How can I legally use copyrighted images from the internet?

I'm writing an internet browser that displays images from websites. The images are simply downloaded into memory and immediately displayed, and they are freed from memory when the next image is displayed. In other words, the image is never stored on the user's hard drive, and there's no way for them to be saved permanently.

When clicking About in the menu, a pop-up dialog tells the user the exact URL where the image comes from, and with a single click they can open said URL in their usual web browser of choice. Optionally, I could also display the URL directly under the image in the main browsing screen, if that would help.

I plan to charge a small amount of money to use the browser.

Is this legal? How can I make it as legal as possible?