If you are dealing with the pain of migrating your site from non-secure plain http to secure SSL/TLS https, then you are also dealing with the headache of making sure the elements on your pages such as images have https sources instead of http.
The reason is that if your pages are accessed over https but they contain http elements they are considered broken (mixed content) by just about all browsers. The point is that if a page is secure, everything in that page must be secure as well.
Different page elements are treated differently by browsers. As of now, Chrome loads non-secure images in the page, but the URL color goes grey instead of the reassuring green with the secure lockpad. Non-secure scripts are not even loaded, leading to page malfunction in many cases.
If you use WordPress, you know how much of a pain it is to mass replace all the image sources in your past posts from http to https. You can manually update posts which will take forever, update the backing MySQL database via SQL but that’s risky, or use a plugin but that may be overkill.
A quick way to handle this is to add a filter to transform all http occurrences to https on the fly. It won’t change the actual posts, only how they are sent to the browser. And it’s not 100%, but it’s good enough for most sites, including this one. And worst case, you can always remove it and you’ll be back to where you started.
As for the filter code, it’s a one-liner that you add to the functions.php file of your theme. It actually converts http URLs for image src’s to protocol-relative, and that does the job. Here it is and good luck: