Facebook link sharing is one of the best way to spread your Joomla links on most powerful social community platform. When someone posts a link on facebook, a script usually scans that link for any images, and displays a quick thumbnail next to the post. But sometimes FB doesn't find & show any image. Why?
Facebook will use any open graph meta tags if present for the title, and image etc., more you will read here Open Graph Protocol.
Facebook scrapes your page every 24 hours to ensure the properties are up to date. FB observes cache headers on your URLs - it will look at "Expires" and "Cache-Control" in order of preference.
FB has released their "URL Linter" (http://developers.facebook.com/tools/lint/) tool that will show you a preview of how your page will appear when being shared on FB, and it will force FB to instantly update its cache of your page.
Where to find the problem in Joomla?
1) Check your .htaccess file, sometimes command "Expires" with JPG files causes that photo on FB are not displayed.
2) Image/photo is to small. The image must be at least 50px by 50px and have a maximum aspect ratio of 3:1. Facebook supports PNG, JPEG and GIF formats.
3) No hash. If you share link with your Joomla article it can't contain hash in url, because Facebook will link without image.
4) Use absolute link to all useful images in article. Change configuration of your default Joomla editor (like JCE in Default Profil tab).
Because Facebook caches the preview images, so if you recently tried to generate a preview and you're still not having luck try using another address (http://site.com/index.html instead of http://site.com)
Adding an img_src share preview image in HEAD section will take away the ability to let users select from various images when sharing your Joomla site. Use this code: <link rel="image_src" href="http://site.com/images/your-logo.png" />