Changing content in widget

Hi All,

I wondering if it is possible to have a different content in the widgets of a right sidebar depending on which page is opened.

For example I have a right sidebar with a widget that displays image A. That is fine for all pages in my website, except for one page. On that particular page I would like to display image B in the sidebar.

I guess that is not the idea of using widgets, but maybe it can be done.