contents = explode("<img>", $content);
    $img_count = 1;
    foreach($contents as $content)
    {
        echo $content;

        if($img_count == $show_after_img)
        {
        ?>
                <p class="page-break"></p>
        <?php
        }
        echo "<img>";
        $img_count++;
    }
}
?>