It depends on what your criteria are for the mobile image?
If you are just rescaling the image to a smaller size then you can use the same image and adjust its dimensions through css and media queries. Of course that assumes that you don't mind serving the higher file-size image to mobile. If on the other hand you are looking for a lighter weight image in the page for mobile then setting the image to display:none will not work as most devices will load all images in the html whether they are display:none or not and you get two hits instead of one. (There are some tricks such as setting the parent to display:none instead of the image but is not consistent between devices.)
If you are talking about images for retina devices then read this article.
More on responsive images here:
At the moment I prefer to use the same image optimised as low as possible and use for all devices.