Pretty basic stuff, I suggest you get to read some PHP tutorials on the internet to get some knowledge on one thing and another.
The ?news= part in your URL is a parameter that can be read by PHP. This type is known as $_GET. To get this part you would need $_GET['news'] so if we'd use your first link and place this inside a script: echo $_GET['news']; the page would say images/largerimages1/13.jpg.
In order to get the image loaded on your website we need some simple steps, I'm changing the news parameter into image, that suits better for your script since it ain't news items:
<?php
// Define the path (used to see if an image exists)
$path = 'your/absolute/path/to/public_html/'; # or wwwroot or www folder
// First check if the parameter is not empty
if($_GET['image'] != "") {
// Then check if the file is valid
if(file_exists($path . $_GET['image'])) {
// If an image exists then display image
echo '<img src="'. $_GET['image'] . '" />;
}
}
?>
Below this script you can put all your thumbnails the way you want. Ofcourse, also for these thumbnails there are some automated options. But I strongly suggest you get a good look at the script above and some beginner PHP tutorials so you completely understand the example given. This still isn't the best method, but it's kicking you in the right direction.