If you need to get the URL for an image file with a drupal style applied, this function is what you need to get the path for the image styles:
$style_name: The name of the style to be used with this image.
$path: The path to the image. Path will look like "public://mypicture.jpg"
The absolute URL where a style image can be downloaded, suitable for use in an <img> tag. Requesting the URL will cause the image to be created.